LHCb Simulation Studies: From Detector Optimization to Data Preparation
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Transcript of LHCb Simulation Studies: From Detector Optimization to Data Preparation
LHCb Simulation Studies:LHCb Simulation Studies:From Detector Optimization to Data Preparation
SAC Review Meeting
May 20, 2005
Marcel Merk
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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
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Past Studies
Theses (2001) Thesis N. Zaitsev (Pile-up and Bs→J (2002) Thesis R. v.d. Eijk (OT and tracking) (2003) Thesis R. Hierck (Tracking and Bs→DsK/)
(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 …
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Evolution since Technical Proposal
• ReducedReduced materialmaterial
• ImprovedImproved level-1 triggerlevel-1 trigger
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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→ Dsms
CP violation with with Bs → DsK CP angle – 2 Search for new physics with Bs → J/Bs mixing angle 2 Study of rare decays with b→s l+l- b→s penguin
Illustrate our studies using the example of the decays Bs → Ds and Bs → DsK
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The Decay Bs→Ds h
Two decays with identical topology: Bs → Ds
-
Bs -> Ds∓ K±
bt
Bs K
K
,K
Ds
Primary vertex
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
p p
Tag the flavour of the B decay Tagging power
Plot the tagged decay rate as function of the decay time Decay time resolution
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( ) 1 cos( )s sB D
t e mt
exp( ) 1 co( ) (1 2 s( [ ]))tags sD agB tA tt e mw tt
Dilutions: A(t) : Trigger acceptance Wtag : Flavour Tagging
t : Decay time Resolution
Fit them together with m
Physics with Bs-→Ds
- + : m
b
s
c
s
du
Bs Ds-
+BR~10-4
1 year data LHCbMeasure Oscillation Frequency!
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Physics with Bs→Ds∓ K± :
b
s
c
s
s
u
Bs Ds-
K+
Bss
b
b
s
Ds-
b
s
u
s
s
c
Bs K++
BR~10-5
iud us ub
CKM cd cs cbi
td ts tb
V V V e
V V V V
V e V V
Vub
Introduce also:
= strong phase difference ; r = ratio between amplitudes
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Physics with Bs→Ds∓ K± :
b
s
c
s
s
u
Bs Ds-
K+
Bss
b
b
s
Ds-
b
s
u
s
s
c
Bs K++2
2 2
2
2 2
(1 ) (2 )( ) 1 cos( ) sin( )sin( )
(1 ) (1 )
(1 ) (2 )( ) 1 cos( ) sin( )sin( )
(1 ) (1 )
s s
s s
t
B D K
t
B D K
t e t tm m
m mt e t t
r r
r r
r r
r r
BR~10-5
Measure Oscillation Amplitude!
4 decay rates to fit the unknown parameters: Ration between diagrams: r Strong phase: Weak phase
Same experimental dilutions as in Ds should be added:
Use the value of A, wtag and t as obtained with Ds fit…
Bs→ Ds- K+
Bs→ Ds-K+
Bs→ Ds+
K-
Bs→ Ds+K-
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The expected signal for Ds and DsK
5 years data:Bs→ Ds
-
Bs→ Ds-K+
ms = 20)degrees)
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
Measureamplitude
Measurefrequency
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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
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The LHC environment
pp collisions @ s=14 TeV inel)=79.2 mb, (bb)=633 b
Bunch crossing @ 40MHz 25 ns separation
inelastic = 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
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Simulation: Switched from GEANT3…
VELORICH1
TT
T1T2
T3
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…to GEANT4 (“Gauss”)
Note: simulation and reconstruction use identical geometry description.
