1. Jeroen van Hunen (for the LHCb collaboration) The sensitivity to  s and  Γ s at LHCb

2. Nagoya, December 15, 2006. 4th International Workshop on the CKM Unitarity Triangle Jeroen van Hunen 2/19 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 vertices. good mass resolution and particle identification

3. Nagoya, December 15, 2006. 4th International Workshop on the CKM Unitarity Triangle Jeroen van Hunen 3/19  s in the Standard Model mixing : Standard Model box diagrams If only SM box diagrams mixing phase  and If NP contributions in B s mixing

4. Nagoya, December 15, 2006. 4th International Workshop on the CKM Unitarity Triangle Jeroen van Hunen 4/19 Measuring  s at LHCb These 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 -  - )  + Flavour-specific decay (control channel needed for determination of  M s and the wrong tag fraction)

5. Nagoya, December 15, 2006. 4th International Workshop on the CKM Unitarity Triangle Jeroen van Hunen 5/19 CP asymmetry in decays CP eigenstates with eigenvalues:  f =  1 CP : interference in mixing and decay (no direct CP) is dominated by a single weak phase The time-dependent CP asymmetry allows us to measure  s and  Γ s (but also untagged events give a sensitivity to  s  cos(  s ) term)

6. Nagoya, December 15, 2006. 4th International Workshop on the CKM Unitarity Triangle Jeroen van Hunen 6/19 Angular analysis (CP-odd/CP-even separation) R T = 0  CP even R T = 0.5  maximum dilution ( but still sensitivity to  s since odd and even contributions have different  tr distribution ) Measurements (Tevatron)  R T  0.2 (full angular analysis, i.e. with 3 angles, started) Complication for

7. Nagoya, December 15, 2006. 4th International Workshop on the CKM Unitarity Triangle Jeroen van Hunen 7/19 The LHCb MC simulation Geant Monte Carlo simulation with : A detailed and realistic detector and material description Realistic detector inefficiencies, noise hits, and effects of events from the previous bunch crossings Full trigger simulation, pattern recognition, and offline event selection

8. Nagoya, December 15, 2006. 4th International Workshop on the CKM Unitarity Triangle Jeroen van Hunen 8/19 Results on the event selections In summary (important for 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 Decay ChannelYield (evts/2fb - 1 ) B/S (fs)  mass (MeV/c 2 ) w tag (%)  tag (%) B s  J/  (  -  + )  (K + K - ) 131k0.1236143357 B s  c (h - h + h - h + )  (K + K - ) 3.0k0.630123166 B s  J/  (  -  + )  (  +  -  0 (  )) 3.0k3.034203062 B s  J/  (  -  + )  (  ) 8.5k2.037343563 B s  D s (K + K -  - ) D s (K + K -  + ) 4.0k0.35663457 B s  D s (K + K -  - )  + 120k0.440143163

9. Nagoya, December 15, 2006. 4th International Workshop on the CKM Unitarity Triangle Jeroen van Hunen 9/19 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 Proper time error distribution for the different decays

10. Nagoya, December 15, 2006. 4th International Workshop on the CKM Unitarity Triangle Jeroen van Hunen 10/19 Toy MC The sensitivities for  s and  Γ s are determined by making use of a fast parameterized MC. The results on the event selections from the full LHCb MC are used as input. The likelihood for the signal transitions is simultaneously maximized with the control sample (B s  D s  ). The wrong tag fraction (w tag ) is assumed to be the same for the control and signal sample. Performed ~200 toy experiments, where each experiment represents 2fb -1 (10 7 seconds 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 the tagged and untagged proper-time distributions (and for B s  J/  to the transversity angle,θ tr ). Standard model values are used as input

11. Nagoya, December 15, 2006. 4th International Workshop on the CKM Unitarity Triangle Jeroen van Hunen 11/19 The mass and  tr distributions Projection of the likelihood on mass distribution for B s  J/ . The mass peak is modeled by an exponential (background) and a Gaussian (signal). 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 of cos(  tr )).  =14 MeV /c 2

