LHCb: Preparing for Data
(A talk on MC events and data expectations)
NIKHEF Colloquium
Feb 4, 2005
Marcel Merk
Contents
 Last year:
 Several excellent overviews of latest B physics results
 An overview of the status of the LHCb detector
 This talk:
 What does LHCb plan to do with incoming data in ~ 2008?
 Illustrate with a single decay mode: Bs→Ds h
 Topics:
 Bs→Dsp & Bs→DsK
 Detector
 Simulation
 Reconstruction and Trigger
 Event Selection and Flavour Tagging
 Physics Sensitivity studies
2
The Decay Bs→Ds h
 Two decays with identical topology:
 Bs → Ds- p +
+,K+
p
 Bs -> Ds∓ K±
Bs
p
Ds
p
Primary vertex
K+
K
p
bt
 Experiment:
 Trigger on B decay of interest.
Signatures:
• “high” Pt tracks
• displaced vertices
 Select the B decay and reject
the background
 Tag the flavour of the B decay
 Plot the tagged decay rate as
function of the decay time
 Physics of these two decays however is different….
3
Physics with Bs-→Ds- p+ :
BR~10-4
Bs b
s
d p+
u
c Ds
s
 B  Dp + (t )  e  (1 + cos(mt ))
m
 Dilutions:
 A(t) : Trigger acceptance
 Wtag : Flavour Tagging
 t : Decay time Resolution
 Fit them together with m

BtagBD
(ptexp
) )Ae(t )e1 +1cos(
+ (1 2Amt
wtag) ) cos(m
[t 
 t ])
cos(
m
)
 + 
+(t
p
D
 B s D p s (st ) s e (1  cos(mt ))
+
s
s
s

s
 
+
 In the fitting
procedure we
use the individual
decay rates

Measure Oscillation
Frequency!

1 year data LHCb
4
Physics with Bs→Ds∓ K± :
s
u
c
Bs b
s
K+
Ds-
Bs
s
VCKM
s
BR~10-5
+
s
b
 Vud

  Vcd
 V e  i
 td
g
Vub
c
u
b B b
s
s
s
Vus
Vcs
Vts
DsK+
s
g
Vub e

Vcb 
Vtb 
i
 Introduce also:
 = strong phase difference
;
r = ratio between amplitudes
5
Physics with Bs→Ds∓ K± :
s
u
c
Bs b
s
K+
Ds-
BR~10-5
s
s
c
u
+
s
Bs
b
b B b
s
s
s
 2t r (1  r )

(2r )

sin(
g
+

)
cos

m
t
 BA
(
t
)

e
1
+
cos(

m
t
)

sin(
g
+

)
sin(

m
t
)



+

  2 (1 + r 2 )
D
D K
s K
(1 + r 2 )

 1 + r 
 (1  r 2 )

(2r )
2
tr
 B  D K (t )  e 1 
cos(

m
t
)
+
sin(
g
+

)
sin(

m
t
)

2 t
AD+ K     2 (1sin(
+ r 2
) g +  ) cos(1+rm
) 

s
 1+ r 
 4 decay rates to fit the
 2 unknown
asymmetries
to fit the
parameters:
unknown parameters:
 Ration between diagrams: r
 Ration between diagrams: r
 Strong phase: 
 Strong phase: 
 Weak phase: g
 Weak phase: g
 Same experimental dilutions
as in Dsp should be added:
2

s
+
s

s
+
s
g
DsK+
s
Measure Oscillation
Amplitude!
Bs→ Ds- K+
Bs→ Ds-K+
Bs→ Ds+ KBs→ Ds+K-
 Use the value of A, wtag and t
as obtained with Dsp fit…
6
Pythia & hep-ph/0005110 (Sjöstrand et al)
B Production @ LHC
O(10%)
O(50%)
O(40%)
qb
qb
Forward (and backward) production
Build a forward spectrometer
7
LHCb detector: a quick reminder
~ 200 mrad
~ 300 mrad
(horizontal)
p
p
10 mrad

 Inner acceptance ~ 15 mrad (10 mrad conical beryllium beampipe)
8
LHCb tracking: vertex region

 VELO: resolve ms oscillations in e.g. Dsp events
9
LHCb tracking: vertex region
Pile-Up
Stations
y
y

