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Sapienza Università di Roma
FACOLTÀ DI SCIENZE MATEMATICHE, FISICHE E NATURALI
Corso di Laurea Specialistica in Fisica
Study of Missing Energy
with Cosmic Rays in the
Compact Muon Solenoid detector
Tesi di Laurea Specialistica
Relatore interno
Prof. Shahram Rahatlou
Relatore esterno
Candidato
Marco Grassi
matr. 1046750
dott. Paolo Meridiani
Anno Accademico 2008/2009
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tesi_grassi 2009/11/16 0:48 page iii #3
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Ai cinque incontri che, forse inconsapevolmente,
hanno reso possibile questa tesi:
Casalbertone,
Prati,
Ginevra,
Londra,
Roma,
ottobre 1997
primavera 2002
luglio 2008
maggio 2009
settembre 2009
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Contents
1
Physics Motivations
1.1
The Standard Model of particle physics
. . . . . . . . . . . .
1
Hierarchy Problem . . . . . . . . . . . . . . . . . . . .
2
Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . .
5
1.1.1
1.2
1.2.1
1.2.2
2
1
R-Parity, lightest supersymmetric particle and missing
energy . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
Dark Matter
7
. . . . . . . . . . . . . . . . . . . . . . .
Compact Muon Solenoid Detector
9
2.1
Large Hadron Collider
. . . . . . . . . . . . . . . . . . . . . .
9
2.2
The overall concept . . . . . . . . . . . . . . . . . . . . . . . .
12
2.3
Magnet
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
2.4
Muon System . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
2.4.1
. . . . . . . . . . . . . . . . . . .
17
Electromagnetic Calorimeter . . . . . . . . . . . . . . . . . . .
19
2.5.1
Design . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
2.5.2
Lead tungstate crystals
21
2.5
Drift tube chambers
. . . . . . . . . . . . . . . . .
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Contents
2.5.3
2.6
2.7
3
Hadron Calorimeter
23
. . . . . . . . . . . . . . . . . . . . . . .
23
2.6.1
Design . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
2.6.2
Performance . . . . . . . . . . . . . . . . . . . . . . . .
29
Inner tracking system
. . . . . . . . . . . . . . . . . . . . . .
29
2.7.1
Strip tracker
. . . . . . . . . . . . . . . . . . . . . . .
30
2.7.2
Pixel Tracker
. . . . . . . . . . . . . . . . . . . . . . .
31
2.7.3
Performance . . . . . . . . . . . . . . . . . . . . . . . .
33
Detection of Cosmic Rays
35
3.1
The Discovery of Cosmic rays . . . . . . . . . . . . . . . . . .
35
3.2
Composition and spectrum
. . . . . . . . . . . . . . . . . . .
36
3.3
Muons at the surface . . . . . . . . . . . . . . . . . . . . . . .
39
3.4
Muon interaction with matter . . . . . . . . . . . . . . . . . .
40
3.5
Muons in the CMS cavern . . . . . . . . . . . . . . . . . . . .
42
3.6
Cosmic Muon Reconstruction
. . . . . . . . . . . . . . . . . .
44
Global muons . . . . . . . . . . . . . . . . . . . . . . .
46
Cosmic Muon Time Measurement . . . . . . . . . . . . . . . .
48
3.7.1
Drift Tube synchronization
. . . . . . . . . . . . . . .
48
3.7.2
Time of arrival
. . . . . . . . . . . . . . . . . . . . . .
50
3.7.3
Time at the Interaction Point . . . . . . . . . . . . . .
51
Cosmic Muon Analysis . . . . . . . . . . . . . . . . . . . . . .
53
3.8.1
Selection Criteria . . . . . . . . . . . . . . . . . . . . .
54
3.8.2
Time Oset Correction . . . . . . . . . . . . . . . . . .
54
3.6.1
3.7
3.8
4
Performance . . . . . . . . . . . . . . . . . . . . . . . .
Missing Energy Measurement
57
4.1
Calorimetric Tower . . . . . . . . . . . . . . . . . . . . . . . .
58
4.2
Missing Transverse Energy . . . . . . . . . . . . . . . . . . . .
59
4.2.1
61
Missing Transverse Energy Resolution and Signicance
4.3
Zero Suppression
. . . . . . . . . . . . . . . . . . . . . . . . .
4.4
Energy Threshold Eects
. . . . . . . . . . . . . . . . . . . .
62
63
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Contents
5
E
/T
4.5
Irreducible
4.6
Eect of noisy channels
4.7
Using Time Information In
. . . . . . . . . . . .
69
4.8
Time of a calorimetric tower . . . . . . . . . . . . . . . . . . .
70
4.9
Time selection criterion using muons . . . . . . . . . . . . . .
73
4.9.1
Muon signal in the calorimeters . . . . . . . . . . . . .
74
4.9.2
Muon requirements . . . . . . . . . . . . . . . . . . . .
75
4.9.3
Optimization of the time window . . . . . . . . . . . .
78
4.9.4
Time selection applied to
E
/T
80
Conclusions
Bibliography
sources
. . . . . . . . . . . . . . . . . . . . . .
64
. . . . . . . . . . . . . . . . . . . . .
68
E
/T
Selection
computation . . . . . . .
91
96
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CHAPTER 1
Physics Motivations
1.1 The Standard Model of particle physics
One of the main themes in the history of science has been unication. Time
and again diverse phenomena have been understood in terms of a small
number of underlying principles and building blocks. The principle that underlies our current understanding of nature is quantum eld theory, quantum
mechanics with the basic observables living at space-time points. In the late
1940s it was shown that quantum eld theory is the correct framework for the
unication of quantum mechanics and electromagnetism. By the early 1970s
it was understood that the weak and strong nuclear forces are also described
by a quantum eld theory. The full theory, the
Model
or
Standard Model,
SU (3)c × SU (2)` × U (1)y
has been conrmed repeatedly in the ensuing
years. Combined with general relativity, this theory is consistent with virtually all physics phenomena down to the scale probed by particle accelerators,
roughly
10−16
cm. It also passes a variety of indirect tests that probe to a
shorter distance, including precision test of quantum electrodynamics [1],
search for rare meson decays [2, 3], limits on neutrino masses [4], searches
for proton decay [5], and gravitational limits on the couplings of massless
scalars. In each of these indirect tests new physics might well have appear,
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Physics Motivations
but in no case has clear evidence for it yet been seen; currently, the strongest
sign is the solar neutrino problem, resulting in non-zero neutrino mass [6].
The Standard Model has a fairly simple structure.
There are four in-
teraction based on local invariance principles. One of these, gravitation, is
mediated by the spin-2 graviton, while the other three are mediated by the
spin-1
SU (3) × SU (2) × U (1) gauge bosons.
In addition, the theory includes
the spin-0 Higgs boson needed for the spontaneous symmetry breaking, and
the spin-1/2 fermions: quarks and leptons. The dynamic is governed by a
Lagrangian that depends upon roughly twenty three parameters.
Though there are no unambiguous experimental results that require the
existence of new physics at the TeV-scale, expectations of the latter are
primarily based on three theoretical arguments. First, a
of the gauge hierarchy, i.e.
natural
explanation
one that is stable with respect to quantum
corrections, is very dicult without new physics at the TeV scale [7]. Second,
the unication of the three gauge couplings at very high energy close to the
Plank scale does not occur in the Standard Model, although unication can
be achieved with the addition of new physics that can modify the way gauge
couplings run above the electroweak scale.
Third, the existence of dark
matter which accounts approximately for one quarter of the total mass
of the Universe cannot be explained within the Standard Model.
1.1.1 Hierarchy Problem
Hierarchy
problem (or
Naturalness
problem) is not really a problem of the
Standard Model, but rather a disturbing sensitivity of the Higgs potential
to new physics in almost every extension of the Standard Model.
The electrically neutral part of the Standard Model Higgs eld is a complex scalar
H
with a classical potential
V = m2H |H|2 + λ|H|4 .
(1.1)
The Standard Model requires a non-vanishing vacuum expectation value for
H
at the minimum of the potential.
This occurs if
λ > 0
and
m2H < 0,
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1.1 The Standard Model of particle physics
resulting in
hHi =
q
−m2H /2λ.
hHi
Since we know experimentally that
is approximately 246 GeV from measurement of the properties of the weak
interactions, it must be that
m2H
is very roughly of order
−(100 GeV)2 .
The
2
problem is that mH receives enormous quantum correction from the virtual
eects of every particle that couples, directly or indirectly, to the Higgs eld.
(a)
Figure 1.1
(b)
One-loop quantum corrections to the Higgs squared mass parameter
m2H ,
due to (a) a Dirac fermion
f,
and (b) a scalar
For example, in gure 1.1a we have a correction to
taining a Dirac's fermion
with a term
−λf Hf f¯
f
with mass
mf .
m2H
S.
from a loop con-
If the Higgs eld couples to
f
in the Lagrangian, then the Feynman's diagram in
gure 1.1a yields a correction
∆m2H = −
Here
Λ2U V
|λf |2 2
Λ + ... .
8π 2 U V
(1.2)
is an ultraviolet momentum cuto used to regulate the loop inte-
gral; it should be interpreted as at least the energy scale at which new physics
enters to alter the high-energy behavior of the theory. The problem is that
if
Λ2U V
is of the order
MP ,
then the quantum correction to
2
orders of magnitude larger than the required value of mH
m2H
is some 30
∼ −(100 GeV)2 .
Moreover there are contributions similar to equation 1.2 from the virtual
eects of new arbitrary heavy scalar particles that might exist, and these
involve the masses of the heavy particles, not just the cuto.
ple, suppose there exist a heavy complex scalar particle
S
For exam-
with mass
mS
2
2
that couples to the Higgs with a Lagrangian term −λS |H| |S| . Then the
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Physics Motivations
Feynman's diagram in gure 1.1b gives a correction
λS 2
2
2
Λ
−
2m
ln(Λ
/m
+
...
.
S
U
V
S
U
V
16π 2
∆m2H =
(1.3)
Contribution in equation 1.3 arises even without the hypothesis of arbitrarily heavy particles, since if we take the scalar particle in gure 1.1b to
be the Higgs boson, we get its self-energy to renormalize
m2H .
diative corrections to the Standard Model Higgs mass of order
the hierarchy between the electroweak and UV scales.
Therefore ra-
ΛU V
destroy
This is a problem
only for corrections to the Higgs scalar boson squared mass, because quantum corrections to fermion and gauge boson masses do not have the direct
quadratic sensitivity to
Λ2U V
found in equation 1.2. However quarks, leptons
and electroweak gauge bosons
Z 0, W ±
all obtain masses from
hHi,
so that
the entire mass spectrum of the Standard Model is directly or indirectly
sensitive to the cuto
Λ2U V .
The only way to avoid this diculty within the Standard Model is to netune the couplings
gi
to one part in
2
& 1028 ,
Λ2U V /Eweak
assuming for
ΛU V
16 GeV grand-unication scale. This is the ne-tuning or
an hypothetical 10
naturalness
problem.
One could argue that there is no satisfying solution to this diculty, in
the sense that a more fundamental theory of everything may just produce
the required nely tuned couplings. Such a theory is not at all understood,
but it seems a priori to be very dicult that electroweak gauge symmetry
breaking at 200 GeV should emerge from a theory which contains gravitational interactions occurring at energy scales greater than or equal to the
Planck scale.
Thinking of a new model to solve this issue, either the Higgs has to decouple from other particles at high energies, in which case it could not break
the electroweak symmetry at the weak scale, or there must be some strongly
non-perturbative eect which invalidates the method of calculation. Though
Jungman et al. stigmatize the latter hypothesis as providing no comfort
in their review on supersymmetric dark matter [8], there is an interesting
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1.2 Supersymmetry
perspective proposed by Amelino-Camelia [9] about how deeply we can rely
on perturbative renormalizability when building a new theory.
An alternative solution could be that there is no fundamental Higgs boson,
as in technicolor models, top-quark condensate models, and models in which
the Higgs boson is composite. Or it could be that the ultimate ultraviolet
cuto scale is much lower than the Planck scale. These ideas are certainly
worth exploring, although they often present diculties in their simplest
forms. But, if the Higgs boson is a fundamental particle, and there really is
physics far above the electroweak scale, then we have two remaining options:
either we must make the rather bizarre assumption that there does not exist
any high-mass particles or eects that couple (even indirectly or extremely
weakly) to the Higgs scalar eld, or else some striking cancellation is needed
between the various contributions to
∆m2H .
The systematic cancellation of the dangerous contributions to
∆m2H
can
only be brought by an underlying symmetry. Comparing equations 1.2 and
1.3 strongly suggests that the new symmetry ought to relate fermions and
bosons, because of the relative minus sign between fermion loop and boson
loop contributions to
∆m2H .
1.2 Supersymmetry
Among the beautiful properties that a quantum eld theory
might possess to make it more beautiful or more mathematically
tractable, there is one higher symmetry with particularly farreaching implications. This is a a symmetry that relates fermions
and bosons, known (without hyperbole) as
supersymmetry.
M. Peskin, 1995
[10]
Low energy supersymmetry (SUSY) is probably the most extensively studied theories beyond Standard Model. Reasons are in its success in solving
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Physics Motivations
some of the Standard Model's drawbacks presented above, such as the stabilization of the Higgs boson mass and the gauge coupling unication, while
not being in contradiction with the precision electroweak measurement. If
unbroken, SUSY predicts the existence of partners of Standard Model particles diering by half a unit of spin, but otherwise sharing the same properties.
There are, for instance, two scalar-quark weak eigenstates
q̃L
and
q̃R
asso-
ciated with the left and the right chirality states of a given quark avour.
Two Higgs doublet are however needed, in contrast to the minimal Standard
Model, in order to give masses to both up-type and down-type quarks, with
vacuum expectation values
v2
and
v1 ,
the ratio of which is denoted
tan(β).
± and charged Higgs boson
The SUSY partner weak eigenstates of the W
mix to form the two chargino mass eigenstates
0
there are four neutralinos χ̃i (i
= 1, 4)
χ̃±
i (i = 1, 2).
associated to the
B,
Similarly,
W 0 and neutral
Higgs boson.
Since no such particles have been observed with the same mass as their
Standard Model counterparts, SUSY is a broken symmetry.
SUSY and SM particles are distinguished by a multiplicative quantum
number,
R-parity, mathematically dened in the next section.
of this quantity is commonly assumed, because if
R-parity
Conservation
is violated the
exchange of SUSY particles may lead to an unacceptably fast proton decay.
Supersymmetry also seems to be an essential ingredient in theories (such
as string or supergravity theories) which unify gravity with the other forces.
In fact, gauging supersymmetry in a manner analogous to the gauging of
symmetries in the standard model, leads directly to gravitational interactions.
1.2.1 R-Parity, lightest supersymmetric particle and missing
energy
As a consequence of the
B−L
conservation, where
B
and
and lepton numbers, SUSY possesses a multiplicative
L
are the baryon
R-parity
invariance,
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1.2 Supersymmetry
with
R = (−1)3(B−L)+2S
for a particle of spin
S.
Note that this implies
that all the ordinary Standard Model particles have even
the corresponding supersymmetric partners have an odd
servation of
R
R-parity,
R-parity.
whereas
The con-
in scattering and decay processes has a crucial impact on
supersymmetric phenomenology. Starting, for example, from an initial state
involving ordinary (R-even) particles, it follows that supersymmetric particles must be produced in pairs. In general, these particles are highly unstable
and they decay into lighter states.
R-parity
invariance also implies that the
lightest supersymmetric particle (LSP) is absolutely stable, and must eventually be produced at the end of a decay chain initiated by an heavy unstable
supersymmetric particle.
In order to be consistent with cosmological constraints, a stable LSP is
almost certainly electrically and color neutral [11]. Consequently, the LSP
in an
R-parity-conserving theory is weakly interacting with ordinary matter,
i.e. it behaves like a stable heavy neutrino and it escapes collider detectors
without being directly observed.
The canonical signature for a
R-parity
conserving supersymmetric theory is therefore missing transverse energy,
the later being caused by the escape of the LSP. .
1.2.2 Dark Matter
In astronomy there is overwhelming evidence that most of the mass in the
Universe is some non-luminous dark matter, of as yet unknown composition. There are also reasons to believe that the bulk of this dark matter is
non-baryonic, i.e. it consists of some new elementary particle.
The most convincing observational evidence for the existence of dark matter involves galactic dynamics. There is simply not enough luminous matter
observed in spiral galaxies to account for their observed rotation curves. If we
take
.
