The latest and greatest tricks in
studying missing energy events
Konstantin Matchev
With: M. Burns, P. Konar, K. Kong, F. Moortgat, L. Pape, M. Park
arXiv:0808.2472 [hep-ph], arXiv:0810.5576 [hep-ph],
arXiv:0812.1042 [hep-ph], arXiv:0903.4371 [hep-ph],
arXiv:0906.2417 [hep-ph], arXiv:090?.???? [hep-ph]
Fermilab, LPC
August 10-14, 2009
1
These slides cover:
• “A general method for model-independent measurements of
particle spins, couplings and mixing angles in cascade decays
with missing energy at hadron colliders”, JHEP (2008)
67 pp
– Burns, Kong, KM, Park
• “Using subsystem MT2 for complete mass determinations in decay 46 pp
chains with missing energy at hadron colliders”, JHEP (2009)
– Burns, Kong, KM, Park
• “s1/2min – a global inclusive variable for determining the mass scale
of new physics in events with missing energy at hadron colliders”, 32 pp
JHEP (2009).
– Konar, Kong, KM
• “Using kinematic boundary lines for particle mass measurements
and disambiguation in SUSY-like events with missing energy”,
JHEP (2009)
47 pp
– Burns, KM, Park
• “Precise reconstruction of sparticle masses without ambiguities”,
JHEP (200?)
37 pp
– KM, Moortgat, Pape, Park
Total No of pages : 229 pp
2
MET events: experimentalist’s view
This is why I am
interested in MET!
• What is going on here?
3
Why MET signatures are
important to study
• WIMP dark matter? Perhaps, but see J. Feng’s
talk for counterexamples.
• Challenging – need to understand the detector
very well.
• Guaranteed physics in the early LHC (late
Tevatron) data!
e
b
e
t
W
n
t
W
n
b
e
W
n
W
n
e
4
This talk is being given
• by a “theorist”
The experimentalist asks:
The theorist answers:
Is it possible to have a theory
model which gives signature X?
Yes.
No.
Are there any well motivated
such models?
Is there any Monte Carlo which
can simulate those models?
You bet. Let me tell you about
those. Actually I have a paper…
No. But I’m the wrong person to
ask anyway.
MC4BSM workshops: http://theory.fnal.gov/mc4bsm/
5
MET events: theorist’s view
• Pair production of new particles (conserved R, KK, T parity)
• Motivated by dark matter + SUSY, UED, LHT
– How do you tell the difference? (Cheng, KM, Schmaltz 2002)
• SM particles xi seen in the detector, originate from two chains
– How well can I identify the two chains? Should I even try?
• What about ISR jets versus jets from particle decays?
• “WIMPs” X0 are invisible, momenta unknown, except pT sum
– How well can I reconstruct the WIMP momenta? Should I even try?
• What about SM neutrinos among the xi’s?
6
In place of a summary
optimism
pessimism
Missing
momenta
reconstruction?
None
Mass measurements
Inclusive
Spin
measurements
2 symmetric
chains
Inv. mass endpoints
and boundary lines
Inv. mass
shapes
Meff,Mest,HT
Wedgebox
Approximate
Smin, MTgen
MT2, M2C, M3C,
MCT, MT2(n,p,c)
As usual
(MAOS)
Exact
?
Polynomial
method
As usual
pessimism
optimism
7
Tuesday: invariant mass studies
Hinchliffe et al. 1997
ATLAS TDR 1999
Nojiri et al. 2000
MET
Allanach et al. 2000
Gjelsten et al. 2004
KM,Moortgat,Pape,Park 2009
• Study the invariant mass distributions of the visible
particles on one side of the event
• Does not rely on the MET measurement
• Can be applied to asymmetric events, e.g.
– No visible SM products on the other side
– Small leptonic BR on the other side
• Well tested, will be done anyway.
8
Thursday: spin measurements
Burns, Kong, KM, Park 08
• Separate the spin dependence from all the rest
– Parameterize conveniently the effect from “all the rest”
 dN 
2
2
2
2
 2   FS ; (m )   FS ; (m )   FS ; (m )   FS ; (m )
 dm  S
• Measure both the spin (S) as well as all the rest:  ,  , 
9
In place of a summary
optimism
pessimism
Missing
momenta
reconstruction?
None
Mass measurements
Inclusive
Spin
measurements
2 symmetric
chains
Inv. mass endpoints
and boundary lines
Inv. mass
shapes
Meff,Mest,HT
Wedgebox
Approximate
Smin, MTgen
MT2, M2C, M3C,
MCT, MT2(n,p,c)
As usual
(MAOS)
Exact
?
Polynomial
method
As usual
pessimism
optimism
10
Wednesday: Meff (HT) and Smin
F. Paige hep-ph/9609373
Konar, Kong, KM 2008
11
In place of a summary
optimism
pessimism
Missing
momenta
reconstruction?
None
Mass measurements
Inclusive
Spin
measurements
2 symmetric
chains
Inv. mass endpoints
and boundary lines
Inv. mass
shapes
Meff,Mest,HT
Wedgebox
Approximate
Smin, MTgen
MT2, M2C, M3C,
MCT, MT2(n,p,c)
As usual
(MAOS)
Exact
?
Polynomial
method
As usual
pessimism
optimism
12
The “Cambridge” mT2 variable
• A. Barr, C. Lester and P.
Stephens, “mT2 : the truth
behind the glamour”
– hep-ph/0304226
• C. Lester and D. Summers,
“Measuring masses of
semiinvisibly decaying
particles pair produced at
hadron colliders”
– hep-ph/9906349
13
Mass measurements
• Single semi-invisibly decaying particle
e
W
n
• Use the transverse mass distribution