Interaction
Region
s=5.3 cm
x
x
10
LHCb tracking: momentum measurement
 Tracking: Mass resolution for background suppression in eg. DsK

B [T]
y
Total Bdl = 4 Tm
Bdl Velo-TT=0.15 Tm
0.15 Tm
11
LHCb tracking: momentum measurement
All tracking stations have four layers:
0,-5,+5,0 degree stereo angles.
~65 m2
~1.41.2 m2

12
LHCb Hadron Identification: RICH
 RICH1
 5 cm aerogel n=1.03
 4 m3 C4F10 n=1.0014
 RICH2
 100 m3 CF4 n=1.0005
3 radiators to cover
full momentum
range:
Aerogel
C4F10
CF4

 RICH: K/p separation e.g. to distinguish Dsp and DsK events.
13
LHCb calorimeters
e
h

 Calorimeter system to identify electrons, hadrons and neutrals
and used in the L0 trigger: hadron Pt trigger for Dsh events
14
LHCb muon detection
m

 Muon system to identify muons and used in L0 trigger
e.g. unbiased trigger on “other B” for Dsp events
15
Simulation Software: “Gaudi” Applications
 Event Generator:
 Pythia: Final state generation
 Evtgen: B decays
 Detector Simulation:
 Gauss: GEANT4 tracking MC particles through the detector and storing MC Hits
 Detector Response (“digitization”):
 Boole: Converting the MC Hits into a raw buffer emulating the real data format
 Reconstruction:
 Brunel: Reconstructing the tracks from the raw buffer.
 Physics:
 DaVinci: Reconstruction of B decays and flavour tags.
 LoKi : “Loops and Kinematics” toolkit.
 Visualization:
 Panoramix: Visualization of detector geometry and data objects
16
Event Generation: Pythia
 Pythia 6.2: proton-proton interactions at √s = 14 TeV .
 Minimum bias includes hard QCD processes, single and
double diffractive events
 sinel = 79.2 mb
 bb events obtained from minimum bias events with b or bhadron
 sbb = 633 mb
 Use parton-parton interaction “Model 3”, with continuous
turn-off of the cross section at PTmin.
 The value of PTmin depends on the choice of Parton
Density Function.
 Energy dependence, with “CTEQ4L” at 14 TeV:
• PTmin=3.47 ± 0.17 GeV/c. Gives:
PT fit
 dNch 
 6.30  0.42


