1. SAC Review Meeting May 20, 2005 Marcel Merk
LHCb Simulation Studies: From Detector Optimization to Data Preparation
SAC Review Meeting
May 20, 2005
Marcel Merk

2. The “Tracking and Physics” Team
The NIKHEF LHCb software “team” 2005:
Staff: M. M., G. Raven
Postdoc (CERN based): E. Rodrigues
Graduate students: E. Bos, B. Hommels, S. Klous, J. Nardulli,
G.Ybeles Smit, J.v.Tilburg, M. Zupan.
Undergraduate students: J. Amoraal, B. M’charek
NIKHEF software activities embedded in:
The LHCb Computing Project (M.M. convenor “Track Fitting”)
The Physics Planning Group (G.Raven convenor “Proper time and mixing”)
Graduate Student “Model”
~ 2 years contribution to hardware or software
~ 1 year contribution to physics studies
~ 1 year thesis writing + other

3. Past Studies Theses Past Simulation studies to optimize LHCb
(2001) Thesis N. Zaitsev (Pile-up and Bs→J/yf)
(2002) Thesis R. v.d. Eijk (OT and tracking)
(2003) Thesis R. Hierck (Tracking and Bs→DsK/p)
(2004) Thesis N. v. Bakel (Velo and Bs mixing)
Past Simulation studies to optimize LHCb
Event yields vs. hadronic interaction lengths
Pattern recognition vs. detector occupancy
Resolutions vs. multiple scattering
LHCb Classic => LHCb Light …

4. Evolution since Technical Proposal
Reduced
material
Improved
level-1 trigger

5. Present Studies Present Studies: preparations for data
OT DAQ simulation and decoding
Track pattern recognition
Track fitting and alignment
Lifetime reconstruction
Bs oscillation and CP violation extraction
Our physics motivations include:
Bs oscillation with Bs→ Dsp Dms
CP violation with with Bs → DsK CP angle g – 2c
Search for new physics with Bs → J/yf Bs mixing angle 2c
Study of rare decays with b→s l+l b→s penguin
Illustrate our studies using the example of the decays
Bs → Dsp and Bs → DsK

6. bt The Decay Bs→Ds h Two decays with identical topology: Bs → Ds- p +
Bs -> Ds∓ K± bt Bs K K
,K  Ds
Primary vertex p p
Experiment:
Trigger on B decay of interest.
“high” Pt tracks and displaced vertices
displaced vertices
Efficient trigger
Select the B decay, reject background:
Mass resolution
Tag the flavour of the B decay
Tagging power
Plot the tagged decay rate as function of the decay time
Decay time resolution

7. Physics with Bs-→Ds- p+ : Dmu Bs
Ds- p+
BR~10-4
Dilutions:
A(t) : Trigger acceptance
Wtag : Flavour Tagging
dt : Decay time Resolution
Fit them together with Dm
Measure Oscillation Frequency!
1 year data LHCb

8. Physics with Bs→Ds∓ K± : gu Bs
Ds- K+
BR~10-5
Ds- b s u c Bs K+
Vub + Bs s b
Introduce also:
d = strong phase difference ; r = ratio between amplitudes

9. Physics with Bs→Ds∓ K± : gu Bs
Ds- K+
BR~10-5
Ds- b s u c Bs K+ + Bs s b
Measure Oscillation Amplitude!
4 decay rates to fit the unknown parameters:
Ration between diagrams: r
Strong phase: d
Weak phase: g
Same experimental dilutions as in Dsp should be added:
Use the value of A, wtag and dt as obtained with Dsp fit…
Bs→ Ds- K+
Bs→ Ds-K+
Bs→ Ds+ K-
Bs→ Ds+K-

10. The expected signal for Dsp and DsK
Nominal expectations for
Efficiency
Background
Resolution
Tagging power
Etc.
Bs mixing relatively easy
CP signal is not self-evident
Use full statistical power in the data
5 years data:
Bs→ Ds-p+
Bs→ Ds-K+
(Dms = 20)
(g = 65 degrees)
Measure
frequency
Measure
amplitude

