1. RooFit toy MC sensitivity studies for  +  s and  m s from B s →D s  /K channels at LHCb Shirit Cohen NIKHEF MSc Colloquium May 11 th 2007

2. 11th May 2007Shirit Cohen Master Colloquium2 Outline Introduction The LHCb detector & physics goals CP violation & interest in B s →D - s π +, B s →D Ŧ s K ± decay channels RooFit sensitivity studies: concept, experimental and physics input parameters, decay models and likelihood function description Results from sensitivity studies Summary & conclusions

3. 11th May 2007Shirit Cohen Master Colloquium3 Introduction Matter dominated universe Matter-anti matter difference in weak force, CP violating processes In the Standard Model via the quark-mixing (CKM) matrix, via its phases LHCb experiment designed to study CP violation, performing measurements in the b-quark sector Motivation for measuring the CKM phase 

4. 11th May 2007Shirit Cohen Master Colloquium4 The LHCb detector  pp ~ 10-250 mrad yz ~ 10-300 mrad xz Non bending plane view

5. 11th May 2007Shirit Cohen Master Colloquium5 Detector detailed Single arm forward spectrometer Limited angular acceptance but very good time and mass resolutions Optimal luminosity 2∙10 32 cm -2 s -1 10 12 bb pairs produced per year Bending magnet 4.2Tm bending power VeLo very close to interaction point Good separation of  -K bb bb

6. 11th May 2007Shirit Cohen Master Colloquium6 Main LHCb physics goals CKM matrix angles, , ,  for example via time dependent CP asymmetry observable  s mixing phase Precision measurement of  m s mass difference CDF measurement Δm s = 17.77 ± 0.1(stat.) ± 0.07(syst.) ps -1  s decay rate difference Rare decays measurements Signs of New Physics b→s  transitions through loop diagrams, sensitive to NP b sb s t t WW V tb V ts V tb V ts * * SM NP

7. 11th May 2007Shirit Cohen Master Colloquium7 B s meson system b sb s tt W WV tb V ts V tb V ts * * flavour eigenstates mass eigenstates B s oscillations box diagram mass eigenstates time dependence decay amplitude into a final state f,, if there is more than one contribution, the decay amplitudes can be written as a sum, strong phase keeps value, weak phase changes sign under CP transformation, Example: B d →    

8. 11th May 2007Shirit Cohen Master Colloquium8 B s time dependent decay probability For charge conjugate final states: f → f, λ f → λ f, A f →A f, p/q → q/p * In this project we assume |p/q|=1 decay oscillations Feynman calculus is in f ! B s →D s - K + B s →D s + K -

9. 11th May 2007Shirit Cohen Master Colloquium9 CP violation in B s meson system In mixing, if |p/q|  1, giving In decay, if |A f |  |A f |, giving can occur only if two decay amplitudes with different strong and weak phases contribute to the same final state In interference, when and possible, and there is a relative phase between mixing (e.g arg(q/p)=  s ) and decay (e.g. arg(A f /A f )) expected to be small ~10 -2 in B s section can occur also in charged mesons and baryons,

10. 11th May 2007Shirit Cohen Master Colloquium10 B s →D s  decay channel Single decay diagram → no CP violation Flavour specific decay Branching fraction: (3.4±0.7)·10 -3 One diagram means  f = λ f =0 (|A f |=|A f |), leading to D f =S f =0, C f =1. (two unique B s →D s  equations) → Parameters to measure: Δm s, Δ Γ s b s c s d u BsBs DsDs ++ 0 -

11. 11th May 2007Shirit Cohen Master Colloquium11 BsBs s b b s B s →D s K decay channel Non flavour specific decay, four decay diagrams exist (four Eq.) 2 diagrams and a relative phase → Time dependent CP violation | λ f |=| λ f | → D f, C f, S f coefficients non 0 → Parameters: |λ f |, arg(λ f ), arg(λ f ) to extract  +  s, Δ T1/T2 B s → D - s K + B s → D + s K - (2.0±0.6)·10 -4 (2.2±0.7)·10 -5 Branching fractions  +  s = [arg(  f ) - arg(  f )] /2 Δ T1/T2 = [arg(  f ) + arg( f )] /2 Ds-Ds- b s u s s c BsBs K+K+ + 0 0 b s c s s u BsBs Ds-Ds- K+K+ 0 b s u s s c BsBs K-K- Ds+Ds+ 0 T1 T2

