1. Peter Fauland (for the LHCb collaboration) The sensitivity for the B S - mixing phase  S at LHCb

2. Monday, October 30, 2006 DPF / JPS 2006, Honolulu, Hawaii Peter Fauland 2/22   s in the standard model  Measuring  s at LHCb  The LHCb MC simulation  Results on the sensitivity to  s (using Toy MC) Outline

3. Monday, October 30, 2006 DPF / JPS 2006, Honolulu, Hawaii Peter Fauland 3/22  s in the standard model Mixing : Standard model box diagrams (  F=2 transitions) If only SM box diagrams Mixing phase  and If NP contributions in B s mixing

4. Monday, October 30, 2006 DPF / JPS 2006, Honolulu, Hawaii Peter Fauland 4/22  s in the standard model Wolfenstein parameterization of the CKM matrix ( V us, A, ,  ) Thus  in the B s system corresponds to  in the B d system (therefore  is also referred to as  s ) B d -system well measured, but B s -system (  M s,  s, , |p/q|) not fully explored  LHCb will have a large statistics

5. Monday, October 30, 2006 DPF / JPS 2006, Honolulu, Hawaii Peter Fauland 5/22 CP asymmetry The time dependent CP asymmetry allows us to measure  s. CP eigenstates with eigenvalues:  f =  1 CP : interference in mixing and decay (no direct CP) is dominated by a single weak phase  q  0 (with  q  0)

6. Monday, October 30, 2006 DPF / JPS 2006, Honolulu, Hawaii Peter Fauland 6/22 Measuring  s at LHCb The following B s -decays have been used to determine the LHCb sensitivity to  s : Thus : measure the B s mixing phase  s and see if it agrees with SM expectation from the box diagrams (check if  s  -2  = -2 2   -0.04) B s  J/  (  -  + )  (K + K - ) CP-odd and CP-even eigenstates B s  c (h - h + h - h + )  (K + K - ) CP-even eigenstate B s  J/  (  -  + )  (  ) CP-even eigenstate B s  J/  (  -  + )  (  +  -  0 (  )) CP-even eigenstate B s  D s (K + K -  - ) D s (K + K -  + ) CP-even eigenstate B s  D s (K + K -  - )  +  M s determination, wrong tag fraction, Control Channel

7. Monday, October 30, 2006 DPF / JPS 2006, Honolulu, Hawaii Peter Fauland 7/22 Angular analysis (CP-odd/CP-even separation) R T = 0  CP even R T = 0.5  maximum dilution ( but still some sensitivity to  s since odd and even contributions have different  tr distribution ) Measurements  R T  0.2 Complication for: Decay into two vector particles The angular distribution is used to separate odd and even components

8. Monday, October 30, 2006 DPF / JPS 2006, Honolulu, Hawaii Peter Fauland 8/22 The LHCb experiment LHCb under construction. It’s real! LHCb Single arm spectrometer with: good vertexing/tracking for reconstruction of the primary and B-decay vertex. good particle identification

9. Monday, October 30, 2006 DPF / JPS 2006, Honolulu, Hawaii Peter Fauland 9/22 The LHCb MC simulation The results in the next slides have been obtained with the LHCb Monte Carlo simulation. Detailed and realistic detector and material description Full pattern recognition, trigger simulation (also HLT), and offline event selection. Realistic detector inefficiencies, noise hits, and effects of events from the previous bunch crossings Geant simulated event

10. Monday, October 30, 2006 DPF / JPS 2006, Honolulu, Hawaii Peter Fauland 10/22 Results on the event selections Yield (10 3 /2 fb -1 ) B/S (fs)  mass (MeV/c 2 ) w tag (%)  tag (%) B s  J/  (  -  + )  (K + K - ) 1310.1236143357 B s  c (h - h + h - h + )  (K + K - ) 30.630123166 B s  J/  (  -  + )  (  ) 8.52.037343563 B s  D s (K + K -  - ) D s (K + K -  + ) 4.00.35663457 B s  D s (K + K -  - )  + 1200.440143163 The sensitivity to  s : B s  J/  : Large yield, but mixture of CP-odd and CP-even eigenstates. B s  J/  ( ’ ), B s  c  : Low yield, high background, but CP-even. B s  D s D s : Low yield, worse proper time resolution, but CP-even.