11. 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
J.Nardulli, J.v.Tilburg: Geometry and MC Hits for the Outer Tracker
Detector Response (“digitization”):
Boole: Converting the MC Hits into a raw buffer emulating the real data format
B.Hommels, J.Nardulli, A.Pellegrino: L1 and DAQ data format Outer Tracker
Reconstruction:
Brunel: Reconstructing the tracks from the raw buffers.
E.Bos, H.Hommels, M.M., J.Nardulli, G.Ybeles Smit, J.v.Tilburg
Physics:
DaVinci: Reconstruction of B decays and flavour tags.
LoKi : “Loops and Kinematics” toolkit.
J.Amoraal, S.Klous, B.M’charek, G.Raven, J.v.Tilburg, M.Zupan,
Visualization:
Panoramix: Visualization of detector geometry and data objects
J.v.Tilburg: Display of tracks

12. The LHC environment pp collisions @ s=14 TeV
s (inel)=79.2 mb, s (bb)=633 mb
Bunch 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

13. Simulation: Switched from GEANT3…TT
RICH1
VELO

14. …to GEANT4 (“Gauss”)
Note: simulation and reconstruction use identical geometry description.

15. Event example: detector hits
J.v.Tilburg

16. Event example (Vertex region zoom)

17. Detector Response Simulation: e.g.: the Outer Tracker
J.Nardulli, J.v.Tilburg
OT double layer cross section
5mm straws
pitch 5.25 mm
Track e-
Geant event display
TDC spec.:
1 bunch
+ Spill-over
+ Electronics
+ T0 calibration

18. Track finding strategy
T track
Upstream track
B. Hommels
G. Ybeles Smit
N. Tuning
T seeds
VELO
seeds
Long track (forward)
Long track (matched)
J.v.Tilburg
VELO track
Downstream track
R.Hierck
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)

19. Result of track finding
On average:
26 long tracks
11 upstream tracks
4 downstream tracks
5 T tracks
26 VELO tracks T3 T2 T1
Typical event display:
Red = measurements (hits)
Blue = all reconstructed tracks 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

20. Robustness Test: Quiet and Busy Events
J.v.Tilburg
Monitor efficiency and ghost rate as function of nrel: “relative number of detector hits”
<nrel> = 1

21. Kalman Track Fit
E.Bos. M.M., E.Rodrigues,
J.v.Tilburg
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

22. Experimental Resolution
dp/p =
0.35% – 0.55%
p spectrum B tracks
sIP=
14m + 35 m/pT
1/pT spectrum B tracks
Momentum resolution
Impact parameter resolution

23. Trigger L0 pT of m, e, h, g L1 Level-0: Level-1: Impact parameter
pile-up L0
40 MHz
Calorimeter
Muon system
Pile-up system
Level-0:
pT of
m, e, h, g
1 MHz
Vertex Locator
Trigger Tracker
Level 0 objects
Level-1:
Impact parameter
Rough pT ~ 20% L1
B->pp
Bs->DsK
40 kHz
ln IP/IP
ln IP/IP
HLT:
Final state
reconstruction
Full detector
information
Signal
Min.
Bias
2 kHz output
OT in L1:
B.Hommels, N.Tuning
ln pT
ln pT

24. B Mass Reconstruction p d ,K K Bs K Ds 
J.v.Tilburg, B.M’charek
S.Klous, J.Amoraal
M.Zupan
Final state reconstruction
Combine K+K-p- into a Ds-
Good vertex + mass
Combine Ds- and “bachelor” into Bs
Pointing Bs to primary vtx Ds Bs K K
,K  d p
47 mm
144 mm
440 mm
Mass distribution:
K/p separation

25. Annual Yields and B/S for Bs→Dsh
Efficiency Estimation:
edet (%)
erec/det (%)
esel/rec (%)
etrg/sel (%)
etot (%)
Bs→Dsp
5.4
80.6
25.0
31.1
0.337
Bs→DsK
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 = ±

26. Decay time reconstruction: t = m d / p
Error distribution
B decay time resolution:
As an illustration, 1 year Bs→Ds-p+
Pull distribution:
Measurement errors understood!