Ω
to be the average density of the universe we measure
ΩLU M . 0.01
Instead from gravitational eects we infer a galactic dark halo of mass
3 ÷ 10
times that of the luminous component. Moreover, by applying New-
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Physics Motivations
ton's laws to the motion of galaxies in clusters, we get a universal mass
density of
Ω ∼ 0.1 ÷ 0.3,
much greater than the luminous one.
If the luminous mass density were the major contribution to the mass density of the Universe, the duration of the epoch of structure formation would
be very short. But such a short epoch requires uctuations in the microwave
background which are larger than those observed. Actually measured microwave background anisotropies correspond indeed to a cosmology where
much of the matter interacts with photons more weakly than the known
forces that couple light interactions to baryonic matter. Likewise, a signicant amount of non-baryonic matter is necessary to explain the large-scale
structure of the universe, implying
Ω & 0.3
[13].
We see that conservative observational limits give
others suggest
Ω & 0.3,
and
Ω=1
Ω & 0.1,
while many
is by far the most attractive possibility
from theoretical arguments since it corresponds to a at Universe (i.e. where
the curvature is zero). On the other hand, big-bang nucleosynthesis suggests
that the baryon density is
matter in the Universe.
Ωb . 0.1
[14], too small to account for the dark
Although a neutrino species of mass
O(30
eV)
could provide the right dark-matter density, N-body simulations of structure
formation in a neutrino-dominated Universe do a poor job in reproducing
the observed structure of the Universe.
Furthermore, it is dicult to see
(from phase-space arguments) how such a neutrino could make up the dark
matter in the halos of galaxies [15]. Then it appears likely that some nonbaryonic, non-relativistic matter (known as
cold dark matter ) is required in
the Universe, and particle physics can provide such a candidate (cf. section
1.2).
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CHAPTER 2
Compact Muon Solenoid
Detector
2.1 Large Hadron Collider
After extended consultation with the appropriate scientic
committees, CERN's Director-General Luciano Maiani announced
today that the LEP accelerator had been switched o for the
last time. LEP was scheduled to close at the end of September
2000 but tantalising signs of possible new physics led to LEP's
run being extended until 2 November. At the end of this extra
period, the four LEP experiments had produced a number of
collisions compatible with the production of Higgs particles with
a mass of around 115 GeV. These events were also compatible
with other known processes. The new data was not suciently
conclusive to justify running LEP in 2001, which would have
inevitable impact on LHC construction and CERN's scientic
programme. The CERN Management decided that the best policy for the Laboratory is to proceed full-speed ahead with the
Large Hadron Collider (LHC) project. 9
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Compact Muon Solenoid Detector
CERN Press Release, 8/11/2000
With this words, at the beginning of November 2000,
Positron collider
Large Electron-
(LEP) gave way to the new two-ring-superconducting-
hadron accelerator and collider: the
Large Hadron Collider.
The rst approval of the LHC project was already been given by the
CERN Council in December 1994.
At that time, the plan was to build a
machine in two stages starting with a centre-of-mass energy of 10 TeV, to
be upgraded later to 14 TeV. However, during 1995-6, intense negotiations
secured substantial contributions to the project from non-member states,
and in December 1996 the CERN Council approved construction of the 14
TeV machine in a single stage. The non-member state agreements ranged
from nancial donations, through in kind contributions entirely funded by
the contributor, to in-kind-contributions that were jointly funded by CERN
and the contributor.
Condence for this move was based on the experi-
ence gained in earlier years from the international collaborations that often
formed around physics experiments. Overall, non-member state involvement
has proven to be highly successful.
The decision to build LHC at CERN (European Center for Nuclear Research) was strongly inuenced by the cost saving to be made by re-using
the LEP tunnel and its injection chain. Although at its founding CERN was
endowed with a generous site in the Swiss countryside, with an adjacent site
for expansion into the even emptier French countryside, the need for space
outstripped that available when the super-proton synchrotron, or SPS, was
proposed. In this instance, the problem was solved by extensive land purchases, but the next machine, LEP, with its 27 km ring, made this solution
impractical. In France, the ownership of land includes the underground volume extending to the centre of the earth, but, in the public interest, the
Government can buy the rights to the underground part for a purely nominal fee. In Switzerland, a real estate owner only owns the land down to a
reasonable depth. Accordingly, the host states reacted quickly and gave
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2.1 Large Hadron Collider
CERN the right to bore tunnels under the two countries, eectively opening
a quasi-innite site that only needed a few islands of land ownership for
shafts.
In 1989, CERN started LEP, the worlds highest energy electron-
positron collider.
In 2000, LEP was closed to liberate the tunnel for the
LHC.
The LHC design depends on some basic principles linked with the latest technology. Being a particle-particle collider, there are two rings with
counter-rotating beams, unlike particle-antiparticle colliders that can have
both beams sharing the same phase space in a single ring. The tunnel geometry was originally designed for the electron-positron machine LEP, and
there were eight crossing points anked by long straight sections for radiofrequency cavities that compensated the high synchrotron radiation losses.
A proton machine such as LHC does not have the same synchrotron radiation
problem and would, ideally, have longer arcs and shorter straight sections
for the same circumference, but accepting the tunnel as built was the costeective solution. However, it was decided to equip only four of the possible
eight interaction regions and to suppress beam crossings in the other four to
prevent unnecessary disruption of the beams. Of the four chosen interaction
points, two were equipped with new underground caverns.
The LHC has two high luminosity experiments, ATLAS (A Toroidal LHC
ApparatuS) [16] and CMS (Compact Muon Solenoid) [see next section],
both aiming at a peak luminosity of
L = 1034 cm−2 s−1
for proton operation.
There are also two low luminosity experiments: LHCb [17] for B-physics,
aiming at a peak luminosity of
L = 1032 cm−2 s−1 ,
and TOTEM [18] for the
detection of protons from elastic scattering at small angles, aiming at a peak
luminosity of
L = 2 × 1029 cm−2 s−1 .
In addition to the proton beams, the
LHC will also be operated with ion beams. The LHC has one dedicated ion
experiment, ALICE [19], aiming at a peak luminosity of
L = 1027 cm−2 s−1
for nominal lead-lead ion operation.
The high beam intensity required for a luminosity of
L = 1034 cm−2 s−1
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excludes the use of antiproton beams, and hence excludes the particle-antiparticle collider conguration of a common vacuum and magnet system for
both circulating beams, as used for example in the Tevatron.
To collide
two counter-rotating proton beams requires opposite magnetic dipole elds
in both rings.
The LHC is therefore designed as a proton-proton collider
with separate magnet elds and vacuum chambers in the main arcs, and
with common sections only at the insertion regions where the experimental
detectors are located. The two beams share an approximately 130 m long
common beam pipe along the insertion regions. Hence dedicated
angle orbit bumps
crossing
separate the two LHC beams left and right from the
interaction point, in order to avoid parasitic collisions.
2.2 The overall concept
The Compact Muon Solenoid (CMS) is one of the two general purpose experiments which will take data at the LHC. Its physics goals range from
the search for the Higgs boson to the searches for new physics beyond the
Standard Model, to the precision measurements of already known particles
and phenomena [20].
The overall layout of CMS is shown in 2.1. At the heart of CMS sits a
13-m-long, 5.9 m inner diameter, 4 T superconducting solenoid. In order to
achieve good momentum resolution within a compact spectrometer without
making stringent demands on muon-chamber resolution and alignment, a
high magnetic eld was chosen.
The return eld is large enough to satu-
rate 1.5 m of iron, allowing four muon stations to be integrated to ensure
robustness and full geometric coverage. Each muon station consists of several layers of aluminium drift tubes (DTs) in the barrel region and cathode
strip chambers (CSCs) in the endcap region, complemented by resistive plate
chambers (RPCs).
The bore of the magnet coil is also large enough to accommodate the inner tracker and the calorimetry inside. The tracking volume is given by a
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2.2 The overall concept
Figure 2.1
An exploded view of the CMS detector.
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cylinder of length 5.8 m and diameter 2.6 m. In order to deal with high track
multiplicities, CMS employs 10 layers of silicon microstrip detectors, which
provide the required granularity and precision. In addition, 3 layers of silicon pixel detectors are placed close to the interaction region to improve the
measurement of the impact parameter of charged-particle tracks, as well as
the position of secondary vertexes. The electromagnetic calorimeter (ECAL)
uses lead tungstate (PbWO4 ) crystals with coverage in pseudorapidity up
|η| < 3.0.
to
The scintillation light is detected by silicon avalanche photo-
diodes (APDs) in the barrel region and vacuum phototriodes (VPTs) in the
endcap region. A preshower system is installed in front of the endcap ECAL
for
π0
rejection. The ECAL is surrounded by a brass/scintillator sampling
hadron calorimeter with coverage up to
|η| < 3.0.
The scintillation light is
converted by wavelength-shifting (WLS) bres embedded in the scintillator
tiles and channeled to photodetectors via clear bres. This light is detected
by novel photodetectors (hybrid photodiodes, or HPDs) that can provide
gain and operate in high axial magnetic elds. This central calorimetry is
complemented by a tail-catcher in the barrel region, ensuring that hadronic
showers are sampled with nearly 11 hadronic interaction lengths. Coverage
up to a pseudorapidity of 5.0 is provided by an iron/quartz-bre calorimeter. The Cerenkov light emitted in the quartz bres is detected by photomultipliers. The forward calorimeters ensure full geometric coverage for the
measurement of the transverse energy in the event.
2.3 Magnet
The required performance of the muon system, and hence the bending power,
is dened by the narrow states decaying into muons and by the unambiguous
determination of the sign for muons with a momentum of
requires a momentum resolution of
∆p/p ∼ 10%
at
p=1
∼1
TeV/c. This
TeV.
CMS chose a large superconducting solenoid, the parameters of which are
given in table 2.1.
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2.4 Muon System
Field
4T
Inner bore
5.9 m
Length
12.9m
Number of turns
Current
Stored energy
Table 2.1
2168
19.5 kA
2.7 GJ
Parameters of the CMS superconducting solenoid.
2.4 Muon System
Centrally produced muons are measured three times: in the inner tracker,
after the coil, and in the return ux.
Measurement of the momentum of
muons using only the muon system is essentially determined by the muon
bending angle at the exit of the 4 T coil, taking the interaction point (which is
known with a precision of
∼ 20 µm) as the origin of the muon.
The resolution
of this measurement (labelled muon system only in gure 2.2) is dominated
by multiple scattering in the material before the rst muon station up to
pT
values of 200 GeV/c, when the chamber spatial resolution starts to dominate.
For low-momentum muons, the best momentum resolution is obtained in
with the silicon tracker (inner tracker only in gure 2.2).
However, the
muon trajectory beyond the return yoke extrapolates back to the beamline because of the compensation of the bend before and after the coil, when
multiple scattering and energy loss can be neglected. This fact can be used to
improve the muon momentum resolution at high momentum when combining
the inner tracker and muon detector measurements (full system in gure
2.2).
Three types of gaseous detectors are used to identify and measure muons
[21].
The choice of the detector technologies has been driven by the very
large surface to be covered and by the dierent radiation environments. In
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Figure 2.2
The muon momentum resolution versus p using the muon system only,
the inner tracker only, or both (full system). Barrel:
cap:
|η| < 0.2;
End-
1.8 < |η| < 2.0.
the barrel region (|η|
< 1.2), where the neutron induced background is small,
the muon rate is low and the residual magnetic eld in the chambers is low,
drift tube (DT) chambers are used. In the two endcaps, where the muon rate
as well as the neutron induced background rate is high, and the magnetic
eld is also high, cathode strip chambers (CSC) are deployed and cover the
region up to
|η| < 2.4.
In addition to this, resistive plate chambers (RPC) are
used in both the barrel and the endcap regions. These RPCs are operated in
2
avalanche mode to ensure good operation at high rates (up to 10 kHz/cm )
and have double gaps with a gas gap of 2 mm. RPCs provide a fast response
with good time resolution but with a coarser position resolution than the
DTs or CSCs. RPCs can therefore identify unambiguously the correct bunch
crossing.
The DTs or CSCs and the RPCs operate within the rst level trigger system, providing two independent and complementary sources of information.
The complete system results in a robust, precise and exible trigger device.
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2.4 Muon System
Figure 2.3
Layout of one quarter of the CMS muon system.
The layout of one quarter of the CMS muon system is shown in gure
2.3. In the Muon Barrel (MB) region, 4 stations of detectors are arranged in
cylinders interleaved with the iron yoke. The segmentation along the beam
direction follows the 5 wheels of the yoke (labeled
wheel in
-z , and YB+2 for the farthest in +z ).
YB-2
for the farthest
In each of the endcaps, the
CSCs and RPCs are arranged in 4 disks perpendicular to the beam, and in
concentric rings, 3 rings in the innermost station, and 2 in the others. In
total, the muon system contains about
25 000 m2
of active detection planes,
and nearly 1 million electronic channels.
2.4.1 Drift tube chambers
The Muon Barrel, consists of 250 chambers organized in 4 layers (stations
labeled MB1, MB2, MB3 and MB4 with the last being the outermost) inside
the magnet return yoke, at radii of approximately 4.0, 4.9, 5.9 and 7.0 m from
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the beam axis. Each of the 5 wheels of the Muon Barrel is divided into 12
sectors, with each covering a
30◦
azimuthal angle (see gure 2.5). Chambers
in dierent stations are staggered so that a high-pT muon produced near
a sector boundary crosses at least 3 out of the 4 stations.
There are 12
chambers in each of the 3 inner layers. In the 4th layer, the top and bottom
sectors host 2 chambers each, thus leading to a total of 14 chambers per
1
wheel in this outermost layer .
Figure 2.4
shown in gure 2.4.
A schematic layout of a DT chamber is
Schematic layout of a DT chamber
In each chamber, there are 12 layers of contiguous
drift tube cells grouped in three
SuperLayers
(SL) with 4 staggered layers
each; the innermost and outermost SLs are dedicated to hits measurement
-φ plane), while in the central SL the hits are
measured along the beam axis (r -z plane). The maximum drift length is 2.0
in the CMS bending plane (r
cm and the single-point resolution is
∼ 200 µm.
to give a muon vector in space, with a
φ
Each station is designed
precision better than
100 µm
in
position and approximately 1 mrad in direction.
1
NB. In the fourth layer of the sectors 10 and 4, only one out of the two chambers is
labeled with the right sector number (see gure 2.5). Therefore in section 3.8.2 we refer to
the top unlabeled chamber as to belong to sector 13, and to the bottom one as to belong
to sector 14.
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2.5 Electromagnetic Calorimeter
Figure 2.5
Transverse view of the CMS detector. [22]
2.5 Electromagnetic Calorimeter
The electromagnetic calorimeter (ECAL) is a hermetic, homogeneous calorimeter comprising
61 200
lead tungstate (PbWO4 ) crystals mounted in the cen-
tral barrel part, closed by
7 324
crystals in each of the two endcaps. These
crystals require use of photodetectors with intrinsic gain that can operate
in a magnetic eld. Silicon avalanche photodiodes (APDs) are used as photodetectors in the barrel and vacuum phototriodes (VPTs) in the endcaps.
The use of PbWO4 crystals has allowed the design of a compact calorimeter
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inside the solenoid that is fast, has ne granularity, and is radiation resistant.
2.5.1 Design
ECAL Barrel
The ECAL barrel (EB) consists of a cylinder with an average inner radius
of 129 cm and a pseudorapidity coverage up to
|η| = 1.479.
It is inserted
between the inner tracker and the hadron calorimeter barrel.
For reasons of ease of construction and assembly, crystals have been
grouped by pairs in
φ,
and by ve in
η,
in the so-called at-pack congura-
tion. This group of 10 crystals is contained in an alveolar structure forming
what is called a submodule (see gure 2.6(a)). Four or ve submodules (depending on the
η
coordinate) are grouped to form a module (gure 2.6(b)),
and 170 submodules are grouped to form a supermodule (gure 2.6(c)).
(a)
(b)
Figure 2.6
(c)
(a) Shape of a submodule.
(b) Shape of a module.
(c) Shape of a
supermodule. [23]
There are 36 identical supermodules, 18 in each half barrel, each covering
◦ in
20
φ
(see gure 2.7(a)).
are tilted at 3
The crystals are quasi-projective (the axes
◦ with respect to the line from the nominal vertex position,
see gure 2.7(b)) and cover 0.0174 (i.e.
have a front face cross-section of
◦
1 ) in
∆φ
∼ 22 × 22 mm2
and
∆η .