12. Nagoya, December 15, 2006. 4th International Workshop on the CKM Unitarity Triangle Jeroen van Hunen 12/19  s = 5  SM value The tagged proper time distributions Sensitivity to  s depends on D (tagging dilution) = 1-2w tag But  also sensitivity to  s with untagged events (w tag =0.5, D=0) from the cos(  s ) term, especially if  s is large. Include: Trigger and Selection bias on  Proper time resolution  s = 5  SM value Red solid line : tagged as initially Blue dashed : tagged as initially (Wrong tag fraction is included) (CP-even)

13. Nagoya, December 15, 2006. 4th International Workshop on the CKM Unitarity Triangle Jeroen van Hunen 13/19 The tagged proper time distributions Projection of the likelihood on the proper time distribution for B s  c  and B s  J/  (now with SM parameters) Blue solid : Total Red dotted : Signal Black dashed : Background B s  c  B s  J/  B s  c  : good proper time resolution  wiggles in the signal are visible B s  J/  : larger background, worse proper time resolution  flattens the wiggles Likelihood for the proper time distribution includes (from full MC) : acceptance function per-event-error for the decay time tagging performance exponential background function

14. Nagoya, December 15, 2006. 4th International Workshop on the CKM Unitarity Triangle Jeroen van Hunen 14/19 Results on the sensitivity to  s Additional studies ongoing : Channels ( sensitivity to  s with 2 fb -1 ) 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 Total LHCb sensitivity with 10 fb -1 : 0.01 rad  0.6 degrees (but statistical uncertainty only)

15. Nagoya, December 15, 2006. 4th International Workshop on the CKM Unitarity Triangle Jeroen van Hunen 15/19 ParameterSensitivity with 2 fb -1 Channels ss 0.021 rad B s  J/ , B s  c , B s  J/ , B s  D s D s Γs/ΓsΓs/Γs 0.0092 B s  J/  RTRT 0.00040 B s  J/  msms 0.007 ps -1 BsDs+BsDs+ w tag 0.0036 BsDs+BsDs+ The sensitivity to B s mixing parameters Input to the likelihood fit Control channel only

16. Nagoya, December 15, 2006. 4th International Workshop on the CKM Unitarity Triangle Jeroen van Hunen 16/19 Results on the sensitivity to  s The effect on the sensitivity of a degraded (   +10% ) or improved (   -10% ) 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

17. Nagoya, December 15, 2006. 4th International Workshop on the CKM Unitarity Triangle Jeroen van Hunen 17/19 Results on the sensitivity to  s Dependence of the  s sensitivity on the CP-odd fraction (R T ).  Sensitive to R T, but we still have a reasonable sensitivity if maximum dilution, i.e. R T =0.5. (full angular analysis will reduce dependence) Dependence of the  s sensitivity on  s /  s.  Not very sensitive to  s /  s. nominal

18. Nagoya, December 15, 2006. 4th International Workshop on the CKM Unitarity Triangle Jeroen van Hunen 18/19 Possible improvements for the sensitivity study Include the J/  e + e - events : ~20% increase of event yields Full angular analysis for B s  J/  Include additional B s decays (, ) Perform a combined fit with all signal channels Study the systematic uncertainty 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/ , etc.) by defining sub-samples with similar tagging performance. …

19. Nagoya, December 15, 2006. 4th International Workshop on the CKM Unitarity Triangle Jeroen van Hunen 19/19 Conclusions The LHCb sensitivity for  s is 0.02 rad (~1.2 degrees) 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 have interesting results on  s The value of  s is not known precisely We aim for a  s result in 2008!

20. Nagoya, December 15, 2006. 4th International Workshop on the CKM Unitarity Triangle Jeroen van Hunen 20/19 Backup: Tree and Penguin Diagrams The transitions are dominated by a single weak phase :