11. Monday, October 30, 2006 DPF / JPS 2006, Honolulu, Hawaii Peter Fauland 11/22 Results on the event selections BsBs ++ K+K+ K-K- DsDs PV  -- K+K+ K-K- DsDs BsBs K+K+ h-h- h+h+ K-K-  h-h- h+h+  cc

12. Monday, October 30, 2006 DPF / JPS 2006, Honolulu, Hawaii Peter Fauland 12/22 Sensitivity Studies using Toy MC As input the results from the full LHCb MC are used. The likelihood for the signal transitions is simultaneously optimized with the control sample (B s  D s  ). The tagging performance is assumed to be the same for the control and signal sample. The statistical uncertainty of control channel is thus included. Perform ~200 toy experiments, where each experiment represents 2fb -1 of data taking (10 7 s at 2  10 32 cm 2 s -1 ). The RMS of the  s distribution is given as the sensitivity. The CP parameters are extracted by performing a likelihood fit to the mass and proper time distributions (and to the transversity angle for B s  J/  ). Standard model values are used as input

13. Monday, October 30, 2006 DPF / JPS 2006, Honolulu, Hawaii Peter Fauland 13/22 Modeling the mass and  tr distributions Projection of the likelihood on mass distribution for B s  J/ . The mass peak is modeled by an Gaussian signal over an exponential background. Projection of the likelihood on the transversity angle distribution for B s  J/ . Blue=total, red dotted = CP-even, red dashed =CP-odd, black=background (is assumed to be independent on  tr.

14. Monday, October 30, 2006 DPF / JPS 2006, Honolulu, Hawaii Peter Fauland 14/22  s is 5  SM value Modeling the tagged proper time distributions Sensitivity to  s depends on D (tagging dilution factor) = 1-2w tag But  also sensitivity if we have untagged events (w tag =0.5, D=0) trough cos(  s ) term Include: Trigger and Selection bias on  Proper time resolution  s is 5  SM value Red solid line : tagged as initially Blue dashed : tagged as initially (Wrong tag fraction is included) For illustration only !

15. Monday, October 30, 2006 DPF / JPS 2006, Honolulu, Hawaii Peter Fauland 15/22 Modeling the tagged proper time distributions Projection of the likelihood on the proper time distribution Blue solid : Total Red dotted : Signal Black dashed : Background B s  c  (Standard model parameters) B s  J/  (Standard model parameters) B s  c  : better proper time resolution  wiggles in the signal are visible B s  J/  : higher background  flattens the wiggles Likelihood for the proper time distribution includes: acceptance function (full MC) per-event-error for the proper time (full MC) tagging performance exponential background function

16. Monday, October 30, 2006 DPF / JPS 2006, Honolulu, Hawaii Peter Fauland 16/22 Results on the sensitivity to  s Additional studies ongoing : The LHCb sensitivity for  s with 2 fb -1 Total LHCb sensitivity with 10 fb -1 : 0.01 rad = 0.6 degrees (but statistical uncertainty only) Channels 0.133 2.6 0.142 2.8 0.109 3.9 0.108 3.9 Combined sensitivity for pure CP eigenstates 0.059 13.2 0.023 86.8 Combined sensitivity for all CP eigenstates (  ) 0.021 100.0

17. Monday, October 30, 2006 DPF / JPS 2006, Honolulu, Hawaii Peter Fauland 17/22 The sensitivity for  s,  M s,  s /  s, R T, w tag with 2fb -1 Only Control sample used. Input to the likelihood fit

18. Monday, October 30, 2006 DPF / JPS 2006, Honolulu, Hawaii Peter Fauland 18/22 Results on the sensitivity to  s The effect of an improved or degraded proper time resolution (   ). And the effect of a larger B/S Dependence of the  s sensitivity on  s (It has been checked that the sensitivity does not depend on the sign of  s ) SM

19. Monday, October 30, 2006 DPF / JPS 2006, Honolulu, Hawaii Peter Fauland 19/22 Possible improvements for the sensitivity at LHCb Include the J/  e + e - events: expect ~20% increase of event yields Full angular analysis for B s  J/  Perform a combined fit with all signal channels Study the systematic uncertainty (extract proper time resolution from data) Optimize the use of the control sample (B s  D s  ) for the determination of the tagging performance of the signal samples (B s  J/ , B s  c , B s  J/  ( ’ ), B s  D s D s ) (define sub-samples with the similar tagging performance)

20. Monday, October 30, 2006 DPF / JPS 2006, Honolulu, Hawaii Peter Fauland 20/22 Conclusions The value of  s is not known very well ! The LHCb sensitivity for  s is 0.02 rad for 2 fb -1 Small dependence of the sensitivity on  s /  s and  s. After a few years of data LHCb will be able to measure also a SM  s. Already with a small data sample (~0.2 fb -1 ) we will have interesting results on  s. We aim for a  s result in 2008!

21. Monday, October 30, 2006 DPF / JPS 2006, Honolulu, Hawaii Peter Fauland 21/22 Thank you...

22. Monday, October 30, 2006 DPF / JPS 2006, Honolulu, Hawaii Peter Fauland 22/22 Results on the sensitivity to  s Dependence of the  s sensitivity on the CP-odd fraction (R T ). The world average is 0.167  0.041.  very sensitive to R T, but we still have a reasonable sensitivity if maximum dilution (i.e. R T =0.5) Dependence of the  s sensitivity on  s /  s. The world average is 0.14  0.06.  not very sensitive to  s /  s. nominal

23. Monday, October 30, 2006 DPF / JPS 2006, Honolulu, Hawaii Peter Fauland 23/22