 d  0
 Describes well direct fit of multiplicity data:
direct fit
 dNch 


d


 0
 Robustness tests…
 6.11  0.29
17
Charged multiplicity distributions at generator level
In LHCb acceptance ( 1.8 <  < 4.9 )
Average charged multiplicity
Minimum bias
bb
CDF tuning at 14 TeV
16.53 ± 0.02
27.12 ± 0.03
LHCb tuning, default pTmin
21.33 ± 0.02
33.91 ± 0.03
LHCb tuning, 3s low pTmin
25.46 ± 0.03
42.86 ± 0.03
18
The LHC environment
 pp collisions @ s=14 TeV
 Bunch crossing @ 40MHz
 25 ns separation
 sinelastic = 80mb
 At high L >>1 collision/crossing
 Prefer single interaction events
 Easier to analyze!
• Trigger
• Flavor tagging
 Prefer L ~ 2 x 1032 cm-2s-1
 Simulate 10 hour lifetime,7 hour fill
 Beams are defocused locally
 Maintain optimal luminosity even
when Atlas & CMS run at 1034
19
Simulation: Switched from GEANT3…
T1
T2
T3
TT
RICH1
VELO
20
…to GEANT4 (“Gauss”)
Note: simulation and reconstruction use identical geometry description.
21
Event example: detector hits
22
Event example (Vertex region zoom)
23
Detector Response Simulation: e.g.: the Outer Tracker
OT double layer cross section
Track
5mm straws
e
e
-
Geant event display
e
-
-
pitch 5.25 mm
e
e-
TDC spec.:
1 bunch
+ Spill-over
+ Electronics
+ T0 calibration
24
Track finding strategy
T track
Upstream track
VELO
seeds
VELO track
Long track (forward)
Long track (matched)
T seeds
Downstream track
Long tracks
 highest quality for physics (good IP & p resolution)
Downstream tracks  needed for efficient KS finding (good p resolution)
Upstream tracks
 lower p, worse p resolution, but useful for RICH1 pattern recognition
T tracks
 useful for RICH2 pattern recognition
VELO tracks
 useful for primary vertex reconstruction (good IP resolution)
25
On average:
26 long tracks
11 upstream tracks
4 downstream tracks
5 T tracks
26 VELO tracks
Result of track finding
Typical event display:
Red = measurements (hits)
Blue = all reconstructed tracks
T1 T2
T3
TT
VELO
2050 hits assigned to a long track:
98.7% correctly assigned
Efficiency vs p :
Ghost rate vs pT :
Ghost rate = 3%
(for pT > 0.5 GeV)
Eff = 94%
(p > 10 GeV)
Ghosts:
Negligible effect on
b decay reconstruction
26
Robustness Test: Quiet and Busy Events
 Monitor efficiency and ghost rate as function of
nrel: “relative number of detector hits”
 <nrel> = 1
27
Kalman Track Fit
 Reconstruct tracks including
multiple scattering.
 Main advantage: correct
covariance matrix for track
parameters!!
z
Impact parameter pull distribution:
s = 1.0
Momentum pull distribution:
s = 1.2
 rrec  rtrue 
r
 prec  ptrue 
p
28
Experimental Resolution
Momentum resolution
Impact parameter resolution
sIP=
14m + 35 m/pT
p/p =
0.35% – 0.55%
p spectrum B tracks
1/pT spectrum B tracks
29
Particle ID
RICH 1
RICH 2
e (K->K) = 88%
e (p->K) = 3%
Example:
Bs->Dsh
Bs
Prim vtx
p+,K+
Ds
K
K+
p
30
m, e, h, g
Calorimeter
Muon system
Pile-up system
1 MHz
Vertex Locator
Trigger Tracker
Level 0 objects
40 kHz
HLT:
Final state
reconstruction
2 kHz output
L1
B->pp
ln IP/sIP
Level-1:
Impact parameter
Rough pT ~ 20%
Bs->DsK
ln IP/sIP
Level-0:
pT of
L0
pile-up
40 MHz
Trigger
Full detector
information
Signal
Min.
Bias
ln pT
ln pT
31
Trigger Acceptance function
Acc
 Impact parameter cuts lead to a decay time
dependent efficiency function: “Acceptance”
Bs→DsK
32
Bs→Dsh Reconstruction
 Final state reconstruction
 Combine K+K-p- into a Ds• Good vertex + mass
 Combine Ds- and “bachelor”
into Bs
• Good vertex + mass
 Pointing Bs to primary vtx
p
47 mm
Bs
d
144 mm
p+,K+
Ds
440 mm
K+
K
p
Mass distribution:
K/p separation
33
Annual Yields and B/S
 Efficiency Estimation:
edet (%)
erec/det (%)
esel/rec (%)
etrg/sel (%)
etot (%)
Bs→Dsp
5.4
80.6
25.0
31.1
0.337
Bs→DsK
5.4
82.0
20.6
29.5
0.269
 Background Estimation:
 Currently assume that the only background is due to bb events
 Background estimates limited by available statistics
Decay
Annual yield
B/S
Bs→Dsp
82k
0.32 ± 0.10
Bs→DsK
5.4k
<1.0 (90%) C.L.
 Estimation of Bs→Dsp background
in the Bs→DsK sample:
B/S = 0.111 ± 0.056
34
Decay time reconstruction: t = m d / p
B decay time
resolution:
Error distribution
As an illustration, 1 year Bs→Ds-p+
Pull distribution:
Measurement errors understood!
35
Flavour tag
K+
 Knowledge of the B flavour at production
is needed for the asymmetries