12. 11th May 2007Shirit Cohen Master Colloquium12 B s →D s h decay channels The topology of the decay channels B s →D s - π + and B s →D s Ŧ K ± is very similar B s →D s - π + can be used for Δm s measurement B s →D s Ŧ K ± can be used to extract the CP angle  +  s Standard Model prediction  ≈ 60°  s ≈ 0.02° can be determined by B s →J/  channel b tag BsBs KK KK   /K   DsDs Primary Vertex~1cm ~6mm Event topology 0 SV

13. 11th May 2007Shirit Cohen Master Colloquium13 Toy MC sensitivity studies Goal - Obtain expected sensitivity for measuring  m s and  +  s at LHCb from B s →D s  and B s →D s K decay channels Approach – Define decay models Probability Distribution Functions (PDF’s) according to decay equations & including experimental effects Generate events for all decay flavours, simulating 5 years of data taking Fit decay models back to the events. Simultaneous fit of both decay channels in order to achieve best sensitivities and have correlations taken care of Repeat experiment many times, estimate sensitivities from collected output Input data - Experiment-related parameters from full LHCb GEANT4 simulation Physics parameter values agreed with WG Tools - RooFit toolkit for data modeling & ROOT data analysis framework Ganga, LHC(b) interface for running jobs on the GRID/ CERN

14. 11th May 2007Shirit Cohen Master Colloquium14 Experimental parameters (1/2) Common B s →D s h selection, topological cuts For D s π: require bachelor particle reconstructed as π For D s K: require bachelor particle reconstructed as K and a cut on Δ L Kπ in order to get rid of misidentified π’s Signal event yields B s reconstructed mass from D s - π + and D s Ŧ K ± channels (after the trigger) Reconstructed B s mass resolution 14MeV B/S limits and central values Specific central values used for toy MC Results for B/S ratios ChannelB/S at 90% CL (bb combinatorial) B/S at 90% CL (bb specific) Bs→Ds-π+Bs→Ds-π+ [0.014,0.05] C.V 0.027±0.008 [0.08,0.4] C.V 0.21±0.06 B s →D s Ŧ K ± [0,0.18] C.V 0.0 [0.08,3] C.V 0.7±0.3 B s reconstructed mass from B s →D s π, signal and major background B s reconstructed mass from B s →D s K, signal and major background B s →D s - π + 140k ± 0.67k (stat.) ± 40k (syst.) B s →D s Ŧ K ± 6.2k ± 0.03k (stat.) ± 2.4k (syst.) Event yields for 2fb -1 (define as 1y)

15. 11th May 2007Shirit Cohen Master Colloquium15 Experimental parameters (2/2) Proper time per-event error distribution Due to detector resolutions on vertices, tracking, momenta etc. PT per-event error distribution parameterization used in toy MC Acceptance function after triggers and offline selection Low PT B s ’s rejected due to misplaced vertex requirements and low significance impact parameter Fraction of high PT B s ’s rejected due to high impact parameter Acceptance parameterization used in toy MC Tagging efficiency  tag =0.5812, mistag fraction  =0.328 Proper time per-event error distribution Acceptance function mean value 33fs most probable value 30fs

16. 11th May 2007Shirit Cohen Master Colloquium16 RooFit sensitivity studies (1/2) Following previous work done with FORTRAN (LHCb-2003-103) Building PDF components using the RooFit package From the components we construct a decay PDF described by PDF B→f (  rec,m rec |Δ  rec ) for the B s →D s  and B s →D s K decay channels (and for the different flavours) Events are generated according to decay PDF, meaning an event is a set of “  rec,m rec,Δ  rec ”

17. 11th May 2007Shirit Cohen Master Colloquium17 RooFit sensitivity studies (2/2) The components that are used in PDF B→f (  rec,m rec |Δ  rec ): Signal  rec distribution – B s decay equation, include ω smearing Signal m rec distribution – Gaussian distribution Background  rec distribution – decaying particle with  Bs /2 Background m rec distribution – flat distribution Resolution function: per-event proper time error (with scale factor) Acceptance function on  rec Construction Implementing the acceptance function on signal proper time distribution (and same for background) Constructing PDF sig = PDF sig (  rec,m rec | Δ  rec ) and same for background Adding signal and background with f sig, f bg (calculated from B/S ratios) Generate events from each decay flavour separately, fit the desired parameters from all decay flavours simultaneously