27. Sensitivity Studies Many GEANT events generated, but:
M.M., G.Raven, J.v.Tilburg
Many GEANT events generated, but:
How well can we measure Dms with Bs→Dsp events?
How well can we measure angle g with Bs→DsK events?
as function of Dms, DGs, r, g, d, and dilutions wtag, dt, …?
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

28. Toy Generator
Generate events according to the “master” formula for B decay
Bs→Ds-K+
Relevant physics parameters:
Bs→Ds+K
Bs→Ds+K-
With:
For Ds+K-:
replace g by -g
For Dsp: Simplify: r=0

29. 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

30. 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

31. 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

32. 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

33. 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

34. Fitting time dependent decay rates
Use unbinned Likelihood fitter
Why use complicated method?
Weigh precisely measured events differently from badly measured events
Rely on the reconstructed event error
Allow for a scale factor and bias in the analysis
Error distr
Pull distr

35. Fit the Physics parameters in Dsp and DsK
M.M.
Use the 4 tagged (B) and (B) Dsp decay rates to fit Dms and Wtag fraction
Use the 4 tagged DsK events to fit r, g, d
5 years data:
Bs→ Ds-p+
Bs→ Ds-K+
(Dms = 20)
Actually perform the Dsp and DsK fits simultaneous
For each setting of the parameters repeat ~100 toy experiments
A task for the GRID

36. The sensitivity of Dms after 1 year
Precision on Dms in ps-1
Dms 15 20 25 30
s(Dms)
0.009
0.011
0.013
0.016
The sensitivity for Dms
Amplitude fit method analogous to LEP
Curves contain 5 different assumptions for the decay time resol. 5s
Sensitivity:
Dms = 68 ps-1
~1000 jobs

37. CP angle g sensitivity for many parameter settings
Dms 15 20 25 30
s(g+d)
12.1
14.2
16.2
18.3
(Ab-)using the GRID
DGs/Gs
0.1
0.2
s(g+d)
12.1
14.2
16.2
g+d 55 65 75 85 95
105
s(g+d)
14.5
14.2
15.0
15.1
Precision on angle g after one year with 1 year data:
s(g) ~ 14o d
-20
-10
+10
+20
s(g+d)
13.9
14.1
14.2
14.5
14.6
Dependence on background
Dependence on resolution

38. Bs mixing phase and b→s penguin
Bs → J/yf
Admixture of CP even and CP odd final states
Sensitive to Bs mixing phase
J.Amoraal, S.Klous
reconstructed
matched to
generated
decay
b→s m+m-
b→s decay (Afb) is sensitive to SUSY parameters
Inclusive event selection
M. Zupan

39. Summary
NIKHEF LHCb group has a relatively large involvement in software
Past: Detector Optimization (4 Theses: N.Z.:2001, R.v.d.E.:2002, R.H.:2003, N.v.B.:2004)
Now: Preparation for Data
Reconstruction Responsibilities (convenor: “Track fitting”) (M.M.)
OT simulation and detector response (J.v.Tilburg, J.Nardulli)
OT region pattern recognition (Online and Offline) (B.Hommels, G.Ybeles Smit)
Kalman track fitting (E.Rodrigues, J.v.Tilburg)
Alignment studies (E.Bos, J.Nardulli)
Physics Responsibilities (convenor: “Proper time and mixing”) (G.Raven)
Measurement of Dms with Bs → Ds p (J.v.Tilburg)
Measurement of g-2c with Bs → DsK (J.v.Tilburg, B.M’charek)
Measurement of 2c with Bs → J/yf (S.Klous, J.Amoraal)
Study of rare decays with b → s l+l (M. Zupan)