B0
tagging strategy:
opposite side lepton tag ( b → l )
opposite side kaon tag ( b → c → s )
(RICH, hadron trigger)
same side kaon tag (for Bs)
opposite B vertex charge tagging
DsB0
D
K-
l
b
b
sources for wrong tags:
Bd-Bd mixing (opposite side)
b → c → l (lepton tag)
conversions…
Combining tags
effective efficiency:
eeff = etag (1-2wtag
)2
tag
[%]
Bs 0
s
s K+
u
u
Wtag
[%]
eff [%]
Bd  p p
42
35
4
Bs  Ds h
54
33
6
36
Sensitivity Studies
 Many GEANT events generated, but:
 How well can we measure ms with Bs→Dsp events?
 How well can we measure angle g with Bs→DsK events?
as function of ms, s, r, g, , and dilutions wtag, t, …?
 Toy MC and Fitting program:
 Generator: Generate Events according to theory B decay formula
• An event is simply a generated B decay time + a true tag.
 Simulator: Assign an observed time and an error
• Use the full MC studies to do the smearing
 Fitter: Create a pdf for the experimentally observed time
distribution and fit the relevant parameters
37
Toy Generator
 Generate events according to the
“master” formula for B decay
Relevant physics parameters:
, , m, r , g , 
RD K + (t ) 
s
RD K + (t ) 
s
Af
2
Bs→Ds-K+
2
e t  I +  t  + I   t  
2
Af
Bs→Ds-K+
2
2
p t
e  I+ t   I t 
q
Bs→Ds+K
Bs→Ds+K-
With:


t  2r cos  g +   sinh
t
2
2
I   t   1  r 2  cos mt  2r sin(g +  ) sin mt
I +  t   1 + r 2  cosh
For Ds+K-:
replace g by -g
For Dsp: Simplify: r=0
38
Toy Simulation
 Smear theoretical events (t=ttrue) into experimental events (trec) and
assign an experimental error (trec). Method:
 From the full simulation make a lookup table with selected events:

ttruei, treci, treci
Generate ttrue in toy and assign trec and trec from look-up table, such that
non-Gausian effects of the full simulation are included
 For etag fraction of the events assign an event tag:
 Statistically assign 1-wtag correct tags, and wtag wrong tags.
 Current studies etag = 54% wtag = 33% .
 Apply an acceptance function A(trec) by statistically accepting events
according to the acceptance value for a given event time.
39
Dilutions in Bs→Dsp
 Plot the MC toy decay rate with the following situation:
1 year data Bs→Ds-p+
Experimental Situation:
• Ideal resolution and tag
40
Dilutions in Bs→Dsp
 Plot the MC toy decay rate with the following situation:
1 year data Bs→Ds-p+
Experimental Situation:
• Ideal resolution and tag
• Realistic tag
41
Dilutions in Bs→Dsp
 Plot the MC toy decay rate with the following situation:
1 year data Bs→Ds-p+
Experimental Situation:
• Ideal resolution and tag
• Realistic tag
• Realistig tag and resolution
42
Dilutions in Bs→Dsp
 Plot the MC toy decay rate with the following situation:
1 year data Bs→Ds-p+
Experimental Situation:
• Ideal resolution and tag
• Realistic tag
• Realistig tag and resolution
• Realistic tag + reso + background
43
Dilutions in Bs→Dsp
 Plot the MC toy decay rate with the following situation:
1 year data Bs→Ds-p+
Experimental Situation:
• Ideal resolution and tag
• Realistic tag
• Realistig tag and resolution
• Realistic tag + reso + background
• Realistic tag+reso+bg+acceptance
44
The signal for Dsp and DsK
 The CP signal is not self-evident
 Use full statistical power in the data
5 years data:
Bs→ Ds-p+
Bs→ Ds-K+
ms = 20)
45
Fitting time dependent decay rates
 Why use complicated Likelihood fit
method?
 Weigh precisely measured events
differently from badly measured events
 Rely on the reconstructed event error
• Allow for a scale factor in the analysis
Error distr
Pull distr
46
Likelihood Fitter (general idea)
 The likelihood that nature produces an event at a given time t =
L  RDs h (m, g ,...; t )
 The probability that this event is reconstructed (i.e. observed) at a
reconstructed time trec with measurement error trec=
 trec  t 
L  RDs h (m, g ,...; t ) G 

  trec 
 Thus the likelihood of observing an event (trec, trec) =
 trec  t 
L   RDs h (m, g ,...; t ) G 
 dt
  trec 
 Fit the physics parameters (m, g,…) in R such that the likelihood is
maximal:.i.e. maximize:
Nevents
 log  L 
i1
47
Likelihood Fitter (for the die-hard)
Maximize an unbinned likelihood describing the best theory curves
simultaneously matching simultaneously the 4 decay rates for Bs->Ds p
and 4 decay rates for Bs-> Ds K
Event probab:
P  trec ,  trec    dt [ 1  f BG  1Rsig
t  G
sig  trec ,  trec , t 
year
data:
- p+
B
->
D
s
s
+ f BG RBG  t  GB-G +trec ,  trec , t ]
Bs -> Ds K
Rsig  t   1  w  R+  t  +  w  R  t  ; RBG  t  
 atrec  + b
3
1 +  atrec 
3
A(trec ) =
1 2 t
e
2
 t  t  
1
; G  rec