The crystals
and a length of 230 mm,
corresponding to 25.8 X0 .
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2.5 Electromagnetic Calorimeter
(a)
Figure 2.7
(b)
(a) 3D view of ECAL. (b) Description of the crystal
φ
-
tilt. [23]
ECAL Endcaps
The endcaps (EE), at a distance of 314 cm from the vertex and covering a
pseudorapidity range of
1.479 < |η| < 3.0,
are each structured as two
Dees
(see gure 2.8), consisting of semi-circular aluminium plates from which are
cantilevered structural units of
5×5
crystals, known as supercrystals. The
endcap crystals, like the barrel crystals, o-point from the nominal vertex
position, but are arranged in an
a front face cross section of
x-y
grid. They are all identical and have
28.6 × 28.6
2 and a length of 220 mm (24.7
mm
X0 ). A preshower device is placed in front of the crystal calorimeter over
much of the endcap pseudorapidity range. The active elements of this device
are two planes of silicon strip detectors, with a pitch of 1.9 mm, which lie
behind disks of lead absorber at depths of 2 X0 and 3 X0 .
2.5.2 Lead tungstate crystals
Lead Tungstate crystals (PbWO4 ) are characterized by high density (8.3
3
g/cm ), short radiation length (0.89 cm) and small Molière radius (2.2 cm),
resulting in a ne granularity and a compact calorimeter. The scintillation
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Figure 2.8
A single endcap with Dees apart. [23]
decay time is of the same order of magnitude as the LHC bunch crossing
time: about 80% of the light is emitted in 25 ns. The light output is relatively
low: about 4.5 photoelectrons per MeV are collected in both the avalanche
photodiodes (APDs) and the vacuum phototriodes (VPTs), where the higher
APD quantum eciency is balanced by their smaller surface coverage on the
back face of the crystal. The crystals emit blue-green scintillation light with
a broad maximum at 420 nm. The light output variation with temperature,
-1.9% per
◦ C at 18 ◦ C, requires the ECAL cooling system to be capable of
extracting the heat dissipated by the readout electronics and of keeping the
crystal temperature stable within
±0.05 ◦ C
to preserve energy resolution.
To exploit the total internal reection for optimum light collection on the
photodetector, the crystals are polished.
This is done on all but one side
for EB crystals. For fully polished crystals, the truncated pyramidal shape
makes the light collection non-uniform along the crystal length, and the
needed uniformity is achieved by depolishing one lateral face.
In the EE,
the light collection is naturally more uniform because the crystal geometry
is nearly parallelepipedic, and just a mild tuning is being considered.
The crystals have to withstand high radiation levels and particle uxes
throughout the duration of the experiment.
Ionizing radiation produces
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2.6 Hadron Calorimeter
absorption bands through the formation of colour centres due to oxygen
vacancies and impurities in the lattice.
The practical consequence is a
wavelength-dependent loss of light transmission without changes to the scintillation mechanism, a damage which can be tracked and corrected for by
monitoring the optical transparency with injected laser light. The damage
reaches a dose-rate dependent equilibrium level which results from a balance
between damage and recovery at 18
◦ C. To ensure an adequate performance
throughout LHC operation, the crystals are required to exhibit radiation
hardness properties quantied as an induced light attenuation length always
greater than 3 times the crystal length even when the damage is saturated.
Hadrons have been measured to induce a specic, cumulative reduction of
light transmission, but the extrapolation to LHC indicates that the damage
will remain within limits required for good ECAL performance [24].
2.5.3 Performance
The performance of a supermodule was measured in a test beam.
Repre-
sentative results on the energy resolution as a function of beam energy are
shown in gure 2.9. The energy resolution, measured by tting a Gaussian
function to the reconstructed energy distributions, has been parametrized
as a function of energy:
S
N
σ(E)
= ⊕√ ⊕
⊕C ,
E
E
E
where
S
is the stochastic term,
N
the noise and
C
(2.1)
the constant term. The
values of these parameters are listed in the gure.
2.6 Hadron Calorimeter
The design of the hadron calorimeter (HCAL) [25] is strongly inuenced by
the choice of the magnet parameters since most of the CMS calorimetry is
located inside the magnet coil and surrounds the ECAL system (see gure
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Figure 2.9
ECAL supermodule energy resolution,
σE /E ,
as a function of electron
energy as measured from a beam test. The upper series of points correspond to events taken with a
20 × 20mm2
trigger. The lower series of
points correspond to events selected to fall within a
The energy was measured in an array of
3×3
4 × 4mm2
region.
crystals with electrons
impacting the central crystal.
2.1). An important requirement of HCAL is to minimize the non-Gaussian
tails in the energy resolution and to provide good containment and hermeticity.
Hence, the HCAL design maximizes material inside the magnet
coil in terms of interaction lengths. This is complemented by an additional
layer of scintillators, referred to as the hadron outer (HO) detector, lining
the outside of the coil.
Brass has been chosen as absorber material as it
has a reasonably short interaction length, is easy to machine and is nonmagnetic. Maximizing the amount of absorber before the magnet requires
keeping to a minimum the amount of space devoted to the active medium.
The tile/bre technology makes for an ideal choice.
It consists of plastic
scintillator tiles read out with embedded wavelength-shifting (WLS) bres.
The WLS bres are spliced to high-attenuation-length clear bres outside
the scintillator that carry the light to the readout system. This technology
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2.6 Hadron Calorimeter
was rst developed by the UA1 collaboration [26] and at Protvino [27] and
has been used in the upgrade of the CDF endcap calorimeter [28]. The photodetection readout is based on multi-channel hybrid photodiodes (HPDs).
The absorber structure is assembled by bolting together precisely machined
and overlapping brass plates so as to leave space to insert the scintillator
plates, which have a thickness of 3.7 mm. The overall assembly enables the
HCAL to be built with essentially no uninstrumented cracks or dead areas
in
φ.
The gap between the barrel and the endcap HCAL, through which
◦ and
the services of the ECAL and the inner tracker pass, is inclined at 53
points away from the centre of the detector.
2.6.1 Design
HCAL Barrel
The barrel hadron calorimeter is an assembly of two half barrels, each composed of 18 identical 20
◦ wedges in
φ.
The wedge is composed of at brass
alloy absorber plates parallel to the beam axis.
The innermost and out-
ermost absorber layers are made of stainless steel for structural strength.
There are 17 active plastic scintillator tiles interspersed between the stainless steel and brass absorber plates. The rst active layer is situated directly
behind the ECAL. This layer has roughly double the scintillator thickness
to actively sample low energy showering particles from support material between the ECAL and HCAL. The longitudinal prole in the barrel going
from an inner radius of 177.7 cm to an outer radius of 287.6 cm is given by
•
(Layer 0) 9 mm Scint/61 mm Stainless Steel;
•
(Layers
1-8)
•
(Layers
-14) 3.7 mm Scint/56.5 mm Brass;
•
(Layers
+16) 3.7 mm Scint/75 mm Stainless Steel/9 mm Scint;
3.7 mm Scint/50.5 mm Brass;
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where the layer number refers to the active scintillator layer. The individual
tiles of scintillator are machined to a size of
∆η × ∆φ = 0.087 × 0.087
and
instrumented with a single WLS. The WLS bers are spliced to clear bers,
and the clear bers are run down the length of the half-barrel where they are
optically added to corresponding projective tiles from each of the 17 active
layers, thus forming 32 barrel HCAL towers in
η.
The exceptions are towers
15 and 16 located at the edge of the HB half-barrel where multiple optical
readouts are present, as shown in gure 2.10.
The optical signal from the HCAL towers is detected with a pixelated
hybrid photodiode (HPD) mounted at the ends of the barrel mechanical
structure.
An additional layer of scintillators, the outer hadron calorime-
ter (HO), is placed outside of the solenoid and has a matching
∆η × ∆φ
projective geometry with a separate optical readout.
Figure 2.10
A schematic view of the tower mapping in
-
rz
of the HCAL barrel and
endcap regions. The shaded regions corresponds to dierent readout
channels.
HCAL Endcaps
The endcap hadron calorimeter is tapered to interlock with the barrel calorimeter and to overlap with tower 16, as shown in gure 2.10. The HE is com-
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2.6 Hadron Calorimeter
posed entirely of brass absorber plates in an 18-fold
φ-geometry
matching
that of the barrel calorimeter. The thickness of the plates is 78 mm while
the scintillator thickness is 3.7 mm, hence reducing the sampling fraction.
There are 19 active plastic scintillator layers. In the high
|η| = 1.74,
the
φ-granularity
η -region, i.e.
above
◦ to accommodate
of the tiles is reduced to 10
the bending radius of the WLS ber readout, as shown in gure 2.11(a).
For the purpose of uniform segmentation in the level-1 calorimeter trigger,
the energies measured in the 10
◦
φ-wedges
are articially divided into equal
shares and sent separately to the trigger. The
that of the barrel in the range
∆η × ∆φ
1.3 < |η| < 1.74.
For
tower size matches
|η| > 1.74,
the
η
size
increases. The number of depth segments in the HE includes a pseudo-EM
compartment starting with tower 18, the rst tower beyond the
η
coverage
of the ECAL barrel.
(a)
Figure 2.11
(a) The
-
η φ
eta < 1.740
in
η
(b)
view of a
and the
10
◦
20◦
HE section showing the
regions for
is also shown. (b) The
-
rφ
η > 1.740.
5◦
regions for
The tower 28/29 split
view of an HF wedge (η at
z
= 11.2
m). The shaded regions correspond to the level-1 trigger sums.
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HCAL Outer
The outer barrel hadron calorimeter consists of layers of scintillator located
outside of the magnet coil. Since these are located within the return yoke
along with the barrel muon detector, the segmentation of these detectors
closely follows that of the barrel muon system. The entire assembly is divided
into 5 rings (2.54 m wide along the
z -axis),
each having 12 sectors.
The
central ring (ring 0) has two layers of 10 mm thick scintillators on either
side of the
tail catcher
iron (18 cm thick) at radial distances of 385 cm and
409.7 cm, respectively. All other rings have a single layer at a radial distance
of 409.7 cm. The panels in the 12 sectors are identical except those in rings
±1.
This is due to the chimney structure in the magnet. To accommodate
this structure, special panels were built with a single row of scintillator tiles
removed. The HO covers
|η| < 1.26 with the exception of the space between
successive muon rings in the
η
direction, the space occupied by 75 mm
stainless steel support beams separating the 12 layers in
structure.
φ
and the chimney
The inclusion of the HO layers extends the total depth of the
calorimeter system to a minimum of
11
interaction lengths for
|η| < 1.26.
HCAL Forward
The forward calorimeters are located 11.2 m from the interaction point.
They are made of steel absorbers and embedded radiation hard quartz bers,
which provide a fast collection of Cherenkov light.
Each HF module is
constructed of 18 wedges in a non-projective geometry with the quartz bers
running parallel to the beam axis along the length of the iron absorbers.
Long (1.65 m) and short (1.43 m) quartz bers are placed alternately with
a separation of 5 mm. These bers are bundled at the back of the detector
and are readout separately with phototubes. The
r-φ
view of an HF wedge
is shown in gure 2.11(b).
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2.7 Inner tracking system
2.6.2 Performance
To test the performance of the HCAL, it is usual to look at the jet energy
resolution and the transverse energy resolution. The granularity of the sampling in the three parts of the HCAL has been chosen such that the jet
energy resolution, as a function of
ET ,
is similar in all three parts. This is
illustrated in gure 2.12. The resolution of the transverse energy (ET ) in
QCD dijet events with pile-up is given by
100%
σ(ET )
∼ √
.
ET
ET
(2.2)
.
Figure 2.12
The jet transverse energy resolution as a function of the simulated jet
transverse energy for barrel jets (|η|
3.0)
and very forward jets (3.0
< 1.4),
endcap jets (1.4
< |η| <
< |η| < 5.0).
2.7 Inner tracking system
By considering the charged particle ux at various radii at high luminosity,
three regions can be delineated:
•
The closest to the interaction vertex where the particle ux is the
highest (∼ 107/s at
r ∼ 10
cm), pixel detectors are placed. The size
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of a pixel is
∼ 100 × 150µm2
, giving an occupancy of about
10−4
per
pixel per LHC crossing.
•
In the intermediate region (20
< r < 55
cm), the particle ux is low
enough to enable use of silicon microstrip detectors with a minimum
cell size of 10 cm
×
80
µm,
leading to an occupancy of
∼ 2-3%/LHC
crossing.
•
In the outermost region (r
> 55
cm) of the inner tracker, the par-
ticle ux has dropped suciently to allow use of larger-pitch silicon
microstrips with a maximum cell size of
the occupancy to
25cm × 180µm, whilst keeping
∼ 1%.
Close to the interaction vertex, in the barrel region, there are three layers
of hybrid pixel detectors at radii of 4.4, 7.3, and 10.2 cm. The size of the
pixels is
100 × 150 µm2 .
are placed at
r
In the barrel part, the silicon microstrip detectors
between 20 and 110 cm. The forward region has 2 pixel and
9 microstrip layers in each of the 2 endcaps. The barrel part is separated
into an inner and an outer barrel.
In order to avoid excessively shallow
track crossing angles, the inner barrel is shorter than the outer barrel, and
there are an additional three inner disks in the transition region between
the barrel and endcap parts, on each side of the inner barrel. The total area
of the pixel detector is
200
∼ 1 m2
, whilst that of the silicon strip detectors is
m2 , providing coverage up to
|η| < 2.4.
The inner tracker comprises 66
million pixels and 9.6 million silicon strips [29].
2.7.1 Strip tracker
The barrel tracker region is divided into two parts: a TIB (Tracker Inner
Barrel) and a TOB (Tracker Outer Barrel).
The TIB is made of 4 layers and covers up to
sensors with a thickness of 320
to 120
µm.
µm
|z| < 65
cm, using silicon
and a strip pitch which varies from 80
The rst 2 layers are made with
stereo
modules in order to
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2.7 Inner tracking system
provide a measurement in both
r-φ
and
r-z
coordinates. A stereo angle of
100 mrad has been chosen. This leads to a single-point resolution of between
23 ÷ 34 µm
in the
r-φ
direction and 230
µm
in
z.
The TOB comprises 6 layers with a half-length of
|z| < 110
cm. As the
radiation levels are smaller in this region, thicker silicon sensors (500
µm)
can be used to maintain a good signal/noise ratio for longer strip length
and wider pitch. The strip pitch varies from 120 to 180
µm.
Also for the
TOB the rst two layers provide a stereo measurement in both
r-z
coordinates.
r-φ
and
The stereo angle is again 100 mrad and the single-point
resolution varies from
35-52µm
in the
r-φ
direction and 530
µm
in
z.
The endcaps are divided into the TEC (Tracker End Cap) and TID
(Tracker Inner Disks).
region
Each TEC comprises 9 disks that extend into the
120 cm < |z| < 280 cm,
and each TID comprises 3 small disks that
ll the gap between the TIB and the TEC. The TEC and TID modules
are arranged in rings, centred on the beam line, and have strips that point
towards the beam line, therefore having a variable pitch. The rst 2 rings
of the TID and the innermost 2 rings and the fth ring of the TEC have
stereo modules. The thickness of the sensors is 320
3 innermost rings of the TEC and 500
µm
µm
for the TID and the
for the rest of the TEC.
The entire silicon strip detector consists of almost
15 400
modules, which
are mounted on carbon-bre structures and housed inside a temperature
controlled outer support tube. The operating temperature is around
−20◦
C.
2.7.2 Pixel Tracker
The pixel detector consists of 3 barrel layers with 2 endcap disks on each
side of them (see gure 2.13). The 3 barrel layers are located at mean radii
of 4.4 cm, 7.3 cm and 10.2 cm, and have a length of 53 cm. The 2 end disks,
extending from 6 to 15 cm in radius, are placed on each side at
|z| = 34.5
cm and 46.5 cm.
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Compact Muon Solenoid Detector
Figure 2.13
Layout of pixel detectors in the CMS tracker.
In order to achieve the optimal vertex position resolution, a design with
an almost square pixel shape of
z
100 × 150 µm2
coordinates has been adopted.
in both the (r, φ) and the
The barrel comprises 768 pixel modules
arranged into half-ladders of 4 identical modules each.