40. Outlook
A possible scenario before the LHCb measurement of g:

41. Outlook
A possible scenario after the LHCb measurement of g:

42. The End
(Some X-tra slides)

43. B Physics: A (quick) comparison
LHCb
TevaTron
Babar/Belle √s
14 TeV
2 TeV
10.4 GeV
L (cm-2 s-1)
2 x 1032 cm-2 s-1
4x1033 cm-2s-1
sbb
500 mb
100 mb
1.05 nb
sbb / sinel
1/160
1/1000
1/4
N bb / year
1012
2 x1011
4 x 107
Distance
10 mm
5 mm
260 mm
Comparison with e+e- factories:
All b hadrons produced:
Bu (40%), Bd(40%), Bs(10%), Bc and b-baryons (10%)
=> Bs physics!
Statistics vs Systematics
B hadrons not coherent: mixing dilutes tagging
Many particles not associated to b hadrons: primary vertex
Decay time resolution
Rare decays
Comparison with hadronic facilities:
CDF & D0:
S/B
Dedicated trigger
PID
BTeV: ~ equivalent
ECAL
Vtx+Trigger

44. BaBar & Belle D0/CDF HERA-B LHCb PEP-II/KEKB Tevatron HERA LHC e+e- pp
mode
e+e- pp pA
Start datataking
1999
2002
200?
2007
s (GeV)
10.4 = M(4S)
2000 42
14000
sbb/sqq
1/4
1/1000 1/
1/160
Nqq/s (Hz) 40
20k
10M
13M
Nbb/s (Hz) 10 20
100K
<B flight distance> (um)
260
450
9000
10000

45. Efficiencies, event yields and Bbb/S ratios
Nominal year = 1012 bb pairs produced (107 s at L=21032 cm2s1 with bb=500 b)
Yields include factor 2 from CP-conjugated decays
Branching ratios from PDG or SM predictions

46. CP Asymmetries and Dilutions
Both mis-tags (w) & finite proper time resolution (σt ) dilute CP asymmetries.
A simplified model (tested on toy MC):
A plausible scenario:
In this (Bs) case σt dominates dilution error, and total systematic significant!
(eg. our expected annual statistical precision on Af for DsK is 0.05 [CHECK])
Hence, we are now investigating ways to maximise understanding of
tagging, proper time resolution and acceptance, and trigger biases.
(Needless to say, any improvement in performance is also useful !)

47. LHCb

48. B Production @ LHC qb O(10%) Pythia & hep-ph/0005110 (Sjöstrand et al)
Forward (and backward) production
Build a forward spectrometer

49.  LHCb detector ~ 200 mrad ~ 300 mrad (horizontal) 10 mrad p p
Inner acceptance ~ 15 mrad (10 mrad conical beryllium beampipe)

50. LHCb tracking: vertex region
VELO: resolve Dms oscillations in e.g. Dsp events

51. LHCb tracking: vertex region
Pile-Up
Stations
Interaction Region
s=5.3 cm y x y x 

52. LHCb tracking: momentum measurement
Tracking: Mass resolution for background suppression in eg. DsK
By[T] 
Total Bdl = 4 Tm
Bdl Velo-TT=0.15 Tm

53. LHCb tracking: momentum measurement
All tracking stations have four layers:
0,-5,+5,0 degree stereo angles.
~1.41.2 m2
~65 m2 

54. LHCb Hadron Identification: RICH
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.

55. LHCb calorimeters e h 
Calorimeter system to identify electrons, hadrons and neutrals and used in the L0 trigger: hadron Pt trigger for Dsh events

56. LHCb muon detection m 
Muon system to identify muons and used in L0 trigger e.g. unbiased trigger on “other B” for Dsp events

57. 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 b-hadron
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:
Describes well direct fit of multiplicity data:
Robustness tests…

