1. 1 Track reconstruction and physics analysis in LHCb Outline Introduction to the LHCb experiment Track reconstruction → finding and fitting Physics analysis → event selection and sensitivity study More details in my thesis: Track simulation and reconstruction in LHCb Seminar: Particle and Astrophysics U Zürich, Physik Institut 07 December 2005, Jeroen van Tilburg, NIKHEF

2. 2 Reminder: CP violation CKM matrix Complex phases in matrix elements → CP violation CKM matrix connects the quark mass eigenstates with the weak interaction eigenstates ~ e -iβ ~ e iχ ~ e -iγ

3. 3 The LHC tunnel The LHCb detector CERN, Geneva The Large Hadron Collider

4. 4 The LHCb detector ~1.4  1.3 m 2 ~6  5 m 2 VELO 21 stations R and φ sensors

5. 5 Different track types, different algorithms Velo tracks:used to find primary vertex. Long tracks:used for most physics studies: B decay products. T tracks:improve RICH2 performance. Downstream tracks:enhance K S finding. Upstream tracks:improve RICH1 performance, moderate p estimate Track types

6. 6 Track event display VELO TT T2T3T1 Outer tracker station Average # of tracks in b-events: 34 VELO, 33 long, 19 T tracks, 6 upstream, 14 downstream + Total106 reconstructed tracks

7. 7 Example: Matching algorithm Matches T tracks with VELO tracks to find long tracks: → estimate momentum of T track → extrapolate T track through magnet to the VELO → find best match (based on χ 2 cut). → add TT hits

8. 8 Matching algorithm: estimate p z magnet VELO T stations T seed zczc p-kick p-kick method Estimate momentum of the T track with p-kick method: → Magnetic field is ~ an instant kick at focal plane z=z magnet. → Assume track originates from interaction point. → Re-evaluate center of magnet (z c ). δp/p=0.7% Bdl ~ 4.2 Tm

9. 9 Matching χ 2 Efficiency = 91.2% Wrong combinations = 4.8% p > 5 GeV

10. 10 Adding TT hits for matched tracks → Extrapolate matched tracks to TT stations. → Group the hits depending on distance to track. → Find best group of TT hits. Group the hits: Distance d to track < 10 mm Δd in same station < 1 mm Δd in other station < 2 mm Group has at least 3 hits Hit can belong > 1 group

11. 11 Adding TT hits Select the group with the lowest q 2. Tune w spread q 2 = d 2 + w 2 spread s d 2 Average distance of group Distance deviation of group

12. 12 Long track performance Average number of hits: 12.7 VELO, 3.0 TT, 2.4 IT, 17.5 OT + Total 35.6

13. 13 Long track performance efficiency ghost rate ε = 94.3% (p>5 GeV) g = 7.7% (p>5 GeV)

14. 14 Tracking robustness Tracking is robust against number of interactions relative multiplicity

15. 15 Track fit The Kalman Fit properties: Adds measurements recursively. Mathematically equivalent to least χ 2 method. Multiple scattering and energy loss can be naturally included. The tracks are fitted using the Kalman Filter. prediction stepfilter step

16. 16 Outlier removal Outliers (hits with high χ 2 contribution) can be removed. → requires a refit → remove only 1 hit per iteration

17. 17 Outlier removal (long tracks) Improves χ 2 distribution Number of iterations

18. 18 Fit quality (long tracks)

19. 19 Momentum resolution LHCb provides an excellent momentum estimate at the vertex. Note: Fitted with single Gaussian in each bin. Reconstructed tracks Ideal tracks

20. 20 Impact parameter @ vertex

21. 21 Physics analysis Two benchmark decay channels of LHCb: 1. B s → D s π measures Δm s (B s oscillation frequency) 2. B s → D s Kmeasures γ-2χ (CP violation) For my thesis I studied the event selection for these decays, and the final sensitivity on Δm s and γ-2χ

22. 22 Branching fractions Decay channelBranching fractionAnnual production B s → D s ± π ± 1.2 * 10 -4 26 M events B s → D s ± K ± 1.0 * 10 -5 2.1 M events Event topology

23. 23 B s → D s * K and B s → D s K * Event topology Included two similar channels: K *± → K 0 π ± (67%) → half decays to K s 0 K ± π 0 (33%) D s *± → D s ± γ (94%) B s → D s * K and B s → D s K *

24. 24 Selection strategy 1.Preselection to reduce background → using standard LHCb applications ( DaVinci and LoKi ) 2.Remove specific backgrounds → using a single cut 3.Tune remaining cuts against generic background → using an optimisation tool

25. 25 1. Preselection Loose cuts

26. 26 2. Specific background B s →D s π background in B s →D s K selection → cut on RICH likelihood

27. 27 2. Specific background For instance, cut at ΔlnL Kπ =3 gives: Fit both mass distributions simultaneously to find the number of signal events (S) and its error (σ S ). ±50 MeV

28. 28 2. Specific background Vary ΔlnL Kπ cut to find the optimum with respect to the statistical significance of the signal:

29. 29 3. Generic background Optimisation tool: Optimise remaining cuts simultaneously Divide each selection variable into equidistant bins. Scan the total selection space. Find the combination of cuts for which is maximal.

30. 30 Final selection cuts

31. 31 Efficiencies and yield Low yield Need to cut harder due to high background Lower detection efficiency Efficiencies quoted in %.

32. 32 Decay time resolution and pull Pull distributionResolution

33. 33 Acceptance function After selection and trigger Selection and trigger cuts reduce efficiency at zero decay time

34. 34 Sensitivity study MatterAntimatter

35. 35 Sensitivity study Use Toy Monte Carlo and Fitting Program: Generate events according to expected annual yield and with realistic time errors from full simulation. Account for acceptance function. Perform an unbinned likelihood fit to “observed” decay time distribution. Fit both B s →D s π and B s →D s K events simultaneously.

36. 36 “Observed” decay times B s →D s K 3 years

37. 37 Default parameters

38. 38 Computing power Submitted ~10k jobs (=experiments) on the DataGrid:

39. 39 Oscillation frequency Sensitivity on Δm s Δm s deviation for 100 “experiments”: Amplitude method: After 1 year

40. 40 Sensitivity on weak phase Sensitivity for 100 “experiments” after 3 years. Weak phase: γ-2χ Error bars represent RMS fluctuation. 1 year: σ = 15.2º

41. 41 Conclusions Different track reconstruction algorithms developed for the different track types (e.g. the matching algorithm). The LHCb experiment provides an efficient track reconstruction of 94% with a ghost rate of 8% (p>5 GeV). LHCb has an excellent spatial (42 um) and momentum resolutions (0.35%) at the interaction point. Three-step event selection for B s →D s π and B s →D s K provides a sufficient background reduction. After 1 year of running LHCb can measure Δm s up to 88 ps -1 and γ-2χ with an error of 15.2º.