LHCb Simulation Studies: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 (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 …

4

Evolution since Technical Proposal

• ReducedReduced materialmaterial

• ImprovedImproved level-1 triggerlevel-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→ 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

6

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

7

( ) 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!

8

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

9

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-

10

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

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

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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

13

Simulation: Switched from GEANT3…

VELORICH1

TT

T1T2

T3

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)

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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

18

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

20

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

21

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

22

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

24

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

25

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-

27

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

28

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:

29

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

30

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

31

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

32

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

33

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-+

34

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

35

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.

36

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

37

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

38

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

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 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)

40

Outlook

A possible scenario before the LHCb measurement of

41

Outlook

A possible scenario after the LHCb measurement of

42

The End(Some X-tra slides)

43

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

44

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

45

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

46

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])

47

LHCb

48

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)

49

LHCb detector

p p

~ 200 mrad~ 300 mrad (horizontal)

10 mrad

Inner acceptance ~ 15 mrad (10 mrad conical beryllium beampipe)

50

LHCb tracking: vertex region

VELO: resolve ms oscillations in e.g. Ds events

51

Pile-Up Stations

Interaction Region

=5.3 cm

LHCb tracking: vertex region

y

x

y

x

52

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

53

LHCb tracking: momentum measurement

All tracking stations have four layers:0,-5,+5,0 degree stereo angles.

~65 m2

~1.41.2 m2

54

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

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

Muon system to identify muons and used in L0 trigger e.g. unbiased trigger on “other B” for Ds 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 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

58

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

59

Particle IDRICH 1 RICH 2

(K->K) = 88%

(p->K) = 3%

Example:Bs->Dsh

K

BsK

,K

DsPrim vtx

60

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

61

Trigger Acceptance function

Impact parameter cuts lead to a decay time dependent efficiency function: “Acceptance”

Bs→DsKAcc

62

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

63

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.

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 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

65

, 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( ) = ;

21

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+

66

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

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· 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

68

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

69

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

70

(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

71

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