◦
eect (Lorentz angle is 23 ) improves the
r -φ
The large Lorentz
resolution through charge
sharing.
The endcap disks are assembled in a turbine-like geometry with blades
◦ to also benet from the Lorentz eect.
rotated by 20
The endcap disks
comprise 672 pixel modules with 7 dierent modules in each blade.
The spatial resolution is measured to be about 10
surement and about 20
using approximately
µm
16 000
for the
z
µm
for the
r-φ
mea-
measurement. The detector is readout
readout chips, which are bump-bonded to the
detector modules.
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2.7 Inner tracking system
2.7.3 Performance
The performance of the tracker is illustrated in gure 2.14, which shows the
transverse momentum resolution for single muons with a
pT
of 1, 10 and
100 GeV/c, as a function of pseudorapidity. The material inside the active
volume of the tracker increases from
|η| ∼ 1.6,
before decreasing to
Figure 2.14
∼ 0.4 X0
∼ 0.6 X0
at
at
η=0
to around 1
X0
at
|η| = 2.5.
Resolution of the transverse momentum as a function of pseudorapidity for single muons with
pT (µ) = 1, 10, 100
GeV/c.
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CHAPTER 3
Detection of Cosmic Rays
Cosmic rays are energetic particles originating from outer space that hit
on the Earth's atmosphere.
The majority of these particles (∼
90%)
are
protons, while the remaining are electrons, helium nuclei (alpha particles)
1
and heavier elements .
They can come from very dierent sources: high
energy processes happening on the Sun as well as explosive events outside
our galaxy; and they cover a wide range of energies, almost up to
1020
eV.
Technically, primary cosmic rays are particles accelerated at astrophysical
sources, and secondaries are particles produced in interaction of the primaries with interstellar gas.
3.1 The Discovery of Cosmic rays
The study of the problem of cosmic rays began in 1903, when it was observed
by several British physicist [30] that the normal charge leakage occurring
in an electroscope was reduced only by thirty per cent by enclosing the
instrument within an air-tight metal box (several centimeters in thickness).
1
For all these particles, respective antiparticles have to be taken into account: when
saying electrons it means electrons
and
positrons.
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This was interpreted to mean that the loss of charge experienced by the
metal foil of the instrument was due to the ionization of the air by some
unknown penetrating radiation; cosmic radiation was the rst name with
which cosmic rays were known.
The rst speculation on what was the nature of this new kind of radiation
turned to the possibility that the rays were emanating from the radioactive elements in the Earth, being perhaps identical with the gamma rays of
radium.
In order to test this hypothesis, A. Glokel [31] took an enclosed
electroscope up with him in a balloon to a height of 4000 m and found that
the rate of discharge at this elevation was not signicantly dierent from
that found at the Earth's surface.
The source of the unknown ray thus
appeared to be located in the upper atmosphere or beyond it.
The possibilities awakened by this report lead V.F Hess [32] and W. Kolhöster [33] to repeat Gokel's measurement between 1911 and 1914.
They
reported that the radiation aecting the electroscope rst decreased slightly
and then increased in a marked manner as a function of the height, reaching
at the ight's highest point a value eight times that at the surface.
The nal conrmation of the existence of a new penetrating radiation was
given by Millikan and Cameron in 1925.
The two experimenters lowered
their electroscopes into the waters of a lake to varying depth down to 20 m,
and the measurements let they conclude:
Our experiments brought to light altogether unambiguously
a radiation of such extraordinary penetrating power that the
electroscope readings kept decreasing down to a depth of 50 feet
below the surface. [34]
3.2 Composition and spectrum
The incoming charged particles are modulated by the solar wind, the expanding magnetized plasma generated by the Sun, which decelerates and
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3.2 Composition and spectrum
partially excludes the lower energy galactic cosmic rays from the inner solar
system. There is a signicant anticorrelation between solar activity (which
has an alternating eleven-year cycle) and the intensity of the cosmic rays
with energies below about 10 GeV. In addition, the lower-energy cosmic
rays are aected by the geomagnetic eld, which they must penetrate to
reach the top of the atmosphere. Thus the intensity of any component of
the cosmic radiation in the GeV range depends both on the location and
time.
Figure 3.1
Vertical uxes of cosmic rays in the atmosphere with
points show measurement of negative muons with
E>1
Eµ > 1
GeV. The
GeV. [35]
Figure 3.1 shows the vertical uxes of the major cosmic ray components in
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Detection of Cosmic Rays
the atmosphere in the energy region where the particles are most numerous.
Except for protons and electrons near the top of the atmosphere, all particles
are produced in interactions of the primary cosmic rays in the air. Muons
and neutrinos are products of the decay of charged mesons, while electrons
and photons originate in decays of neutral mesons. Most measurements are
made at ground level or near the top of the atmosphere, but there are also
measurements of muons and electrons from airplanes and balloons.
Figure 3.2
The all-particle cosmic rays spectrum from air shower measurements.
[35]
Figure 3.2 shows a compilation of the cosmic ray all-particle spectrum
over the whole range of energies observed through dierent experimental
strategies. The spectrum exhibits power law behavior over a wide range of
energies, but comparison with a t to a single power law shows signicant
breaks at
∼
∼ 4 × 1015
5 × 1018 eV (the
eV (the
ankle ).
knee )
and, to a somewhat lesser extent, at
The three behaviours are represented by a
E −2.7
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3.3 Muons at the surface
law up to the knee and a
E −3.1
law up to the ankle; beyond the ankle the
spectrum can be described only approximately with a
E −2.7
trend. The ux
is expressed in number of particles over unit surface area, second, solid angle
−2 s−1 sr −1 GeV −1 ). The sharpness of the knee is a not yet
and energy (m
resolved experimental issue, particularly because it occurs in the transition
region between the energy range where direct measurements are available
and the energy range where the data come from indirect detection by the
ground array techniques (whose energy resolution is typically 20% or worse
[36]).
From the theoretical point of view, if we assume the cosmic ray spectrum
below
1018
eV to be of galactic origin, the knee could reect the fact that
most cosmic accelerators in the galaxy have reached their maximum energy.
Some types of expanding supernova remnants, for example, are estimated
not to be able to accelerate protons above energies in the range of
1015
eV. Concerning the ankle, one possibility is that it is the result of a higher
energy population of particles overtaking a lower energy population, for
example an extragalactic ux beginning to dominate over the galactic ux
[37]. Another possibility is that the dip structure in the region of the ankle
is due to
γp → e+ e−
energy losses of extragalactic protons on the 2.7 K
cosmic microwave radiation [38].
3.3 Muons at the surface
Muons are the most numerous charged particles at sea level (see gure 3.1).
Most muons are produced high in the atmosphere (typically 15 km) and lose
about 2 GeV to ionization before reaching the ground.
Their energy and
angular distributions reect a convolution of production spectrum, energy
loss in the atmosphere, and decay. For example, 2.4 GeV muons have a decay
length of 15 km, which is reduced to 8.7 km by energy loss. The mean energy
of muons at the ground is
∼ 4 GeV. The energy spectrum is almost at below
1 GeV, steepens gradually to reect the primary spectrum in the
10 ÷ 100
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Detection of Cosmic Rays
GeV range, and steepens further at higher energies. The integral intensity
of vertical muons with
often reported as
I∼
p>1
GeV/c at sea level is
∼ 70 m−2 s−1 sr−1
[39],
1 cm−2 min−1 for horizontal detectors.
The overall angular distribution of muons at the ground is
is characteristic of muons with
Eµ ∼ 3
∝ cos2 θ, which
GeV. At lower energy the angular
distribution becomes increasingly steep, while at higher energy it attens,
approaching a
sec θ
distribution.
3.4 Muon interaction with matter
A muon interacts with matter through four dierent processes:
•
bremsstrahlung;
•
ionization;
•
pair production;
•
photonuclear interactions.
Moderately relativistic muons lose energy in matter primarily by ionization and atomic excitation (photonuclear interactions). Since the production
of an ion pair (usually a positive ion and a negative electron) requires a xed
amount of energy (for example, 34 eV in air), the density of ionisation along
the path is proportional to the stopping power of the material. The mean
rate of energy loss (dE/dx) for muons on copper is shown by the solid curve
in gure 3.3. For all practical purposes in high-energy physics,
given material is a function only of
β,
dE/dx
in a
the particle's speed.
Often we refer to the average energy loss of the particle per unit path
length as the stopping power. The stopping power function is characterized
by a broad minimum, whose position drops from
βγ = 3.5
to 30 as the
atomic number (Z ) of the crossed medium goes from 7 to 100.
At suciently high energies, radiative processes become more important
than ionization for all charged particles; the position of the spectrum where
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3.4 Muon interaction with matter
Figure 3.3
Stopping power (dE/dx) for positive muons in copper as a function
of momentum
p = M βcγ .
Solid curves indicate the total stopping
power. Vertical bands indicate boundaries between dierent theoretical approximations or dominant physical processes.
Nuclear losses
indicates non-ionizing nuclear recoil energy losses, which are negligible
here. [40]
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the transition takes place is called critical energy (Eµc ). For muons in materials such as iron, critical energy occurs at several hundred GeV. Radiative
processes are characterized by small cross sections, hard spectra, large energy
uctuations, and the associated generation of electromagnetic and hadronic
showers (the latter only in the case of photonuclear interactions). As a consequence, at these energies the treatment of energy loss as a uniform and
continuous process is inadequate.
It is convenient to write the average rate of muon energy loss as [41]
−
where
a(E)
dE
= a(E) + b(E)E ,
dx
is the ionization energy loss, and
b(E)
(3.1)
is the sum of
e+ e−
pair production, bremsstrahlung, and photonuclear contributions. With this
parametrisation we get
Eµc = a/b.
3.5 Muons in the CMS cavern
Only muons and neutrinos penetrate to signicant depths underground. Interacting with matter, the muons may produce tertiary uxes of photons,
electrons, and hadrons.
Experimental measurements of the cosmic muon
ux intensity at dierent depths [42] shows that the muon absorption coecient decreases as the thickness of the crossed material increases. Therefore
the mean energy of the muons soaking in the rock increases with depth.
The intensity of muons underground can be estimated from the muon
intensity in the atmosphere and their rate of energy loss. To the extent that
the mild energy-dependence of
a
and
b
can be neglected, equation 3.1 can
be integrated to provide the following relation between the energy
a muon at production in the atmosphere and its average energy
traversing a thickness
X
Eµ0
Eµ
of
after
of rock (or ice or water):
Eµ = (Eµ0 + Eµc ) e−bX − Eµc
(3.2)
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3.5 Muons in the CMS cavern
Figure 3.4
Vertical muon intensity vs depth (1 km.w.e =
rock).
105 g cm−2
of standard
The shaded area at large depths represents neutrino-induced
muons of energy above 2 GeV. The upper line is for horizontal neutrinoinduced muons, the lower one for vertically upward muons.
There are two depth regimes for equation 3.2 due to the surface momentum
spectrum. For
while for
X b−1 ∼ 2.5
km water equivalent,
X b−1 Eµ0 ∼ (Eµc + Eµ (X)) ebx .
Eµ0 ∼ Eµ (X) + aX ,
Thus at shallow depths, the
dierential muon energy spectrum is approximately constant for
and steepens to reect the surface muon spectrum for
X > 2.5
Eµ < aX ,
Eµ > aX ; whereas for
km.w.e., the dierential spectrum underground is again constant
for small muon energies but steepens to reect the surface muon spectrum
for
Eµ > Eµc ∼ 0.5
TeV. In the deep regime, the shape is independent of
depth, although the intensity decreases exponentially with depth. In general
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the muon spectrum at slant depth
X
is
dNµ dEµ0
dNµ bX
dNµ
=
=
e ,
dEµ
dEµ0 dEµ
dEµ0
where
Eµ0
(3.3)
is the solution of equation 3.2.
Figure 3.4 shows the vertical muon intensity versus depth, where the standard rock is dened as a material with
A = 22, Z = 11 and ρ = 2.65 g cm−3 .
The at portion of the curve is due to muons produced locally by chargedcurrent interactions of
νµ .
The study presented in this thesis is based on a cosmic data-taking with
the CMS detector. The detector is displaced 85 m underground, hence the
cosmic muons have to cross three dierent materials to reach it: air, rock
and concrete. The parameters of the energy loss function for concrete and
rock are very similar, as their values of
Z/A
and density are almost equal.
A diagram of the material crossed by a muon is shown in gure 3.5.
The cosmic muon momentum distribution detected with CMS is shown in
gure 3.6. We note that the majority of the cosmic muons have a momentum
corresponding to
hdE/dxi
close to the minimum (cf. with gure 3.3), thus
they are said to be minimum ionizing particles (or mip's)
3.6 Cosmic Muon Reconstruction
When a muon is going downwards from the surface to the cavern, the muon
chambers are the rst detectors to measure its passage. They are composed
of Drift Tubes (DTs), Resistive Plate Chambers (RPCs) and Cathode Strip
Chambers (CSCs). Each time a particle releases some energy in one of these
hit ; the hits within
matched to form segments (track stubs).
detectors we have one
each DT or CSC chamber are
In the oine reconstruction the segments built in the muon chambers
are used to generate
seeds,
consisting of position and direction vectors and
an initial estimate of the muon transverse momentum. The seeds serve as
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3.6 Cosmic Muon Reconstruction
Figure 3.5
Sketch of the material in the CMS cavern.
Air is in yellow, rock is
in light blue, and concrete walls are in purple. The gure on the left
shows the
the
z<
z > 0
side of the cavern, whereas the central gure shows
side.
starting points for the track ts in the muon system based on the Kalman
lter technique [43, 44].
The result is a collection of tracks reconstructed
using only information in the muon spectrometer, which are referred to as
standalone muons.
The standard reconstruction algorithm for standalone muons was developed to reconstruct muons produced in
pp collisions.
It assumes that muons
are produced at or close to the nominal interaction point, and that they
travel from the center of the detector to its periphery. Therefore, a number
of modications to the standard algorithm is necessary to eciently reconstruct muons coming from outside the detector, in particular those traversing
detector far from its center. A detailed description of the modications implemented at various stages of the standalone muon reconstruction can be
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Figure 3.6
Momentum spectrum of muons detected with CMS.
found in [45]. However a description of the modications involving the DT
trigger and the DT time computation is given in section 3.7.1.
3.6.1 Global muons
At low
pT
values, optimal momentum resolution for a muon is obtained from
measurements in the inner tracker alone. As a track's momentum increases
and its curvature decreases, however, momentum resolution in the tracker
becomes limited by position measurement resolution (including misalignment eects). One can then benet from the large lever arm between the
tracker and the muon system by including hits in the muon chambers. For
each standalone muon track, a search for tracks matching it among those
reconstructed in the inner tracking system (referred to as
tracker tracks )
is carried out, and the best-matching tracker track is selected.
For each
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3.6 Cosmic Muon Reconstruction
Figure 3.7
Events display of a cosmic muon passing through CMS (x,y view).
tracker track - standalone muon pair, a new t using all hits in both tracks
is performed, again based on the Kalman lter technique. The result is a
collection of tracks referred to as
global muons.
As in the case of the stan-
dalone muon reconstruction, some modications to the default global-muon
algorithm were implemented for cosmic muons, this mainly to enable reconstruction of tracks consisting of two standalone muon tracks at opposite
ends of the detector and a tracker track sandwiched between them. These
modications are described in [45].
Various types of global muons are produced by the reconstruction algo-
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rithm:
• 1-leg muons ;
these muons typically consist of a tracker track sand-
wiched between two standalone muon tracks, and yield the best estimate of the parameters of the muon.
• 2-leg muons ;
the track of a single particle that crosses the top and
the bottom part of CMS is broken in two legs, one for
for
y < 0,
point.
y>0
and one
as if there were two particles coming from the interaction
Since the two 2-leg muons are treated independently at all
stages of reconstruction, they provide fully unbiased measurements of
reconstruction performance, though care must be taken to ensure that
they were produced by the same muon.
Figure 3.7 shows an event display of a 2-leg global muon passing through
CMS. DT hits, tracker hits and calorimetric deposits are visible.
3.7 Cosmic Muon Time Measurement
The muon time measurement is performed by mean of the muon track reconstructed by the muon system. Since in the barrel each hit composing the
track is generated by a DT cell, by measuring the time when the hit occurs
we get the time of arrival tA of the muon on that cell. On average each muon
leg is composed by
20 ÷ 30
hits, resulting in
DT synchronization let all the
tA
20 ÷ 30 tA
measurements. The
values to be function of the DT distance
from the interaction point (dIP ), and a linear t to the relation
tA
vs
dI P
provides the extrapolation of the muon time at the interaction point.