18. 11th May 2007Shirit Cohen Master Colloquium18 Likelihood description Likelihood function with, signal proper time including mistagged events signal reconstructed B s mass bg proper time bg reconstructed B s mass acceptance function resolution function: proper time per-event error, with signal scale factor resolution function: proper time per-event error, with bg scale factor

19. 11th May 2007Shirit Cohen Master Colloquium19 Physics and experimental input parameters for toy MC central values of specific background used for B/S estimation acceptance function per-event proper time error distribution ParameterInput value ΔΓ s /Γ s 0.1 ΔmsΔms 17.5 (ps) -1 |λf||λf|0.37 Arg( λ f ) = Δ T1/T2 - (  +  s ) -60° = -1.047 rad Arg( λ f ) = Δ T1/T2 + (  +  s ) 60° = 1.047 rad ω0.328 Event yield (1y) Dsπ Event yield (1y) DsK 140K 6.2K B/S ratio for Dsπ B/S ratio for DsK 0.2 0.7 ε tag 0.5812 σ(m rec )14MeV Physics Experimental

20. 11th May 2007Shirit Cohen Master Colloquium20 Example for single decay flavor PDF B s →D s - π + projections on (  rec,m rec,Δ  rec ) B s →D s - K + projections on (  rec,m rec,Δ  rec ) Δ  rec m rec  rec Δ  rec m rec  rec (5y)

21. 11th May 2007Shirit Cohen Master Colloquium21 Sensitivity results from tagged events Two D s π equations, four D s K equations, simultaneous fit performed Collected data from many “experiments” of 5y tagged data, scaled results to 1y Fit a Gaussian to the fitted values from all the “experiments”, make pull distribution ParameterΔm s (ps) -1 ωArg(λ f ) rad |λf||λf| +s °+s ° Δ T1/T2 ° input value17.50.3281.047-1.0470.37600 fitted value17.50.3281.056-1.0420.3760.290.5 resolution 5y0.0030.0010.1160.1430.035.685.43 resolution 1y 0.007 0.0030.260.320.07 12.712.14 pull fitted mean0.04-0.070.060.1 -0.010.1 pull fitted sigma1.0211.051.041.0111.03 Data from 400 “experiments”

22. 11th May 2007Shirit Cohen Master Colloquium22 Example for distributions for 400 exper.  +  s ° values Δm s (ps) -1 values Δm s pull  +  s pull # events

23. 11th May 2007Shirit Cohen Master Colloquium23 B s → D s K untagged events Meaning events with no information if the decaying meson was a B s or a B s Decay equations for B s →D s K untagged events: One cannot observe the B s oscillations using untagged events Untagged events still hold information on the phases through Re f, Re f Add untagged events to the analysis in order to increase the sensitivities to the phases

24. 11th May 2007Shirit Cohen Master Colloquium24 Adding untagged D s K events Projections over proper time (ps)

25. 11th May 2007Shirit Cohen Master Colloquium25 Results from tagged+untagged events Two D s π equations, four D s K equations + two untagged D s K equations. Collected data from 400 “experiments” of 5y tagged+untagged data, scaled results to 1y Fit a Gaussian to the fitted values from all the experiments, check pulls ParameterΔmsΔms ωArg(λ f ) rad |λf||λf| +s °+s ° Δ T1/T2 ° input value17.50.3281.047-1.0470.37600 fitted value17.50.3251.064-1.0440.3760.370.48 resolution 5y0.0030.0010.1050.1180.034.594.61 resolution 1y 0.007 0.0030.230.260.06 10.2610.31 pull fitted mean0.06-0.090.10.030.050.060.1 pull fitted sigma1.0311.011.051.080.950.97 Δm s (ps) -1 values  +  s ° values # events

26. 11th May 2007Shirit Cohen Master Colloquium26 Results with different input values Including tagged+untagged events, similar as in last section Running with different strong phase values (all other parameters unchanged;  +  s = 60° ) Running with different B/S ratios for B s → D s K channel (all other parameters unchanged;  +  s = 60°, B s →D s - π + B/S value = 0.2 ) Δ T1/T2 ° -20020 σ(  +  s )° 11.210.310.4 Different strong phase input value B s →D s K B/S value 0.00.72.0 σ(  +  s )° 9.610.311.1 Different B/S input value for B s → D s K