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Event example: detector hits
J.v.Tilburg
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Event example (Vertex region zoom)
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Detector Response Simulation: e.g.: the Outer Tracker
Geant event displayOT double layer cross section
5mm straws
pitch 5.25 mm
Tracke- e
-e-
e-e
-
1 bunch+ Spill-over+ Electronics+ T0 calibration
TDC spec.:
J.Nardulli, J.v.Tilburg
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Track finding strategy
VELO seeds
Long track (forward)
Long track (matched)
T seeds
Upstream track
Downstream track
T track
VELO track
T tracks useful for RICH2 pattern recognition
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
VELO tracks useful for primary vertex reconstruction (good IP resolution)
B. HommelsG. Ybeles SmitN. Tuning
J.v.Tilburg
R.Hierck
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Result of track finding
Typical event display:Red = measurements (hits)
Blue = all reconstructed tracks
Efficiency vs p : Ghost rate vs pT :
Eff = 94% (p > 10 GeV)
Ghost rate = 3%(for pT > 0.5 GeV)
VELO
TT
T1 T2T3On average:
26 long tracks11 upstream tracks4 downstream tracks5 T tracks26 VELO tracks
2050 hits assigned to a long track: 98.7% correctly assigned
Ghosts:Ghosts:Negligible effect onNegligible effect onb decay reconstructionb decay reconstruction
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Robustness Test: Quiet and Busy Events
Monitor efficiency and ghost rate as function of nrel: “relative number of detector hits”
<nrel> = 1
J.v.Tilburg
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Kalman Track Fit
Reconstruct tracks including multiple scattering.
Main advantage: correct covariance matrix for track parameters!!
z
Impact parameter pull distribution:
= 1.0
rec truer r
r
Momentum pull distribution:
= 1.2
rec truep p
p
E.Bos. M.M., E.Rodrigues,J.v.Tilburg
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Experimental Resolution
p/p = 0.35% – 0.55%
p spectrum B tracks
IP= 14 + 35 /pT
1/pT spectrum B tracks
Momentum resolution Impact parameter resolution parameter resolution
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Trigger40 MHz
pil
e-u
p
1 MHz
40 kHz
2 kHz output
Level-1:Impact parameterRough pT ~ 20%
HLT:Final state
reconstruction
CalorimeterMuon system
Pile-up system
Vertex LocatorTrigger TrackerLevel 0 objects
Full detectorinformation
L0L0
Level-0:Level-0:ppTT of of
, e, h, , e, h,
ln pT ln pT
ln
IP/
IP
ln
IP/
IP
L1L1
Signal
Min.Bias
B-> Bs->DsK
OT in L1:B.Hommels, N.Tuning
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B Mass Reconstruction
Final state reconstruction Combine K+K-- into a Ds
-
• Good vertex + mass
Combine Ds- and “bachelor”
into Bs
• Good vertex + mass
Pointing Bss to primary vtx
K/ separation
Mass distribution:
Ds
BsK
K
,K
d
p47 m 144 m
440 m
J.v.Tilburg, B.M’charekS.Klous, J.AmoraalM.Zupan
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Annual Yields and B/S for Bs→Dsh
Efficiency Estimation:
det (%) rec/det (%) sel/rec (%) trg/sel (%) tot (%)
Bs→Ds 5.4 80.6 25.0 31.1 0.337
Bs→Ds 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→Ds 82k 0.32 ± 0.10
Bs→Ds 5.4k <1.0 (90%) C.L.
Estimation of Bs→Dsbackground in the Bs→Ds sample: B/S = 0.111 ± 0.056
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Decay time reconstruction: t = m d / p
B decay time resolution:
Pull distribution:
Error distribution
Measurement errors understood!
As an illustration, 1 year Bs→Ds-
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Sensitivity Studies
Many GEANT events generated, but: How well can we measure ms with Bs→Dsevents? How well can we measure angle with Bs→DsK events?