58. Charged multiplicity distributions at generator level
In LHCb acceptance ( 1.8 < h < 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

59. Particle ID RICH 2 RICH 1 e (K->K) = 88% e (p->K) = 3% Example:
Bs->Dsh K  Bs K
,K Ds
Prim vtx

60. Flavour tag eff = tag (1-2wtag )2K+
Knowledge of the B flavour at production is needed for the asymmetries B0
Ds-
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 B0 D K- l b
Bs0 b s
sources for wrong tags:
Bd-Bd mixing (opposite side)
b → c → l (lepton tag)
conversions… s K+ u u 4 35 42
εeff [%]
Wtag [%]
εtag [%] 6 33 54
Bd  p p
Bs  Ds h
Combining tags
effective efficiency:
eff = tag (1-2wtag )2

61. Trigger Acceptance function
Impact parameter cuts lead to a decay time dependent efficiency function: “Acceptance”
Acc
Bs→DsK

62. Bs→Dsh Reconstruction
J.v.Tilburg, B.M’charek
S.Klous, J.Amoraal
M.Zupan
Final state reconstruction
Combine K+K-p- into a Ds-
Good vertex + mass
Combine Ds- and “bachelor” into Bs
Pointing Bs to primary vtx Ds Bs K K
,K  d p
47 mm
144 mm
440 mm
Mass distribution:
K/p separation

63. Toy Simulation
Smear theoretical events (t=ttrue) into experimental events (trec) and assign an experimental error (dtrec). Method:
From the full simulation make a lookup table with selected events:
ttruei, treci, dtreci
Generate ttrue in toy and assign trec and dtrec 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.

64. Likelihood Fitter (general idea)
The likelihood that nature produces an event at a given time t =
The probability that this event is reconstructed (i.e. observed) at a reconstructed time trec with measurement error dtrec=
Thus the likelihood of observing an event (trec, dtrec) =
Fit the physics parameters (Dm, g,…) in R such that the likelihood is maximal:.i.e. maximize:

65. 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:
1 year data:
Bs -> Ds- p+
Bs -> Ds- K+
(Slow computation!)
Normalization of the probability:
Create the Likelihood:
Fit parameters:
-Physics:
-Experimental:
Normalization of the Likelihood is interesting!
See also LHCb note…LHCb
(Include information of the relative overall rates)

66. 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:
Calibrate the experimental time resolution
Fit the acceptance function on the untagged sample of Bs->Dsp events
Fit simultaneously the values of Dms, wtag with Dsp events.
Fit the values of the r, g, d with the DsK sample

67. 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· dtrec . => S = 0.99 ± 0.04
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.
L1 trigger
10% of 1 year untagged Bs→Dsp S=
trec

68. 2. Fitting the acceptance function
The acceptance function is modelled as:
The function can easily be determined using the unbiased sample
1 year untagged Bs→Dsp
Acc
trec
trec

69. 3. + 4. Fit the Physics parameters
Use the 4 tagged (B) and (B) Dsp decay rates to fit Dms and Wtag fraction
Use the 4 tagged DsK events to fit r, g, d
5 years data:
Bs→ Ds-p+
Bs→ Ds-K+
(Dms = 20)
Actually perform the Dsp and DsK fits simultaneous
For each setting of the parameters repeat ~100 toy experiments
A task for the GRID

70. (My) Conclusions
The decay Bs→Dsp can provide an observation of Dms 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

71. b  s m+m-
reconstructed
matched to
generated
decay
lepton spectrum allows theoretically clean calculations of certain coefficients in OPE of electroweak interactions
charge AFB sensitive to SUSY parameters
pole of AFB sensitive to SUSY parameters
Signal events
(generated within LHCb acceptance of 400 mrad)
92500
Selected events
455
Trigger (L0&L1) efficiency on selected events
87.3%
Total selection efficiency
0.149%
Annual yield estimate
9500