27. 11th May 2007Shirit Cohen Master Colloquium27 Extra check: fitting mistag fraction & signal scale factor simultaneously Signal scale factor used for checking PT error estimation Mistag fraction and PT errors damp the B s oscillations Fitting both parameters simultaneously could be problematic, correlated effects Fitting the five regular floating parameters + signal scale factor Running 400 “experiments”, fits converge Decreased resolution on ω, signal scale resolution of ~10%. Weak, strong phase and Δm s resolutions remain unchanged. ParameterΔm s (ps) -1 ωArg(λ f ) rad |λf||λf| +s °+s ° Δ T1/T2 ° Signal scale factor input value17.50.3281.047-1.0470.376001.175 fitted value17.50.3281.05-1.040.3760.30.431.176 resolution 5y0.003 0.10.110.034.74.650.04 resolution 1y 0.0070.006 0.230.250.06 10.510.40.1 pull fitted mean0.03 -0.1 0.090.040.090.04 0.11 pull fitted sigma1 1.19 0.981.0711.01 1.28

28. 11th May 2007Shirit Cohen Master Colloquium28 Summary & conclusions Code for RooFit toy MC sensitivity studies developed Sensitivity results look good, pulls are fine Including untagged events improves the  +  s resolution 12° → 10° Expect LHCb to measure  (Δm s ) = 0.007(ps) -1 and  (  +  s ) = 10.3° for nominal input values CDF measurement Δm s = 17.77 ± 0.1(stat.) ± 0.07(syst.) ps -1 Obtained resolutions with different input values for strong phase and B s →D s K B/S ratio LHCb-2007-041, results quoted in the “Flavour at the era of LHC” Yellow Report

29. 11th May 2007Shirit Cohen Master Colloquium29 Backup slides

30. 11th May 2007Shirit Cohen Master Colloquium30 Outlook A possible scenario before the LHCb measurement of 

31. 11th May 2007Shirit Cohen Master Colloquium31 Outlook A possible scenario after the LHCb measurement of 

32. 11th May 2007Shirit Cohen Master Colloquium32 Backup I likelihood description extract from LHCb-2007-041 Total likelihood PDF models, smearing: mistag fraction, background, detector’s acceptance & resolution Likelihood function for B→f Physics parameters that go in

33. 11th May 2007Shirit Cohen Master Colloquium33 Fitting signal scale factor and mistag fraction simultaneously - pull distributions Backup II  +  s pull  pull S sig pull

34. 11th May 2007Shirit Cohen Master Colloquium34 The LHCb detector Non bending plane view

35. 11th May 2007Shirit Cohen Master Colloquium35 Interesting parameters D s π case: flavor specific decay, two decay diagrams exist. For this channel: λ f = λ f =0 (|A f |=|A f |), leads to D f =S f =0, C f =1. → Parameters to measure: Δm s, Δ Γ D s K case: non flavor specific decay, 4 decay diagrams exist, time dependent CP violation. | λ f |=| λ f |. → Parameters: |λ f |, arg(λ f ), arg(λ f ) to extract  +  s, Δ T1/T2 arg(λ f ) = Δ T1/T2 - (  +  s ) arg(λ f ) = Δ T1/T2 + (  +  s ) Assume |p/q|=1 Only 2 unique D s π equations 4 unique D s K equations B s → D s - π + (3.4±0.7)·10 -3 B s → D - s K + B s → D + s K - (2.0±0.6)·10 -4 (2.2±0.7)·10 -5 Estimated branching fraction % (used for DC04 selection study)

36. 11th May 2007Shirit Cohen Master Colloquium36 B s meson system b sb s t t WW V tb V ts V tb V ts * * b sb s tt W WV tb V ts V tb V ts * * flavour eigenstates mass eigenstates B s oscillations box diagrams mass eigenstates time dependence decay amplitude into a final state f,, decay amplitudes can be written as a sum, strong phase keeps value, weak phase changes sign under CP transformation

37. 11th May 2007Shirit Cohen Master Colloquium37 B s decay equations f : final state, D s - π + or D s - K + For charge conjugate final states: B → B, f → f, λ f → λ f, A f →A f, p/q → q/p B s →D s - π + B s →D s π physics decay model * In this project we assume |p/q|=1

38. 11th May 2007Shirit Cohen Master Colloquium38 Matter dominated universe Matter-anti matter difference in weak force, CP violating processes In the Standard Model via the quark-mixing (CKM) matrix, via its phases LHCb experiment designed to study CP violation, performing measurements in the b-quark sector Motivation for measuring the CKM phase 