as function of ms, s, r,,, 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
M.M., G.Raven, J.v.Tilburg
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Toy Generator
Generate events according to the “master” formula for B decay
2
2
2
( )
)
2
(2
s
s
f t
D
f t
D K
K
A
A pR t
R t e I t
e I t I t
I t
q
2
2
1 cosh 2 cos sinh2 2
1 cos 2 sin( )sin
t tr r
r m rI tm
I
t
t
t
, , , , ,m r Relevant physics parameters:
For Ds+K-:
replace by-
For Ds: Simplify: r=0
Bs→Ds-K+
Bs→Ds-K+
Bs→Ds+K
Bs→Ds+K-
With:
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Dilutions in Bs→Ds
Plot the MC toy decay rate with the following situation:
1 year data Bs→Ds-+
Experimental Situation:
• Ideal resolution and tag
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Dilutions in Bs→Ds
Plot the MC toy decay rate with the following situation:
1 year data Bs→Ds-+
Experimental Situation:
• Ideal resolution and tag• Realistic tag
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Dilutions in Bs→Ds
Plot the MC toy decay rate with the following situation:
1 year data Bs→Ds-+
Experimental Situation:
• Ideal resolution and tag• Realistic tag• Realistig tag and resolution
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Dilutions in Bs→Ds
Plot the MC toy decay rate with the following situation:
1 year data Bs→Ds-+
Experimental Situation:
• Ideal resolution and tag• Realistic tag• Realistig tag and resolution• Realistic tag + reso + background
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Dilutions in Bs→Ds
Plot the MC toy decay rate with the following situation:
Experimental Situation:
• Ideal resolution and tag• Realistic tag• Realistig tag and resolution• Realistic tag + reso + background• Realistic tag+reso+bg+acceptance
1 year data Bs→Ds-+
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Fitting time dependent decay rates
Use unbinned Likelihood fitterWhy 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
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Fit the Physics parameters in Ds and DsK
Use the 4 tagged (B) and (B) Ds decay rates to fit ms and Wtag fraction
Use the 4 tagged DsK events to fit r, ,
5 years data:Bs→ Ds
-
Bs→ Ds-K+
ms = 20)
Actually perform the Dsand DsK fits simultaneous
For each setting of the parameters repeat ~100 toy experiments A task for the GRID
M.M.
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The sensitivity of ms after 1 year
The sensitivity for ms
Amplitude fit method analogous to LEP
Curves contain 5 different assumptions for the decay time resol.
5Sensitivity:
ms = 68 ps-1
ms 15 20 25 30
(ms) 0.009 0.011 0.013 0.016
Precision on ms in ps-1
~1000 jobs
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CP angle sensitivity for many parameter settings
+ 55 65 75 85 95 105
(+)
14.5 14.2 15.0 15.0 15.0 15.1
-20 -10 0 +10 +20
(+) 13.9 14.1 14.2 14.5 14.6
ms 15 20 25 30
(+) 12.1 14.2 16.2 18.3
ss/s0 0.1 0.2
(+) 12.1 14.2 16.2
Precision on angle after one year with 1 year data:
14o
Dependence on background Dependence on resolution
(Ab-)using the GRID
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Bs mixing phase and b→s penguin
Bs → J/ Admixture of CP even and CP odd final states Sensitive to Bs mixing phase
b→s
b→s decay (Afb) is sensitive to SUSY parameters
Inclusive event selection
reconstructedmatched togenerated decay
J.Amoraal, S.Klous
M. Zupan
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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 ms with Bs → Ds (J.v.Tilburg)
Measurement of -2 with Bs → DsK (J.v.Tilburg, B.M’charek)
Measurement of 2 with Bs → J/(S.Klous, J.Amoraal)
Study of rare decays with b → s l+l- (M. Zupan)
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Outlook
A possible scenario before the LHCb measurement of
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Outlook
A possible scenario after the LHCb measurement of
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The End(Some X-tra slides)
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B Physics: A (quick) comparison
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• S/B• ECAL• Vtx+Trigger
LHCb TevaTron Babar/Belle
√s 14 TeV 2 TeV 10.4 GeV
L (cm-2 s-1) 2 x 1032 cm-2 s-1 2 x 1032 cm-2 s-1 4x1033 cm-2s-1
bb 500 b 100 b 1.05 nb
bb / nel 1/160 1/1000 1/4
N bb / year 1012 2 x1011 4 x 107
Distance 10 mm 5 mm 260 m
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BaBar & Belle D0/CDF HERA-B LHCb
PEP-II/KEKB Tevatron HERA LHC
mode e+e- pp pA pp
Start datataking 1999 2002 200? 2007
s (GeV) 10.4 = M(4S) 2000 42 14000
bb/qq 1/4 1/1000 1/1000000 1/160
Nqq/s (Hz) 40 20k 10M 13M
Nbb/s (Hz) 10 20 20 100K
<B flight distance> (m) 260 450 9000 10000
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Efficiencies, event yields and Bbb/S ratios
Nominal year = 1012 bb pairs produced (107 s at L=21032 cm2s1 with bb=500 b)Yields include factor 2 from CP-conjugated decaysBranching ratios from PDG or SM predictions
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CP Asymmetries and Dilutions
w 0.330.01 t 0.0400.005 ps
ms 25 ps 1 known
Dtag 0.34 0.02 ( 6% rel. uncert.)Dres 0.610.08 (13% rel. uncert.)