3.7.1 Drift Tube synchronization
The DT muon barrel detector provides the majority of the triggers during
a cosmic data taking.
The rst level trigger signal (L1) is given by the
coincidence of at least two DT local triggers happening in dierent chambers
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(in the same or in neighboring sectors), and being in the same 25 ns time
window (called
pp
bunch crossing as it is the time passing between two following
collisions).
Since the cosmic rays cross the detector with dierent angles and rates, a
local trigger synchronization is specically adjusted for cosmics triggering.
The synchronization prevents a single muon to generate two dierent triggers
when crossing the
y >0
region and the
y <0
region of CMS at dierent
times.
The DT chambers are synchronized computing the mean value of the
tA
distribution for each chamber (using the default set-up designed for muons
coming from the interaction point), and providing a tuned time delay for each
chamber. The time delays are implemented increasing the trigger latency of
the chambers in the top sectors, accounting for a maximum time of ight
to the bottom chambers of about 50 ns; in this way the two L1 muon track
candidates are generated at the same bunch crossing when a single muon
passes through the two sides of the detector.
Figure 3.8
Scheme of DT time latencies in cosmic data taking. Blue circles are the
times and positions of a muon going from the outside of CMS towards
the center. Red circles are the time hits of the same muon once time
latencies are applied.
Figure 3.8 shows how the time delays allow to trigger a muon coming
downwards as if it were originating from the interaction point (IP). The
distance from the IP of a muon entering inside CMS (dark circles) decreases
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with time, resulting a negative slope in a space-time diagram. Introducing in
each chamber a latency proportional to its distance from the IP, we change
the sign of the slope, and the muon distance from the IP increases as a
function of time (light circles), exactly as a muon produced in the middle of
the detector.
3.7.2 Time of arrival
In a DT cell, the passage of a muon ionizes the gas producing an ion-electron
pair; the eect of the high electrical eld is to let the charges drift and to
collect them on the central wire. The time employed by the charge to reach
the wire is called drift time (tdrif t ), and is measured with a TDC. To get
the actual tdrif t , the pedestal has to be subtracted from the raw TDC value,
where the pedestal is composed by all the TDC counts preceding the charge
collection (see gure 3.9).
As soon as in a DT chamber there are enough aligned hits to generate a
DT local trigger and to form a DT segment, the
the candidate track to a bunch crossing.
tdrif t
measurement assigns
At this stage, the muon time
of arrival has a 25 ns granularity, and the ne structure inside the 25 ns
window is computed by retting the segment. Th procedure is based on the
conversion of the time measurements to hit positions assuming a constant
drift velocity, that is
hit position = tdrif t × vdrif t .
Since
tdrif t
allows only a
one dimensional reconstruction of the hit position, for each TDC value there
are two possible positions, reecting the left-right ambiguity with respect to
the anode wire inside the cell (see gure 3.10). This ambiguity is solved at
the track segment building stage by the local pattern recognition algorithm,
that uses the one-dimensional hits as input. The pattern recognition links
together all the hits and it is independently performed in the
r-φ
and
r-z
planes of each chamber, to deliver the so called 2-dimensional (2D) track
segments in each view. The 2D segments are paired using all the possible
combinations in the chamber, to form collections of 4D segments carrying
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Figure 3.9
Distribution of the signal arrival time; the arrival time in all the cells
from a single superlayer in a chamber are superimposed.
The curve
shows the result of a t to the rising edge of the distribution with the
integral of a Gaussian function, used for the time pedestal determination.
complete spatial information.
Since the 4D segment has to be retted to determine the nal position
and the direction of the segment, the
tA
can be treated as a free parameter,
thus allowing a precise measurement of the muon time of arrival.
3.7.3 Time at the Interaction Point
Since the cosmic muons are not constrained to pass through the interaction
region, the muon time at the interaction point (tip ) is just a way to refer to
the result of a t method. However the
tip
is the only possible muon time
measurement that can be used to implement a time selection criterion, as it
provides a unique time value for each muon.
A cosmic muon crosses the CMS detector almost at the speed of light light
(β
= 1).
Since the speed is constant, there is a linear relation between the
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Figure 3.10
tA
Section of a DT cell.
values measured by the DT chambers and the distances of the chambers
from the interaction point. The tip value is computed with a linear t to this
Figure 3.11
Fit to DT hits to extract the muon time at the interaction point. Each
point represents a DT hit; solid line is the linear t. [46]
relation, where the slope is xed to be 30 cm/ns (i.e.
β = 1)
and the only
free parameter is the intercept. The constant term of the linear function is
indeed the time at which a muon should have left the interaction point in
order to pass through the muon chambers at the measured
Figure 3.11 shows the
tA
tA s.
values (hit times) versus the distance of the
chambers from the interaction point. The solid line is the linear t, and the
intersection with the
tIP
y
axis measures the the
tIP
value. The distribution of
has a Gaussian shape, with a mean of about 0 ns and a width of about
10 ns, and it is shown in gure 3.12.
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3.8 Cosmic Muon Analysis
In the following we refer to the muon time at interaction point simply as
the muon time.
Figure 3.12
Distribution of muon times at the interaction point
3.8 Cosmic Muon Analysis
During the Autumn 2008 the CMS detector collected about 300 million
cosmic events, selected by triggering system in various detector and trigger
conditions. the large majority of the data was collected with a nominal magnetic eld of 3.8 T (inside the solenoid). As discussed in the introduction,
we use this data sample to study the noise of the calorimeters and to set-up
a time selection criterion based on the muon time.
In section 3.8.1 we discuss the properties that a muon has to have in order
to be considered as a time reference for the event.
we perform turns out to bias the
tIP
However the selection
measurement, and a time correction is
needed to account for this eect. Our strategy for the correction is discussed
in section 3.8.2.
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3.8.1 Selection Criteria
1. Selection of the muon direction. In order to reconstruct a global muon,
we need the hits coming both from the inner tracker and from the
muon system; therefore we ask for the muon to pass through the inner
tracker. Since the passage through the tracker implies the crossing of
the calorimeters, we are sure that the selected muons can be also used
to study the calorimeter response.
2. Selection of the muon
pT .
To avoid that the muons stop in the detector
without escaping from the bottom, we require
pT (µ) > 10
GeV/c;
3. Selection of the distance of closest approach. Since the usage of the
muon time at the interaction point can result untting if the track
passes far away from the interaction region, we introduce a selection on the distance of closest approach.
and
dz < 30 cm,
where
dz
is the
z
We ask for
d0 < 30 cm
component of the smallest vector
connecting the interaction point to the muon track, and
d0
is dened
as the transverse component of the same vector (z direction is along
the LHC beam line).
3.8.2 Time Oset Correction
We note that computing the tIP distribution separately for each CMS sector,
we get the mean value to be dierent from zero. We ascribe this eect to the
application of wrong DT latencies to the
tA
values composing
tIP .
The DT
synchronization (see section 3.7.1) is indeed tuned using the tA mean values
evaluated with all the muons crossing a given chamber. On the contrary, in
the analysis we select only those muons passing through the tracker. This
mismatch between the two samples makes the DT synchronization untting
to provide the correct
tIP
values.
Figure 3.13 shows the spread of the time osets belonging to dierent
sectors.
Each point is the mean value of a single sector
tIP
distribution,
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Figure 3.13
Muon time osets for selected sectors.
Error bars are almost com-
pletely covered by data. Vertical lines identify the CMS wheels, going
from -2 on left to +2 on the right.
while the vertical error bar represents the root mean square (rms) of the
same distribution.
Since the osets are dierent for each sector, it is impossible to use the
same time selection criterion for the whole detector, and an oset correction
is required to equalize the distributions (i.e. to intercalibrate the muon sector
responses). Every CMS wheel is composed by 14 sectors, totally resulting
in 70 sectors, and for each one we t the
tIP
distribution with a Gaussian.
We consider the tted mean of the distribution to be the time oset of the
sector, and we perform the correction by subtracting the oset to the
A drawback of the t-based correction is that the
tIP
tIP .
distribution can no
longer be tted if the sector is low populated, because its shape is highly
irregular. The side sectors are the most aected by lack of events since the
cosmic muons come mainly from the surface. Figure 3.14a shows the time
distribution of a top sector, while gure 3.14b shows the same distribution
for a side sector.
In order to select which sectors are enough populated to be tted, we study
the time distributions coming from all the 70 sectors of the detector. We keep
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only those sectors where the distribution is similar to one in gure 3.14(a)
and the result is that we can use only eight sectors per wheel, resulting in
40 useful time distributions to be tted and corrected. The considered ones
are sectors no. 3, 4, 5, 13 (on the top side of the experiment) and sectors no.
9,10,11,14 (on the bottom side). Unfortunately we are discarding a relevant
fraction of the total muon sample; however only the corrected muon time
allows us to dene a trustworthy time reference.
We note that a side eect of the oset correction is the improvement of
the tIP resolution. The corrected time distribution has a width
∼ 10% lower
with respect to the raw one.
(a)
Figure 3.14
(b)
Muon time distribution for: (a) top sector, (b) side sector. Solid line
is a Gaussian t.
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CHAPTER 4
Missing Energy Measurement
Within the Standard Model of particle physics (SM), proton-proton interactions produce many weakly interacting neutral particles, most of which
do not release enough energy in the CMS detector to be detected.
Their
presence can be inferred with the four-momentum conservation: if in the
nal state there is less energy than in the initial state, one or more particles
must have escaped detection.
In an hadronic collider it is not possible to use the total energy balance of
the collision as a useful constraint, both because the colliding partons do not
carry the total beam energy, and because low
pT
interaction products mov-
ing in very forward direction can escape detection. However on the plane
orthogonal to the beam direction (transverse plane), the beam's focusing
guarantees no relevant momentum to be present. As a result, any significant imbalance of the transverse momentum (pT ) in the event represents the
signature of the production of a weakly interacting particle in the collision.
Many extensions of the SM predict the existence of new weakly interacting
stable or quasi-stable particles. These particles are supposed to be massive,
hence to provide high values of
events with a significant
pT
pT
imbalance (or missing
pT ).
If an excess of
imbalance is still observed after accounting for
all the SM processes, it would constitute a strong evidence for new physics
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beyond the SM. This makes the total missing
pT
an important variable for
searches of new physics.
Historically, missing
pT
is often referred to as missing transverse energy.
This notation is somewhat confusing, as it commonly refers to either the
2D-vector of missing
notations:
E
/T
pT
or to its magnitude.
is the scalar variable, which describes the magnitude of the
missing transverse momentum vector, while
We also use
E
/x , E
/y
Finally, we use
Here we use the following
φ(E
/ T)
−
→
E
/ T refers to the 2D-vector itself.
to denote the two components of the
E
/T
to denote the azimuthal direction of the
2D-vector.
E
/T
vector.
4.1 Calorimetric Tower
The
E
/T
computation is based on the
φ
distribution of the energy deposits
measured with both the HCAL and the ECAL. Although the two detectors have a similar geometry, their granularity is completely dierent and a
dedicated tool is needed to match the energy deposits coming from the two
calorimeters.
We dene a calorimetric tower (calo-tower) to be a projective tower in
the calorimetry system crossing both the ECAL and the HCAL, and linking
together the energy deposits of the two subdetectors. Since the HCAL has
the lower granularity, a calo-tower is composed by a single HCAL tower and
all the ECAL crystals being inside the tower boundaries. In the barrel, for
example, there is a
5×5
matrix of crystals matching in
η -φ
a single HCAL
tower.
The calo-tower has an electromagnetic and hadronic energy. The former
is given by the energy sum of all the crystals composing the calo-tower, the
latter by the energy sum of all the layers of the tower at dierent depths.
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4.2 Missing Transverse Energy
4.2 Missing Transverse Energy
The missing transverse energy (E
/ T ) is computed [47] from the transverse
1 projective calo-towers:
vector sum over energy deposits in raw
X
−
→
E
/T = −
(En sin θn cos φn ı̂ + En sin θn sin φn ̂) = E
/x ı̂ + E
/ y ̂
(4.1)
n
where the
n index runs over all calorimeter input objects, i.e.
in calorimetric cells. Here ı̂,
̂ are the unit vectors in the direction of x and y
axis of the CMS right-handed coordinate system, where
z
energy deposits
x
is horizontal and
is pointed in the direction of the west-going (or Jura-going) beam.
In the absence of
E
/T
from physics sources in the event,
E
/x
and
E
/y
are
expected to be distributed as Gaussians with the mean of zero and the width
of
σ,
while
E
/T
has a more complicated shape described by
√
2π
θ(E
/ T)E
/ T × G(E
/ T, 0, σ) ,
σ
where
θ(x)
θ(x) = 0
for
(4.2)
is the ordinary Heaviside function (θ(x)
x < 0),
Gaussian with mean
and
G(x, µ, σ) = exp(−(x −
µ and width σ .
E
/ T is the same of the E
/x
and
E
/y
The width
σ
= 1
for
x ≥ 0
√
2πσ
µ)2 /2σ 2 )/
and
is a
of the Gaussian describing
distributions. It can be demonstrated that:
r
hE
/ Ti = σ
r
σ (E
/ T) = σ
π
≈ 1.235σ
2
(4.3)
4−π
≈ 0.655σ
2
(4.4)
Montecarlo QDC events are a good example of events without relevant
real
E
/ T,
because the latter comes only from few neutrinos in hadronic jets
(E
/T
<2
GeV in
p̂T
range
80 ÷ 120
GeV). The
E
/T
detected in these events
is completely generated by the detector noise, and for this reason we call it
1
In this chapter the word raw will be used as without any applied correction.
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Figure 4.1
E
/T
detected with CMS in a QCD sample of
case there is no relevant physical
Gaussian while
instrumental.
E
/T
p̂T ∈ [80, 120]
the event, hence
GeV. In this
E
/x
and
E
/y
are
follows the distribution described by equation 4.2.
Figure 4.1 shows that the instrumental
while the instrumental
The
E
/T
E
/ T in
E
/x
is almost Gaussian,
E
/ T follows the distribution described by equation 4.2.
is a quantity extremely sensitive to detector malfunctions and
particles hitting poorly instrumented regions. Any dead or hot channel in
the detector may result in an articial energy imbalance, thus mimicking a
new physics signal. Consequently great care is required to understand the
E
/T
distribution as measured by the detector, and to ensure that
E
/T
is a
trustworthy variable for searches.
To minimize the instrumental
E
/ T in the event it is necessary to reduce the
calorimetric noise imposing an energy threshold in the calo-tower building.
CMS has three levels of selection (scheme A, B, C), the most used being
scheme B. Energy selection criteria are applied on a subdetector basis, because usually the cut is two sigmas above the mean noise, and each one has
its own energy noise. The HCAL single tower energy has to be above 0.9
GeV in the HCAL barrel (HB) and 1.4 GeV in the HCAL endcaps (HE)
to enter in
E
/T
computation, while the hadronic outer calorimeter (HO) and
the forward one (HF) have thresholds equal to 1.1 GeV and 1.8 GeV. Since
a calo-tower is made of several ECAL crystals, there are thresholds both
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4.2 Missing Transverse Energy
Scheme B thresholds for HCAL and ECAL. Values are in GeV and refers
Table 4.1
to energy measured n a single tower or crystal, except for last two
columns where
inside a 5
×
P
symbol stands for the sum of energies over all crystals
5 matrix forming a calo-tower.
HCAL thresholds (GeV)
ECAL thresholds (GeV)
HB
HE
HO
HF
EB
EE
0.9
1.4
1.1
1.8
0.09
0.45
P
EB
0.2
P
EE
0.45
for the single crystal energy and for the summed energy of all the crystals
in the calo-tower. The former is set to 90 MeV in ECAL barrel (EB) and
450 MeV in ECAL endcaps (EE), while the latter is 200 MeV in the barrel
(ΣEB) and 450 MeV in the endcaps (ΣEE). A further selection is required on
the whole calo-tower, asking that HCAL and ECAL energies once combined together pass a 0.5 GeV threshold. Calo-towers not satisfying these
requirements (summarized in table 4.1) do not enter in
E
/T
computation.
In principle one could think that a tighter selection always produces a
better
E
/ T,
but this is denitely not true.
that a threshold tighter than
2σ
In section 4.4 we demonstrate
above the mean noise level spoils the
E
/T
distribution.