 2 
 2
2
2
M W  mT (e,n )   peT  pnT    peT  pnT 
14
Mass measurements
• A pair of semi-invisibly decaying particles
e
W
Lester,Summers 99
Barr,Lester,Stephens 03
n
n
W

• Use the “stransverse” mass (mT2) Kong, KM 04

 2 
 2
2
2
M W  mT (e,  )  peT  pT   peT  pT 


• This formula is valid for mn=0.
15
Definition of MT2
• A pair of semi-invisibly decaying particles
e
W
W
Lester,Summers 99
Barr,Lester,Stephens 03
n
n

• If
and
were known:
• But since unknown, the best one can do :
16
What is mT2 good for?
• Provides a relation between the two unknown
masses of the parent (slepton) and child (LSP)
– Vary the child (LSP) mass, read the endpoint of mT2
• So what? We still don’t know exactly the LSP mass
17
LSP mass measurement from kinks
• Include pT recoil due to ISR
Varying PT
ISR with some PT
• A kink appears at the true masses of the parent
18
and the child
How big is this kink?
• It depends on the hardness of the ISR and
the mass spectra
FR
M0
M1
FL
PT
M1
19
Origin of the MT2 “kink”
• A kink may arise due to
– “Composite” particle on
each side
FR
Cho, Choi, Kim, Park 2007
– ISR recoils
FL
Barr, Gripaios, Lester 2007
– Heavy particle decays
Burns, Kong, KM, Park 2008
20
Subsystem MT2
Burns, Kong, KM, Park 2008
• Generalize the MT2 concept to MT2(n,p,c)
– “Grandparents” (n): The total length of decay chain
– “Parents” (p): Starting point of MT2 analysis
– “Children” (c): End point of MT2 analysis
21
Mass determination: Subsystem MT2
Burns, Kong, KM, Park 2008
NP : Number of unknowns
Nm : Number of measurements
NP= number of BSM particles
= n+1
Sub MT2
Nm=
How many undetermined
parameters (masses) are left?
22
n : Length of decay chain
Opening a parenthetical remark
(
23
In place of a summary
optimism
pessimism
Missing
momenta
reconstruction?
None
Mass measurements
Inclusive
Spin
measurements
2 symmetric
chains
Inv. mass endpoints
and boundary lines
Inv. mass
shapes
Meff,Mest,HT
Wedgebox
Approximate
Smin, MTgen
MT2, M2C, M3C,
MCT, MT2(n,p,c)
As usual
(MAOS)
Exact
?
Polynomial
method
As usual
pessimism
optimism
24
Mass determination – polynomial method
Cheng,Gunion,
Han,Marandella,
McElrath, 2007
Sub MT2
n : Length of decay chain
25
Closing the remark
...)
26
Subsystem MT2 applied to top pairs
• Don’t assume prior knowledge of the W and
neutrino masses
• Traditional MT2 variable: MT2(2,2,0)
MT2(220)
e
b
t
n
W
n
W
t
b
e
Combinatorial problem!
27
Subsystem MT2 applied to top pairs
• Genuine subsystem variable: MT2(2,1,0)
MT2(210)
e
b
t
n
W
n
W
t
b
e
No combinatorial problem!
28
Subsystem MT2 applied to top pairs
• Another genuine subsystem variable: MT2(2,2,1)
MT2(221)
e
b
t
n
W
n
W
t
b
e
No combinatorial problem!
29
Mass measurements
in the TTbar system
• We have just measured three MT2
endpoints which are known functions of
the hypothesized Top, W and neutrino
masses.
– MT2(2,2,0)
– MT2(2,1,0)
– MT2(2,2,1)
• Problem: they are not independent, need
an additional measurement
– MT2(1,1,0)
– Endpoint of the lepton+b-jet inv. mass distribution
30
MT2 applied to W pairs
• Yet another MT2 variable: MT2(1,1,0)
e
n
W
MT2(110)
n
W
e
No combinatorial problem!
31
Full T, W, Nu mass determination
• Hybrid method: Inv. mass
b
t
n
n
W
b
M(bl)max =
e
W
t
Subsystem MT2
Correct bl pairs
e
32
On a positive note
• MT2 can be used for background suppression
Barr, Gwenlan 2009
• The dominant background to SUSY is TTbar
• For illustration, let us choose a very challenging
example with an identical signature
– Stop pair production, with decays to chargino and LSP.
e
b
t
n
W
n
W
t
b
b
e
e
stop
chargino
LSP
stop
chargino
LSP
b
e 33
Top-Stop separation
• What do we know about the stop sample?
– Absolutely nothing.
• What do we know about TTbar?
– The endpoints of the subsystem MT2 variables that we just
saw. All TTbar events fall below these endpoints, and
there are none above!
KM, Park preliminary
34
Combination MT2 cut
• Accept the event if it is beyond at least one of the
three subsystem MT2 endpoints.
• This greatly enhances the signal acceptance,
compared to a single MT2 cut, or an HT cut.
35
BACKUPS
36
Wedgebox technique
• Scatter plot of the invariant masses of the
visible decay products on both sides
Bisset,Kersting,Li,Moortgat,Moretti,Xie 2005
37
MTgen
Lester,Barr 2008
• Inclusive application of
MT2: minimize MT2 over all
possible partitions of the
visible decay products
between two chains
– Brute force way to deal
with combinatorial issue
– Preserves the endpoint,
provides a measure of the
scale
– Endpoint smeared in the
presence of ISR
– Does not measure the LSP
mass
– Difficult to interpret when
many processes contribute
38
39
40
41
Polynomial method
Cheng,Gunion,Han,Marandella,McElrath 2007
Cheng,Engelhardt,Gunion,Han,McElrath 2007
Cheng,Han 2008
42