DtagDres 0.210.03 (14% rel. uncert.)
Afmeas(t rec) Dtag Dres Af (t
rec)
tagging dilution : Dtag 1 2w
resolution dilution : Dres exp 12
(m t )2
Both mis-tags (w) & finite proper time resolution (σt ) dilute CP asymmetries.
A simplified model (tested on toy MC):
A plausible scenario:
Hence, we are now investigating ways to maximise understanding oftagging, proper time resolution and acceptance, and trigger biases. (Needless to say, any improvement in performance is also useful !)
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])
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LHCb
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B Production @ LHC
Forward (and backward) productionBuild a forward spectrometer
b b
O(50%)
O(10%)
O(40%)
Pyt
hia
& h
ep
-ph/
000
511
0 (
Sjö
stra
nd
et a
l)
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LHCb detector
p p
~ 200 mrad~ 300 mrad (horizontal)
10 mrad
Inner acceptance ~ 15 mrad (10 mrad conical beryllium beampipe)
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LHCb tracking: vertex region
VELO: resolve ms oscillations in e.g. Ds events
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Pile-Up Stations
Interaction Region
=5.3 cm
LHCb tracking: vertex region
y
x
y
x
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LHCb tracking: momentum measurement
0.15 Tm
By[T]
Total Bdl = 4 TmBdl Velo-TT=0.15 Tm
Tracking: Mass resolution for background suppression in eg. DsK
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LHCb tracking: momentum measurement
All tracking stations have four layers:0,-5,+5,0 degree stereo angles.
~65 m2
~1.41.2 m2
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LHCb Hadron Identification: RICH
3 radiators to coverfull momentum range: Aerogel C4F10
CF4
RICH2 100 m3 CF4 n=1.0005
RICH: K/ separation e.g. to distinguish Ds and DsK events.
RICH1 5 cm aerogel n=1.03 4 m3 C4F10 n=1.0014
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LHCb calorimeters
e
h
Calorimeter system to identify electrons, hadrons and neutrals and used in the L0 trigger: hadron Pt trigger for Dsh events
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LHCb muon detection
Muon system to identify muons and used in L0 trigger e.g. unbiased trigger on “other B” for Ds events
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Event Generation: Pythia
Pythia 6.2: proton-proton interactions at √s = 14 TeV . Minimum bias includes hard QCD processes, single and
double diffractive events inel = 79.2 mb
bb events obtained from minimum bias events with b or b-hadron bb = 633 b
Use parton-parton interaction “Model 3”, with continuous turn-off of the cross section at PT
min.