4.2.1 Missing Transverse Energy Resolution and Signicance
The
E
/ T resolution can be parametrized according to the following expression
usually employed when describing calorimetric uctuations [48]:
A
σ(E
/ T)
=P
⊕B
E
/T
ET
where the
A
noise
term (
pP
P
ET − D
( ET − D)
P
P
⊕C
,
ET
ET
(4.5)
term) represents eects due to electronic noise,
pile-up, and underlying-event; the
B
term (
stochastic
term) represents the
statistical sampling nature of the energy deposits in individual calorimetric
towers; the
C
constant
term (
term) represents residual systematic eects
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due to non-linearities, cracks, and dead material; and
represents the eects of noise and pile-up on
P
D
term (
oset
term)
ET .
For QCD dijets events discussed in section 4.2, no or little
E
/ T is
expected
from physical sources, so any energy imbalance measured in the event is due
to the nite calorimeter resolution and acceptance. According to equations
4.3 and 4.4, in these events the
E
/T
E
/ T uncertainty is proportional to the average
value:
σ (E
/ T) ∼ 0.52 E
/T .
If we dene the
(4.6)
E
/ T significance to be the ratio hE
/ Ti/σ (E
/ T), and we assume
that only stochastic eects are important, the
E
/T
number of standard deviations of the measured
pothesis. If stochastic eects dominate, the
events is constant for all
P
ET
E
/T
signicance estimates the
E
/T
from the
E
/T = 0
hy-
significance of QCD dijet
values and close to 2:
hE
/ Ti
0.52 hE
/ Ti
/ Ti
. hE
∼ pP
∼ 1.91 .
∼
sig (E
/ T) =
σ (E
/ T)
hE
/
B
ET
Ti
Any residual dependence of the
E
/T
significance on
P
ET
(4.7)
is an indica-
tion of the importance of non-linearities (i.e. the constant term) in the
E
/T
resolution.
Moreover, a
terms of
E
/T
sig(E
/ T):
excess of events over the SM predictions is measurable in
the more the
sig(E
/ T)
increases, the most the measure is
untting with the SM.
4.3 Zero Suppression
The zero suppression is a detector's read-out mode where just few channels
out of the total are read and stored by the data acquisition system. Usually the selection is energy based. This solution is required when an high
occupancy of the detector is expected, and the data acquisition bandwidth
is insucient to transmit the data coming from all the channels.
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4.4 Energy Threshold Eects
For example the ECAL has
∼ 77 000
channels, each one producing 2
bytes of information every 25 ns. If all the crystals were read-out, about 2.4
Mbytes would need to be handled for each triggered
pp event.
By agreement,
the ECAL fraction of the data acquisition bandwidth is constrained to be
approximately 10% of the CMS total, bringing the average data rate to 200
Mbyte/s, for the maximum rst-level trigger rate (100kHz). Techniques such
as the zero suppression are then necessary to reduce the output size of the
detector.
The ECAL crystal mean noise is about 1 ADC count.
Therefore, the
ECAL zero suppression is set to read and store information coming only from
crystals giving a signal above 1 ADC. Such a setup holds also in cosmic data
taking, even if it is not strictly necessary. On the contrary the HCAL runs
without zero suppression: all the channels are read-out for each triggered
event, regardless of the channel energy.
4.4 Energy Threshold Eects
Here we demonstrate that an energy threshold tighter than
E
/T
the
distribution.
E
/x
and
E
/y
2σ
spoils the
Indeed a tight energy selection on calo-towers results in
distribution to be no longer Gaussians, and consequently
the instrumental
E
/T
distribution does not follow anymore the probability
density function in equation 4.2. The reason is that too many calo-towers
are discarded from
E
/T
computation.
an eect because if the instrumental
We have to take into account such
E
/T
distribution is dierent from what
we expect, we are not able to account for instrumental
E
/T
in the total
E
/T
distribution, hence we cannot distinguish a new physics signal from the noise
uctuations.
To prove that the eect exists, we implement a toy Monte Carlo simulation
of the HCAL barrel energy response, using 2160 towers displaced in
as in the reality. Since we want to study the instrumental
E
/ T,
η
and
φ
each tower is
simulated to provide a Gaussian energy deposit with a mean value of zero,
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exactly as the real tower's noise. The
E
/T
is computed using the denition
in equation 4.1, considering only the tower energies that are above a given
threshold. We study three possible values for the thresholds: 1
σ,
where
σ
σ,
2
σ
and 3
is the width of the Gaussian employed in the single tower noise
simulation. Since there is no real
E
/T
in the event, we expect the
distributions to be Gaussians around zero, and the
E
/x
and
E
/y
E
/ T distribution to follow
equation 4.2, as in the QCD sample.
The simulation shows that increasing the tower energy threshold reduces
the instrumental
2
σ
E
/ T, while keeping its shape, until the threshold is under the
value. Once above that value, both
E
/x
and
E
/T
distributions lose their
usual shape. This situation is illustrated in gure 4.2. Each row shows the
E
/x
σ
and
E
/T
distributions, respectively for a calo-tower energy threshold of 1
(rst row), 2
σ
(second row) and 3
σ
(third row) over the noise level. Till
the second row, the Gaussian shape is preserved and instrumental
E
/T
mean
value decreases, while description given by equation 4.2 still holds; but on
the third row we note that such a tight selection spoils both the
E
/T
E
/x
and the
distributions.
The scheme B thresholds provides an optimal choice of the energy thresholds for
E
/T
reconstruction.
4.5 Irreducible E/ T sources
There at least three irreducible sources of
E
/T
in a
pp
collision other than
SM processes, new physics processes and instrumental noise. They are the
parton motion in the transverse plane, the calorimeter limited hermeticity
and the crossing angle between the proton beams. We call them irreducible
sources of
E
/T
because experimentally we cannot avoid them, contrary to
the instrumental
E
/T
that in principle could be reduced as far as we could
increase the calorimeter resolution.
Here we briey describe the sources of irreducible
E
/ T and we give a rough
estimation of their contribution, showing that they are not relevant (or at
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4.5 Irreducible E/ T sources
Figure 4.2
Simulation of pure instrumental
E
/x
ferent calo-tower energy thresholds.
and
E
/T
distributions with dif-
First row:
in the hypothesis
of Gaussian noise for a single calorimetric channel, the
puted just with calo-towers having an energy deposit 1
Second row:
the selection is
Ecalotower > 3 σnoise ; E
/x
Ecalotower > 2 σnoise .
σ
E
/T
is com-
above noise.
Third row:
distribution starts to depart from a Gaus-
sian behaviour, while both in
E
/T
and
E
/x
emerge a peak at zero value
accounting for events where no calo-tower passes the energy threshold.
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most of the same order) when compared with the instrumental
E
/T
distribu-
tion.
Parton motion
Since the hadrons are not elementary particles, the collisions happen among
the partons (hadron constituents).
hadron, i.e.
The partons are conned inside the
they experience a strong potential well that keep them to-
gether. Following the Heisenberg's principle, each particle conned in
has an associate momentum spread
sional and holds for
x, y
and
z
∆p ∼ ~/∆x.
∆x
This relation is unidimen-
separately. Therefore the collision between
partons can have a non-zero transverse momentum even if proton's motion
takes place only along the beam direction.
To make a numerical estimation we take the
∆x
to be the proton radius,
dened as the quadratic mean radius of the proton charge distribution (measured with the proton form factor). Applying the Heisenberg's principle we
have
∆p ∼
10−34 J s
Js
~
∼ −15
∼ 10−19
∆x
10
m
m
(4.8)
p(eV) ∼ ∆p · c · (1.60 · 10−19 (J/eV))−1 ∼ 100 MeV .
If we assume the parton momentum to be Gaussian in the
x
(4.9)
and
y
direc-
tions with a spread of about 100 MeV around zero, the resulting mean
O(120 MeV) (see equation 4.3).
pT
is
This eect can be therefore easily neglected
if compared with a 20 GeV mean instrumental
E
/T
(see gure 4.1).
Calorimeter Limited Hermeticity
The CMS detector has nearly 4π solid angle coverage, but it is not completely hermetic as it must have an opening in the very forward regions to
let the beams pass through. Since the calorimetry system covers
η
region
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from -5 to +5, the particles moving in the very forward direction can escape the detection. However, although such particles can carry signicant
longitudinal momentum, they cannot carry a large
pT .
Indeed, in order to
| η |> 5 which corresponds to
p
p
pT =
<
< 0.013 × p .
cosh(η)
cosh(5)
escape a particle must have
For a particle with an energy of about 1 TeV, the
E
/T
(4.10)
due to limited
hermeticity is lower than 13 GeV, being then comparable with instrumental
E
/ T.
Beams' crossing angle
Two bunches of protons circulating in the opposite LHC directions do not
z
collide head-on in the
zero angle (α).
direction, but they cross each other with a non-
The latter has been introduced to minimize beam-beam
eects due to the length of the bunches. Each beam has indeed a transverse
size of few microns but spans more than 7 cm in the longitudinal direction;
therefore, if the two beams collided head-on, the interaction region would
have span several centimeters, resulting in many parasitic encounters.
The choice of
produces a
E
/T
α ∼ 285 µrad [49],
bias since the
φ
although reduces the beam-beam eects,
distribution of the energy in the event is no
longer perfectly symmetrical. Projecting an average 5 TeV beam energy in
the transverse plane, we get an upper bound to the
E
/ T caused by the beams'
crossing angle:
E
/ Tα = 2pbeam · sin
α
∼ Ebeam · α ≤ 1.5 GeV .
2
(4.11)
* * *
We conclude that no
E
/ T is produced above few GeV by parton motion and
beams' crossing angle, providing only a small correction to a much bigger
value of
E
/T
due to instrumental noise. The calorimeter limited hermeticity
instead generates a
E
/T
almost comparable with the instrumental
will have to be considered in
pp
E
/ T,
and
collisions.
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4.6 Eect of noisy channels
If the energy deposit uctuations are random and of the same order of magnitude for all the calorimetric cells, the central limit theorem allows us to
consider the
E
/x
and
E
/y
distributions to be Gaussians, resulting in the
E
/ T to
be distributed according to equation 4.2. But even if a single channel is hot,
the
E
/T
distribution changes completely. Great care has to be paid to this
eect, because a hot channel introduces a bias in the energy reconstruction,
simulating a
E
/T
signal, and mimicking the signature of an escaping weakly
interacting particle.
A channel is dened to be hot when its energy output is above a given
energy threshold in more than the 5% of the events.
(a)
Figure 4.3
(a)
(b)
E
/ T distribution computed with HF and HO energy deposits;
distribution as a function of
(b)
E
/T
φ(E
/ T).
A good example of this phenomenon is shown in gure 4.3(a), where a
noisy HCAL channel in the forward region (mean energy of 200 GeV), once
projected in the transverse plane, gives a peak in the
Figure 4.3(b) shows the
at
E
/T
at about 25 GeV.
E
/ T distribution as a function of φ(E
/ T).
The hot area
φ(E
/ T) ∼ 0.8 suggests that the 25 GeV E
/ T hits are generated always in the
same region of the calorimeter, thus being compatible with a noisy channel.
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While the ECAL hot channels are already removed from the reconstruction, HCAL's are not. These channels can be easily identied with a 2D map
in (η, φ) coordinates of the mean energy release. The maps of the HCAL
subdetectors are shown in gure 4.4. We note that the all the channels in
the barrel (HB) and in the endcaps (HE) have a mean energy below 150
MeV. Instead in the hadron outer (HO) there is a single channel with a
mean energy of 12 GeV (gure 4.4(b)).
Moreover in the hadron forward
(HF) we note a channel accounting for almost 200 GeV of average energy
(gure 4.4(c)).
Given that HO and HF are not relevant for the studies with cosmic
rays, we remove them altogether in the
E
/ T vs φ(E
/ T)
E
/T
computation. The new
E
/T
and
distributions are shown in gure 4.5.
4.7 Using Time Information In E/ T Selection
Here we investigate the possibility of using the time information of the ECAL
and HCAL hits
2 to reduce the instrumental
E
/ T by rejecting the calorimetric
noise.
A noise energy deposit occurs at a random time; on the contrary we
assume that the energy of a given physics event is released in few nanoseconds, namely the time for the particles to reach the detector and to interact.
Therefore, if we compute the total energy of an event discarding the calotowers that are not
in time
with the physics process, we throw away most
of the noise deposits. In the introduction we discussed the motivations for
using the muon to obtain a reference time for the event.
We dene the time muon selection criterion for the calo-towers to be :
tmin < tcalotower − tµ < tmax ,
2
(4.12)
A hit is dened to be the set of an energy measurement and a time measurement
due to a deposit in the calorimeter.
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where
tµ
is the time of the muon as described in section 3.7.3,
the time of the calo-towers used in
tmin , tmax
E
/T
tcalotower
is
computation (see section 4.8), and
are to be determined.
Before to apply the selection criterion in equation 4.12 to the
E
/T
compu-
tation, we test it on the calo-towers. That is, we compute the energy and
the time distributions for all the calo-towers in the event, and we estimate
the values of
tmin
and
tmax
that maximize the noise rejection. The analysis
is discussed in section 4.9.
4.8 Time of a calorimetric tower
The ECAL and the HCAL scintillation signals are detected and amplied by
photodetectors. The photodetector generate an electrical signal output amplied and digitized by ADCs, where the digitizations consist in a sequence
of samplings of the signal at 40 MHz (one sample each bunch crossing).
When a trigger res, the data acquisition system keeps a buer of ten ADC
count values spaced by 25 ns for each crystal (tower) of ECAL (HCAL).
The set of values in the buer give the time development of the signal pulse,
called the pulse shape, from which we can extract both the pedestal and
the peak of the energy release (see gure 4.6). For the sake of completeness
we note that the ECAL electronics actually samples the signal, while the
HCAL electronics integrates the pulse shape over each 25 ns window.
In collision data taking, both the ECAL and the HCAL will use a digital
ltering technique (the
weight method
[51]) to reconstruct amplitude and
time of the deposit from the digitized samples.
amplitude
With this algorithm the
A is computed from a linear combination of discrete time samples:
A=
N
X
wi × S i
(4.13)
i=0
where
wi
are the weights,
Si
the time sample values in ADC counts and
N
is the number of samples used in the ltering. Requiring that the estimator
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4.8 Time of a calorimetric tower
of the amplitude be not just proportional, but equal to the amplitude (i.e.
E[A] = A),
implies that
PN
i=0 wi
× fi = 1,
where
fi = f (t = ti )
and
f (t)
is
a function which corresponds to the time development of the signal pulse,
normalized to have an amplitude of 1. The function
f
that best represents
the electronic signal is a digital representation (prole histogram) directly
built from the test beam data (see gure 4.6). The weights are then extracted
by minimizing the
χ2 ,
and the time reconstruction of the energy deposit is
directly given by the amplitude measurement.
The method is fast and robust, but relies on the precise knowledge of
the collision time. It is indeed fundamental to know how long the pedestal
will last and at what sample the peak will occur in order to apply the right
weight to the right sample. Of course this is not possible during cosmic runs
as muons are distributed at in time. Due to this issue, the ECAL chose to
switch to the
analytic t method,
consisting in tting the samples with the
function
f (t) = A
t − tof f
tpeak
α
(t − tof f ) − tpeak
· exp −α
tpeak
,
(4.14)
where tpeak is the time corresponding to the maximum of the pulse, and tof f
accounts for the samples recorded before the start of the signal, giving a time
oset between the start of the pulse and the rst sample. The independence
from a xed
t0
represents the big improvement with respect to the weight
method in cosmic runs. But this algorithm has also a drawback: to make
the t converge it is necessary a minimum energy deposit in the crystal,
otherwise all the bins will contain just pedestal energy and the hypothetical
shape in equation 4.14 will not describe the actual shape. The price to pay
is therefore to introduce an energy threshold.
Since the ECAL read-out is zero suppressed, the ECAL energy deposits
forming the pulse shape already passed an energy selection. Thus the ECAL
time computed with the t method turns out to be quite accurate, showing
a peaked distribution with a mean value of about 5 ns and an RMS of about
10 ns (see gure 4.7).