e

2p trec
  trec 
Normalization of the probability:
Create the Likelihood: Log ( L) 
Probi 
 P  t
;
1  t t 
  S rec 
2   trec 
P  trec ,  trec 
rec
f BG = B /( B + S )
2
,  trec  dtrec d  trec
(Slow computation!)
 Log (Prob )
i
i
Normalization of the Likelihood is interesting!
See also LHCb note…LHCb 2003-124
(Include information of the relative overall rates)
Fit parameters:
-Physics:
, , ms , r , g , 
-Experimental:
w, f BG , S , a, b
48
Strategy for Dsp / DsK fits
 It turns out to be difficult to fit simultaneously the wrong
tag fraction, resolution and acceptance function.
 A small bias in the acceptance function biases the resolution fit
 A possible solution could be a 4 step procedure:
1. Calibrate the experimental time resolution
2. Fit the acceptance function on the untagged sample of Bs->Dsp
events
3. Fit simultaneously the values of ms, wtag with Dsp events.
4. Fit the values of the r, g,  with the DsK sample
49
1.Fitting the measurement errors
 Resolution can be determined from the negative tail of the lifetime
distribution. Fit with 10% of 1 year data: S· trec . => S = 0.99 ± 0.04
L1 trigger
10% of 1 year
untagged Bs→Dsp S=0.99+-
0.04
trec
 Can L1 trigger be tuned to provide unbiased Bs-> Dsp events?
 What would be the required bandwidth for this?
 In any case unbiased samples of J/y events are foreseen.
50
2. Fitting the acceptance function
 The acceptance function is modelled as:
Rbiased  A(trec )  Runbiased (trec )
A(trec ) =
 atrec 
3
1 +  atrec 
3
+b
1 year untagged
Bs→Dsp
trec
Acc
 The function can easily be determined using the unbiased sample
trec
51
3. + 4. Fit the Physics parameters
 Use the 4 tagged (B) and (B) Dsp decay rates to fit ms
and Wtag fraction
 Use the 4 tagged DsK events to fit r, g, 
 Actually perform the
Dsp and DsK fits
simultaneous
5 years data:
Bs→ Ds-p+
Bs→ Ds-K+
ms = 20)
 For each setting of the
parameters repeat
~100 toy experiments
 A task for the GRID
52
The sensitivity of ms after 1 year
 Precision on
ms in ps-1
ms
15
20
25
30
s(ms)
0.009
0.011
0.013
0.016
 The sensitivity for ms
 Amplitude fit method
analogous to LEP
 Curves contain 5
different assumptions
for the decay time resol.
 Sensitivity:
ms = 68 ps-1
5s
~1000 jobs
53
CP Sensitivity for many parameter settings
ms
15
20
25
30
s(g+)
12.1
14.2
16.2
18.3
s/s
0
0.1
0.2
12.1
14.2
16.2
s(g+)
g+
55
(Ab-)using the GRID
65
75
85
95
105
s(g+) 14.5
14.2
15.0
15.0
15.0
15.1

-20
-10
0
+10
+20
s(g+)
13.9
14.1
14.2
14.5
14.6
Dependence on background
 Precision on angle g
after one year with 1
year data:
sg ~ 10o
Dependence on resolution
54
(My) Conclusions
 The decay Bs→Dsp can provide an observation of ms
oscillations in the first year of data taking. Important are:
 A working hadronic trigger
 A good tagging procedure
 Fairly good resolution
 The decay Bs→DsK can provide an observation of angle g
in subsequent years. Important are:
 Very good mass resolution for background suppression
 Full understanding of time resolution and tagging for systematics
 An efficient K/p separation
55
Outlook
 A possible scenario before the LHCb measurement of g:
56
Outlook
 A possible scenario after the LHCb measurement of g:
57
The End
58