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…
direct fit
0
6.11 0.29chdN
d
TP fit
0
6.30 0.42chdN
d
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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, 3 low pTmin 25.46 ± 0.03 42.86 ± 0.03
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Particle IDRICH 1 RICH 2
(K->K) = 88%
(p->K) = 3%
Example:Bs->Dsh
K
BsK
,K
DsPrim vtx
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Flavour tag
l
B0
B0D
Ds-
K-
bb
s
u
s
u
Bs0
K+
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
43542
eff [%]Wtag [%] tag [%]
63354
Bd
Bs Ds h
Combining tags
effective efficiency:
eff = tag (1-2wtag )2
sources for wrong tags:
Bd-Bd mixing (opposite side)b → c → l (lepton tag) conversions…
Knowledge of the B flavour at production is needed for the asymmetries
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Trigger Acceptance function
Impact parameter cuts lead to a decay time dependent efficiency function: “Acceptance”
Bs→DsKAcc
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Bs→Dsh Reconstruction
Final state reconstruction Combine K+K-- into a Ds
-
• Good vertex + mass
Combine Ds- and “bachelor”
into Bs
• Good vertex + mass
Pointing Bss to primary vtx
K/ separation
Mass distribution:
Ds
BsK
K
,K
d
p47 m 144 m
440 m
J.v.Tilburg, B.M’charekS.Klous, J.AmoraalM.Zupan
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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, trec
i, 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 tag fraction of the events assign an event tag:
Statistically assign 1-wtag correct tags, and wtag wrong tags.
Current studies tag = 54% wtag = 33% .
Apply an acceptance function A(trec) by statistically accepting events according to the acceptance value for a given event time.
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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 trec=
Thus the likelihood of observing an event (trec, trec) =
Fit the physics parameters (m, ,…) in R such that the likelihood is maximal:.i.e. maximize:
, ; ),..( .sD h mR t L
( ; ), ,...s
recD h
rec
t tR t G
tm
L
, ,.. ).( ;s
recD h
rec
t tR t G
tm dt
L
1
logeventsN
i L
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, 1 , ,
, ,
[
]rec rec recsig
B
sig
BG G
rec
r
BG
BG ec rec
P t t dt t t t tf
t t t t
G
GRf
R
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 and 4 decay rates for Bs-> Ds K
Normalization of the Likelihood is interesting!See also LHCb note…LHCb 2003-124(Include information of the relative overall rates)
i
,Prob
,rec rec
rec rec rec rec
P t t
P t t dt d t
(Slow computation!)
Event probab:
Normalization of the probability:
Create the Likelihood: ( ) (Prob )ii
Log L LogFit parameters:-Physics:
-Experimental:
2
2
3 1
2
3
11 ; ; = /( )
2
1( ) = ;
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rec
rec
t
t t
trec recrec
r
BGsig B
ec re
G
cr c
S
e
w w f
ab
R R R Rt t t t e B B S
t t tt e
ttG
aA
t
, , , , ,sm r
, , , ,BGw f S a b
1 year data: Bs -> Ds
- +
Bs -> Ds-
K+
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Strategy for Ds/ 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->Ds events
3. Fit simultaneously the values of ms, wtag with Ds events.
4. Fit the values of the r, , with the DsK sample
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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
Can L1 trigger be tuned to provide unbiased Bs-> Ds events? What would be the required bandwidth for this?
In any case unbiased samples of J/events are foreseen.
S=0.99+- 0.04
L1 trigger
trec
10% of 1 year untagged Bs→Ds
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2. Fitting the acceptance function
The acceptance function is modelled as:
The function can easily be determined using the unbiased sample
3
3( ) = 1
recrec
rec
tt
t
a
aA b
( ) ( ) biased rec unbiased recR t R tA
1 year untagged Bs→Ds
trec trec
Acc
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3. + 4. Fit the Physics parameters
Use the 4 tagged (B) and (B) Ds decay rates to fit ms and Wtag fraction
Use the 4 tagged DsK events to fit r, ,
5 years data:Bs→ Ds
-
Bs→ Ds-K+
ms = 20)
Actually perform the Dsand DsK fits simultaneous
For each setting of the parameters repeat ~100 toy experiments A task for the GRID
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(My) Conclusions
The decay Bs→Dscan 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
in subsequent years. Important are: Very good mass resolution for background suppression Full understanding of time resolution and tagging for systematics An efficient K/ separation
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reconstructedmatched togenerated decay
b s
lepton spectrum allows theoretically clean calculations of certain coefficients in OPE of electroweak interactionscharge AFB sensitive to SUSY parameterspole 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