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On the other side, the HCAL chose to use the weight method even with
cosmics, although we already showed that it is not an optimal solution. Since
there is no collision time dening a
the following choice for
shape,
t0
t0 :
t0
for the pulse shape, the HCAL made
given the rst two non-zero samples of the pulse
is dened to be the time whereby the second sample begins to ex-
ceed the rst in amplitude. With such t0 denition, the weight method performs a rst order time reconstruction that calculates an amplitude-weighted
peak sample as follows:
W eighted peak sample =
(k − 1)A[k − 1] + kA[k] + (k + 1)A[k + 1]
,
A[k − 1] + A[k] + A[k + 1]
(4.15)
where
A[i]
represents the amplitude of the time sample
i,
and
k
repre-
sents the number of the time sample that contains the peak amplitude
within the window of samples.
Normalizing the
weighted peak sample
the range of possible peak values, accounting for the
t0
to
oset, and sub-
sequently multiplying by the time sample width (25 ns) yields a linear
approximation (t` ) to the time of the hit within the peak sample:
(25 ns) × N orm(Weighted
t` =
peak bin).
Since the HCAL read-out is not zero suppressed, each time that the noise
uctuations give two consecutive energy deposits the second rising with
respect to the rst we get a
t0 .
Such a
t0
is completely random, because
it reects the random nature of the noise. As a consequence, the formula in
equation 4.15 results in the HCAL time to be spread in a range wider than
200 ns (see gure 4.8).
The lack of zero suppression is also responsible for the 25 ns spaced peaks
in gure 4.8. If the energy deposits are too small, the linear approximation in
equation 4.15 trivially gives the time of the middle sample (k in the equation
4.15). Therefore all the low energy HCAL hits (i.e. the majority of the hits)
have no ne structure time inside the 25 ns window, and they are displaced
at the beginning of the bunch crossing.
So far it seems that introducing an energy threshold in the HCAL tower
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4.9 Time selection criterion using muons
selection (equivalent to the zero suppression) would improve the quality of
the HCAL time hits, resulting in a less wide time distribution. Therefore
one might think that a time selection is no longer required after an energy
selection. But gure 4.9 shows that even the time distribution of the towers
with
E > 1.5
GeV has a width of several bunch crossings.
Finally we need the time of the calo-tower.
A calo-tower stores time
information separately for the HCAL and the ECAL, but has even its own
time calculated by energy weighting of the times stored in ECAL and HCAL
hits.
Since a muon releases much more energy in the HCAL than in the
ECAL, the calo-tower time is dominated by the HCAL time.
4.9 Time selection criterion using muons
The eectiveness of a time selection criterion strongly depends on the considered time window. To nd the values of tmin and tmax (see equation 4.12)
that maximize the noise rejection, we should perform an analysis of the calotower time distribution. However at the end of section 4.8 we showed that
the calo-tower time is dominated by the HCAL time, hence it is sucient
to consider the time information of the HCAL hits.
Since the selection criterion is based on the muon time, we investigate the
quantity (tcalotower
quality muon.
− tµ )
using only the HCAL hits matched with an high
In section 4.9.1 the matching is discussed, i.e.
the use of
the muon track to identify which HCAL towers have been crossed, while
the muon requirements are described in section 4.9.2.
The time window
boundaries are determined in section 4.9.3, and we conclude showing the
application of the time selection criterion to the
E
/T
computation in section
4.9.4.
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4.9.1 Muon signal in the calorimeters
The muon system and the inner tracker allow the reconstruction of the
muon track for all its path length inside the detector.
Starting from the
track, we can extrapolate the points of intersection with the calorimeters'
surfaces.
The ECAL crystal and HCAL tower crossed by the muon track
are considered to be matched with the muon. But for at least two reasons
the muon energy deposit is not contained in a single crystal or tower. First,
because a cosmic muon takes several
side, or several
η
φ
values if crosses the detector on the
values if it is not exactly heading for the interaction point.
Second, because of bremsstrahlung photons (emitted by the muon) that
could cross the single cell
we read a
5×5
3 borders. To consider this nearby energy releases,
matrix of crystals in ECAL (towers in HCAL) surrounding
the crossed one (see gure 4.10).
The energy distribution inside the
5×5
is shown in gure 4.11.
On
average, the central cell holds the majority of the energy, and those more
external are almost empty.
However, in some
5×5
matrices the largest
energy deposit is not owned by the crystal/tower crossed by the track (i.e.
the central cell), and we ascribe this eect to the matching algorithm. Indeed
if the track passes through several cells, only the rst one is said to be
crossed by the muon. Therefore if the muon path in the other cells is longer
than in the rst one, the largest energy deposit is released in one of the
neighbours.
Since an ECAL crystal has a cross-section of approximately
∆η × ∆φ = 0.0174 × 0.0174
and it is 23 cm tall, the probability that a
cosmic muon crosses more than a single crystal is high. It is sucient an
angle of incidence on the crystal face greater than
The same is true for an HCAL tower, having a
5◦
to make it happen.
∆η × ∆φ = 0.087 × 0.087
cross-section, and being 1 m tall. In this case the angle of incidence has to
be greater than
3
6◦ .
To avoid such a wrong choice of the leading cell, we
Here we use cell to refer both to an ECAL crystal and to an HCAL tower.
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select the maximum energy crystal (tower) inside the
5×5
matrix to be the
one most correlated with the muon.
Given the
5×5 matrices due to all the muons crossing the detector, we can
distinguish the calorimetric hits in two separate samples: the rst composed
by the maximum energy hit of each
the hits that are outside each
the latter
background
5 × 5.
5 × 5,
and the second composed by all
We call the former
signal
sample, and
sample.
4.9.2 Muon requirements
Since we have a large amount of cosmic data, we choose to perform a very
tight selection on the muon features in order to have a very clean sample at
the expense of loosing eciency (requirements are summarized in table 4.2).
Usually there are up to ten reconstructed muons for each event, and our
rst selection is to keep only those events having two global muons, i.e.
two
legs
of the same physical muon. This is to avoid ambiguities both in
the matching with the calorimetric deposits and in the choice of the event
reference time. About the matching, for example, if there are three legs in
the detector, it is not trivial to understand the event topology: there could
be two muons, one entering and then leaving the detector, and a second one
entering and being stopped in the calorimeters; but the same three legs are
compatible with a single muon, where one leg is reconstructed as a pair.
About the time, we already discussed that we need the muon time to have
a valid benchmark with respect to dene a time selection. But if we have
more than one muon, we do not know which one to use as a reference time.
The top leg of the muon has to be detected before the bottom leg, thus
accounting for a downwards muon.
This condition allows us to compute
dierent time distributions for the legs crossing the top part and the bottom
part of the calorimeters, and to make a time of ight measurement.
condition is obtained constraining the
(yin ) to be in the muon system (yin
y
The
component of top leg inner position
> 200 cm),
and the outer to be in the
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Selection Criteria
Variable
Threshold
Comment
To perform a top/bottom study
nMuons
=
2
pT (µ)
>
10 GeV
DT top sectors
=
3, 4, 5, 13
DT bottom sectors
=
9, 10, 11, 14
top muon inner
y
position
>
200 cm
top muon outer
y
position
<
200 cm
bottom muon inner
y
position
>
-200 cm
bottom muon outer position
<
-200 cm
max EHCAL
i
i∈5×5
max EECAL
j
>
1.5 GeV
>
120 MeV
d0
<
30 cm
dz
<
30 cm
j∈5×5
Side sectors have low statistics:
cannot perform t correction
Selecting downwards muons
(±200 cm are approximately
tracker boundaries )
Muon passing near the
interaction point
Selection criteria to have a very pure muon sample to perform a sig-
Table 4.2
nal/noise study in the calorimeters.
tracker (yout
< 200 cm).
Analogously, for the bottom leg we ask the inner
position to be in the tracker and the outer to be in the muon system.
The muon must have a valid time, that is the t procedure discussed in
section 3.7.3 must have converged. Moreover we want to correct the muon
time on a sector basis, hence we keep only the muons passing through the
sectors located in the top and in the bottom part of the experiment. Those
sectors are the most populated and a large statics allows us to perform a t
based correction (see section 3.8.2).
Since
tµ
is extrapolated at the interaction point, we also ask the track's
point of closest approach to be not very distant from interaction point; we
impose
d0 < 30
cm and
dz < 30
cm.
We require the muon to be hard, i.e.
to have
pT > 10
GeV. This is
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to prevent the muon to be stopped in the detector, as well as to avoid an
excessive bending in the magnetic eld. In the latter hypothesis, the muon
would escape from the side of the detector passing through an excluded
sector.
Finally, we want the muon to release in the calorimeters enough energy
to be not confused with a noise uctuation. Therefore we ask the maximum
energy tower in the HCAL
5×5
to have
E > 1.5
GeV, and the maximum
energy crystal in the ECAL
5×5
to have
E > 120
MeV. The ECAL energy
threshold has been chosen to be
3σ
above the mean energy level, whereas
the HCAL energy threshold has been tuned also to improve the HCAL time
reconstruction. This because the HCAL time reconstruction is weaker than
the ECAL's, as discussed in section 4.8, and needs to be improved.
Figure 4.12 shows the time distribution of all the maximum energy HCAL
towers (white histogram).
Though the two central bunch crossings are
favoured, still there is a relevant number of hits spread all over the 200
ns range. Moreover we note the spikes at
t = −10
ns and
t = 15
ns typical
of the weight method failure (in section 4.8 we described that the spikes
occur when there is not enough energy to properly reconstruct HCAL time).
In order to understand what is the minimum energy to have a valid time, we
select all those towers with
t = −10 ns or t = 15 and we compute the energy
distribution shown in gure 4.13 (shaded histogram). The same gure shows
the energy distribution of all the HCAL towers (white histogram). We note
that if we introduce a 1.5 GeV threshold, we throw away the majority of the
towers with unreconstructed time, but at the same time we save a signicant
fraction of the total sample. The HCAL time distribution of the maximum
energy towers satisfying
E > 1.5
GeV is the shaded histogram shown in
gure 4.12.
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4.9.3 Optimization of the time window
The aim of the time window optimization is to separate the signal and the
background samples only with the time information. Since the HCAL time
has to be referred to the muon time, in the following we consider the quantity
tHCAL − tµ ,
where
tHCAL
is the HCAL time (see section 4.8) and
muon time at the interaction point (see 3.7.3).
tcalotower
We use
tHCAL
tµ
in the
instead of
since we know that the time of a calo-tower is mainly due to the
HCAL time.
|tHCAL − tµ | <
In principle the selection criterion could be symmetrical:
threshold.
To verify if it is possible, we make a time distribution of the
signal HCAL hits matched with a top leg muon (tHCAL (top leg)), and of
the hits matched with a bottom leg muon (tHCAL (bottom leg)). The gure
4.14 shows
tHCAL (top leg)
distribution (vertical lines) and
tHCAL (bottom leg)
distribution (horizontal lines), and the latter is properly peaked after the
former. Since the muon is downwards the two peaks are about 20 ns distant,
consistently with the time of ight of a cosmic muon into the HCAL. Indeed
the HCAL external radius is about 3 m, and a cosmic ray travels almost
at the speed of light.
Therefore a rough calculation gives
(600 cm) / (30 cm · ns−1 )
∆Ttop−bottom ∼
∼ 20 ns, and this value actually reects the spacing
between the two distributions. But. However we note that the peaks are not
displaced at the same distance from zero: the mean value of
is zero, whereas the mean value of
tHCAL (bottom leg)
tHCAL (top leg)
is about 20 ns.
We
conclude that the time window cannot be symmetrical and we have to nd
dierent values for
tmin
and
tmax .
Figure 4.14 also shows that the HCAL time hits belonging to the signal
sample, once referred to the muon time, span a range between -25 ns and
+45 ns. To understand the outcome that this time window would have in the
noise rejection, we study the distribution of (tHCAL −tµ ) using the background
sample (i.e. the HCAL hits outside the
5 × 5).
Since the HCAL is not zero
suppressed, the background sample is composed by more than 3000 towers
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per event, although just few of them have a relevant amount of energy. Our
rst choice is to apply to the background sample the same energy threshold
used in the signal sample (Ehit
> 1.5
GeV). The distribution of the selected
hits is shown in gure 4.14 with the solid dark histogram, and it's clearly
visible that we have very few hits satisfying the constraint. However the 1.5
GeV threshold was tuned to have a very clean signal sample and it is not
related with the selection of the hits entering in the
then misleading to suppose that the instrumental
E
/T
E
/T
computation. It's
is merely given by the
background hits obtained with this selection.
A more realistic estimation of the noise contributing to the instrumental
E
/T
requires the relaxation of some selection criteria:
•
nMuons ) in the event can be dierent from two.
the number of muons (
It follows that we can no longer dene a top leg and a bottom leg of
the same muon to perform a time of ight measurement. Moreover we
have to deal with the time ambiguity (i.e. which muon represents the
time reference), hence we consider the rst reconstructed muon in the
event to be the benchmark.
•
An HCAL hit and an ECAL hit are no longer required to occur in the
same
•
η -φ
region to enter in the background sample.
We introduce a new HCAL energy threshold at 0.5 GeV. We call the
latter the loose energy selection, and we call the 1.5 GeV threshold
the tight selection. The value of 0.5 GeV is more realistic because it
is the same threshold applied to the calo-tower energy during the
E
/T
reconstruction.
Special attention has to be paid in relaxing the selection on
nMuons
nMuons.
If
is an odd number, it is unlikely we really have a muon entering
but not leaving the detector, as the calorimeter stopping power for cosmic
muons is really low.
More probably there is a muon crossing the whole
detector, but the reconstruction succeeds in tting just one leg out of the
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total track (see gure 4.15). Therefore when the muon passes through the
HCAL gives a hit in time with
sample since it is outside the
tµ ;
but this hit enters into the background
5×5
matrix surrounding the reconstructed
leg. The result is that a set of events belonging to the signal sample goes
into the background sample, thus lowering the signal/background ratio. To
perform a more trustworthy study we select only events with an even number
of muons.
The gures 4.16 and 4.17 show the outcome of the new selection criteria,
respectively for the tight and the loose energy selection. In both the gures,
the hashed histogram is the distribution of (tHCAL −tµ ) for the signal sample.
Since there is no distinction between the time of a top or a bottom leg, the
two peaked distribution in gure 4.14 are now added to form a wider shape.
Notwithstanding, the majority of the signal sample appears to be in the
range (-15,+35) ns. In the same two gures, the solid histogram is the distribution of the background sample. We note that even with a tight energy
selection (gure 4.16) it is not possible to remove all the noise hits. However,
many of them can still be discarded with a time selection, reducing noticeably the noise hits entering in the instrumental
E
/T
computation. Moreover
if we consider the more realistic loose energy selection (gure 4.17), we note
that a time selection allows to reject a huge quantity of noise deposits.
Finally we set the the thresholds in equation 4.12 as follows:
tmin = −15 ns
(4.16)
tmax = 35 ns .
(4.17)
4.9.4 Time selection applied to E/ T computation
The time selection criterion discussed in the previous section can be employed to lter the calorimetric hits entering in the
a
E
/T
E
/T
computation. Such
is expected to be much less aected by the noise, and we call it
ltered E
/ T.
time
Since the selection concerns the calo-towers, the time ltered
E
/T
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has to be reconstructed for each event, and the reconstruction takes place
in four steps:
1. the energy hits coming both from the ECAL and the HCAL are selected on the basis of scheme B thresholds;
2. the calo-towers merging HCAL and ECAL energies are built, applying
a further 0.5 GeV threshold on the whole calo-tower energy;
3. a time lter holds only the calo-towers in time with the muon, i.e.
those satisfying (−15
4. the
E
/x
and the
E
/y
gies weighted with
< tcalotower − tµ < 35)
are computed with the sum of the calo-tower ener-
(sinθ cosφ)
sing transverse energy is the
The time ltered
ns;
(sinθ sinφ) respectively;
p
/x 2 + E
/y 2.
obtained as E
/T = E
and
E
/ T distribution is shown in gure 4.18.
the mis-
We note that the
tail is signicantly suppressed, and that the mean value is lower than 1 GeV.
The rst bin is empty because of the 0.5 GeV energy threshold in the calotower building. Moreover we remove from the distribution all those events
where there are no calo-towers left after the selection criterion. Indeed in
these events the
E
/T
is zero because there is no energy left.
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(a)
(b)
(c)
Figure 4.4
HCAL (η
-φ
) map of the mean energy deposits for the dierent subde-
tectors: a) HCAL barrel and endcaps (HB, HE); b) HCAL outer (HO);
c) HCAL forward (HF).
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4.9 Time selection criterion using muons
(a)
Figure 4.5
(a)
E
/T
distribution computed without both HF and HO; (b)
bution as a function of
Figure 4.6
(b)
E
/T
distri-
φ(E
/ T).
ECAL pulse shape. Dots represent 10 samples corresponding to a 10
GeV deposit. Solid line is the function
f (t)
which corresponds to the
time development of the signal pulse. Amplitude, pedestal and time of
the energy deposit are indicated. [50]
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Figure 4.7
Figure 4.8
ECAL time distribution.
Time distribution of all the HCAL towers.
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4.9 Time selection criterion using muons
Figure 4.9
Figure 4.10
Time distribution of HCAL towers with energy above 1.5 GeV.
Matrix of crystals in ECAL (towers in HCAL) surrounding the one
crossed by the muon.
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Missing Energy Measurement
(a)
Figure 4.11
(a) HCAL energy distribution of all the
(b)
5×5
matrices of towers sur-
rounding the muon tracks. (b) ECAL energy distribution of all the
5×5
Figure 4.12
matrices of crystals surrounding the muon tracks.
Time distribution of the most energetic HCAL hit in the
selection
E > 1.5
5×5.
Energy
sample (shaded histogram) is composed by the hits with
GeV.
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4.9 Time selection criterion using muons
Figure 4.13
Energy distribution of the HCAL hits.
Time selection sample (shaded
histogram) is composed by the hits with
Figure 4.14
Distribution of
tHCAL − tµ .
t = −10 ns or t = 15 ns GeV.
Shaded histograms are composed by the
signal sample hits matched with a muon. Solid histogram is composed
by the background sample.
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Figure 4.15
A cosmic muon crossing HCAL, where only one leg out of two is
reconstructed.
Figure 4.16
Distribution of the HCAL time with respect to the muon time. Tight
energy selection:
E > 1.5
GeV.
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4.9 Time selection criterion using muons
Figure 4.17
Distribution of the HCAL time with respect to the muon time. Loose
energy selection:
E > 0.5
GeV.
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Figure 4.18
Time ltered
E
/T
distribution
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CHAPTER 5
Conclusions
In the Autumn 2008 the CMS detector collected about 300 million cosmic
muon events with a nominal magnetic eld of B=3.8 T inside the solenoid.
A sample of 4 million muons is selected to pass through the inner tracker,
therefore crossing all the subdetectors. For such a sample, the inner tracker
provides a precise measurement of the muon
pT
and the muon system is
responsible for the muon time measurement; the two subdetectors together
are responsible for the reconstruction of the whole muon track. Since the
muon energy deposits in the calorimeters are small and well localized (most
of the muons behave as minimum ionizing particles), these particles can be
used to study the calorimetric response.
In this dissertation we perform a data driven study of the calorimetric
noise with cosmic muons, and we investigate the use of the time information to reject the noise energy deposits aecting the
E
/T
computation. The
calorimetric noise rejection is indeed one of the main theme in the comprehension of the
E
/ T tails and therefore in the commissioning of supersymmetry
searches.
We perform a data driven study based on cosmic ray data because of
several reasons:
•
a data driven description of the noise improves as long as the statistics
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Conclusions
grows, hence a data driven method for rejecting the noise improves
with the time;
•
it is very dicult to fully simulate a complex detector as CMS, and it
is better to use data instead of Monte Carlo simulations whenever it
is possible; to work with real data implies even to learn how to deal
with problem like dead/hot channel and imperfect calibrations;
•
the muons produce no real
E
/ T in the event,
therefore the measured
E
/T
is fully instrumental;
•
to dene a time selection we need a benchmark, and the muon time
can provide a reference time for the event.
The time method rejects the calorimetric noise by discarding from the
E
/T
computation all those energy deposits that are out of time with respect to
the muon time (tµ ). We dene
tcalotower
to be the time of a calo-tower, and
we consider an energy deposit to be in time with a muon if
(−15 = tmin < tcalotower − tµ < tmax = 35) ns .
To nd
tmin
and
tmax
(5.1)
values we use a subset of the muon sample on which
we require a very tight selection on muon features. Such a selection is necessary to be sure that the cosmics cross both the ECAL and the HCAL,
and have a valid time reconstructed in all the crossed subdetectors. A geometrical matching between the track and the calorimetric deposit position
allows us to distinguish between energy hits due to the muon and noise oveructuations. The correct time window is then determined by looking at the
time information of matched and unmatched hits.
The time selection succeeds in ltering most of the noise, and the
E
/T
computed with the in time energy deposits shows a mean value lower than
1 GeV. We note that the tails are very suppressed and the instrumental
E
/T
has been signicantly reduced.
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Conclusions
Figure 5.1
Missing transverse energy distribution. White: calo-tower based
shaded: time ltered calo-tower
E
/T ;
E
/ T.
Figure 5.1 shows the comparison between the instrumental
E
/T
computed
with scheme B energy thresholds (white histogram), and the instrumental
E
/T
computed with a further selection based on the time method (dashed
histogram).
We note that the latter distribution has a mode value lower
than 1 GeV, and the tails are signicantly reduced.
We conclude that the time information remarkably improves the noise
rejection in
E
/T
computation. Though we did not study the
detail, the signicant reduction of the instrumental
much more sensitive to new sources of
thus maximizing the
E
/T
signicance.
E
/ T,
E
/T
E
/T
resolution in
makes the detector
like supersymmetric particles,
Moreover a technique based on the
time selection of the energy deposits can be very useful in the
events.
pp
collision
In that case, the cosmic muons as well as the beam halo events
represent the noise to be rejected. Both of them are not synchronized with
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Conclusions
the LHC clock, hence we can use the time information to identify those
particles not being produced in the collision.
Figure 5.2
ATLAS
E
/T
distribution. [52]
Finally, since even the ATLAS experiment investigates the
E
/ T distribution
in cosmic muon events, we can try to make a comparison with the results
obtained in this dissertation. The ATLAS hadronic calorimeter is a sampling
tile calorimeter with a resolution of
√
σ(E)/E ∼ 46%/ E
[16], about two
times better than the CMS HCAL (cf. section 2.6). Figure 5.2 shows the
raw
E
/T
E
/ T distribution (red circles) detected by with ATLAS, and the improved
computed with the
topocluster 4/2/0
algorithm (blue squares) [16]. We
note that after 8 GeV the tail of the improved
suppressed, rejecting the noise with a factor
raw
E
/T
distribution (red circles) and the
time selection.
E
/T
E
/ T distribution
103 .
is completely
Figure 5.3 shows the CMS
distribution obtained with the
We note that we reach the same order of magnitude in
3 )), but our method allows to suppress the tail of
rejecting the noise (O(10
the distribution already at 5 GeV. Although we do not have enough statistics
to make a more quantitative comparison, we note that at 10 GeV the ATLAS
raw
E
/T
is one order of magnitude lower than the the peak value, while the
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Conclusions
CMS
E
/T
is still increasing.
Therefore the CMS time ltered
E
/T
and the
ATLAS topocluster behave in a similar way even if the CMS noise is larger.
For this reason the suppression of the calorimetric noise reached with the
time selection criterion can be considered a great success.
Figure 5.3
CMS
E
/T
distribution.
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Conclusions
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i
i
Bibliography
[1]
ALEPH, DELPHI, L3 and OPAL Collaboration. LEP Electroweak Working Group,
Precision electroweak measurements and constraints on the standard
model,
arXiv:0712.0929v2 [hep-ex], December 2007.
[2] D. Bryman, Rare kaon decays,
International Journal of Modern
Physics A, vol. 4, p. 79, January 1989.
[3] G. D'Ambrosio, G. Ecker, and G. Isidori, Radiative non-leptonic decays, in
The DAΦNE Physics Handbook (second edition), vol. 1, Fras-
cati: eds. L. Maiani, G. Pancheri and N. Paver, 1995.
[4] C. K. et al., Final results from phase ii of the mainz neutrino mass
searchin tritium
β
decay,
European Physical Journal C, vol. 40, p. 447,
April 2005.
[5] M. S. et al. (Super-Kamiokande Collaboration), Search for proton decay via
p → e+ π 0
in a large water cherenkov detector,
Physical Review
Letters, vol. 81, pp. 3319 3323, 1998.
[6] Q. R. A. et al. (SNO Collaboration), Measurement of the Rate of
νe + d → p + p + e−
Interactions Produced by
8 B Solar Neutrinos at
97
i
i
i
i
i
i
tesi_grassi 2009/11/16 0:48 page 98 #105
i
i
Bibliography
the Sudbury Neutrino Observatory,
Physical Review Letters,
vol. 87,
p. 071301, 2001.
[7] L. Susskind, The gauge hierarchy problem, technicolor, supersymmetry, and all that,
Physics Reports, vol. 104, pp. 181 193, 1984.
[8] G. Jungman, M. Kamionkowski, and K. Griest, Supersymmetric dark
matter,
[9] G.
Physics Reports, vol. 267, p. 195, 1996.
Amelino-Camelia,
Notes
from
the
The
Quantum
Quantum-Gravity
Gravity
course,
Problem.
available
at
http://www.roma1.infn.it/%7Eamelino/appunti1.pdf, 2009.
[10] M. Peskin and D. Schroeder,
An Introduction o Quantum Field Theory.
Westview Press, 1995.
[11] J. E. et al., Supersymmetric relics from the big bang,
Nuclear Physics
B, vol. 238, no. 2, pp. 453 476, 1984.
[12] A. R. Liddle and D. H. Lyth, The cold dark matter density perturbation,
Physics Reports, vol. 231, no. 1-2, pp. 1 105, 1993.
[13] M. Kamionkowski and D. Spergel, Large-angle cosmic microwave background anisotropies in an open universe,
The Astrophysical Journal,
vol. 432, p. 1, 1994.
[14] T. Walker, G. Steigman, H. Kang, and D. S. K. Olive, Primordial
nucleosynthesis redux,
The Astrophysical Journal, vol. 376, p. 51, 1991.
[15] S. Tremaine and J. E. Gunn, Dynamical role of light neutral leptons in
cosmology,
[16]
Physical Review Letters, vol. 42, no. 6, pp. 407410, 1979.
ATLAS Collaboration,
Atlas: technical proposal for a general-purpose
pp experiment at the large hadron collider at cern,
43.
CERN-LHCC-94-
http://cdsweb.cern.ch/record/290968.
98
i
i
i
i
i
i
tesi_grassi 2009/11/16 0:48 page 99 #106
i
i
Bibliography
[17]
LHCb Collaboration,
CERN-LHCC-98-004.
Lhcb technical proposal,
http://cdsweb.cern.ch/record/622031.
[18]
TOTEM Collaboration,
Total cross section,
elastic scattering and
diractive dissociation at the lhc: Technical proposal,
99-007.
[19]
http://cdsweb.cern.ch/record/385483.
ALICE Collaboration,
ion
CERN-LHCC-
collider
Alice:
experiment
at
Technical
the
cern
proposal
lhc,
for
a
large
CERN-LHCC-95-7.
http://cdsweb.cern.ch/record/293391.
[20]
The CMS Collaboration,
CMS Physics Technical Design Report Vol-
ume II: Physics Performance,
[21]
The CMS Collaboration,
Design Report,
CERN/LHCC-06-021, p. 1023, 2006.
CMS TDR 3: The Muon Project Technical
CERN/LHCC-97-032, 1997.
[22] P. Giacomelli, The CMS muon detector,
Nuclear Instruments and
Methods in Physics Research A, pp. 147 152, 2002.
[23]
The CMS Collaboration,
Design Report,
[24]
The Electromagnetic Calorimeter Technical
CERN/LHCC-97-033, 1997.
M. Huhtinen et al.,
High-energy proton induced damage in pbwo4
calorimeter crystals,
Nuclear Instruments and Methods in Physics Re-
search A, pp. 6387, 2005.
[25]
The CMS Collaboration,
Report,
[26]
The Hadron Calorimeter Technical Design
CERN/LHCC-97-031, 1997.
M.G. Albrow et al.,
bre readout,
A uranium scintillator calorimeter with plastic-
Nuclear Instruments and Methods in Physics Research
A, 1987.
99
i
i
i
i
i
i
tesi_grassi 2009/11/16 0:48 page 100 #107
i
i
Bibliography
[27]
V.I. Kryshkin et al.,
calorimeters,
An
optical
fiber
readout
for
scintillator
Nuclear Instruments and Methods in Physics Research
A, 1986.
[28]
G.W. Foster et al.,
at fnal,
[29]
Scintillating tile/fiber calorimetry development
Nuclear Physics Proceedings Supplements B, 1991.
L. Borrello et al., Sensor design for the cms silicon strip tracker, CMS
Note 2003-020.
[30]
J.C. Mc Lennan, E.F. Burton,
Some experiments on the electrical con-
ductivity of atmospheric air,
Physical Review, pp. 814 192, 1903.
[31] A. Glokel, Observation of atmospheric electricity from a balloon,
Physikalische Zeitschrift, vol. 11, pp. 280282, 1910.
[32] V. Hess, Measurement of the earth's penetrating radiation on a balloon,
[33] W.
Physikalische Zeitschrift, vol. 12, p. 998, 1911.
Kolhorster,
Penetrating
atmospheric
radiation,
Physikalische
Zeitschrift, vol. 14, pp. 10661069, 1913.
[34] Millikan and Cameron, High frequency rays of cosmic origin, iii. measurement in snowfed lakes at high altitude,
Physical Review,
p. 855,
1926.
[35]
C.Amsleretal.,
Particle physics booklet,
Physics Letters B667, vol. 1,
2008.
[36] T. Shibata, Cosmic-ray spectrum and composition; direct observation,
Nuovo Cimento C, p. 713, 1996.
[37]
D.J. Bird et al.,
eye,
The cosmic-ray energy spectrum observed by the y's
Astrophysical Journal, pp. 491502, 1994.
[38] V.Berezinsky,
A.Z.Gazizov,
and S.I.Grigorieva
Physical Review D,
vol. D74, p. 043005, 2006.
100
i
i
i
i
i
i
tesi_grassi 2009/11/16 0:48 page 101 #108
i
i
Bibliography
[39]
M.P.DePascaleetal. Journal Of Geophysical Research,
p. 3501, 1993.
[40] D. Groom, N. Mokhov, and S. Striganov, Muon stopping power and
range tables 10MeV - 100TeV,
Atomic Data and Nuclear Data Tables,
vol. 78, no. 2, 2001.
[41]
P.H. Barrett et al. Reviews of Modern Physics,
[42]
P.N. Bath, P.V. Ramana Marthy,
vol. 24, p. 133, 1952.
Intensity measurement of low en-
ergy cosmic ray muons underground,
Journal of Physics A, 1973.
[43] R. Kalman, A new approach to linear ltering and prediction problems,
Journal of Basic Engineering, vol. 82, no. 1, 1960.
[44] R. Fr
[45]
C. Liu et al.,
Reconstruction of cosmic and beam-halo muons with the
European Physical Journal C, pp. 449 460, 2008.
cms detector,
[46] P. Traczyk, Muon Timing in the reco::Muon object,
Muon POG meet-
ing, November 2008.
[47] S. E. et al., Missing Energy Performace in CMS,
Cms Analysis Note,
vol. CMS AN-2007/041, January 2008.
[48] R. Wigmans,
Calorimetry. Energy Measurement in Particle Physics.
Oxford: Clarendon Press, 2000.
[49] L. Evans and P. Bryant, LHC Machine,
Journal of Instrumentation,
vol. 3, 2008.
[50] R. Bruneliére,
Cms electromagnetic calorimeter performance and
Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated
Equipment, vol. 572, no. 1, 2007.
test beam results,
101
i
i
i
i
i
i
tesi_grassi 2009/11/16 0:48 page 102 #109
i
i
Bibliography
[51] R. Bruneliére and A. Zabi, Reconstruction of the signal amplitude of
the CMS electromagnetic calorimeter,
Cms Analysis Note,
vol. CMS
AN-2006/037, February 2006.
[52]
ATLAS Collaboration,
E
/ T performance.
https://twiki.cern.ch/
twiki/bin/view/Atlas/ApprovedNoisePlotsJetEtMiss,
April 2009.
102
i
i
i
i
i
i
tesi_grassi 2009/11/16 0:48 page 103 #110
i
i
i
i
i
i
i
i
tesi_grassi 2009/11/16 0:48 page 104 #111
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Che potea io ridir, se non Io vegno?
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