1. Gavril Giurgiu, Carnegie Mellon 1 B s Mixing at CDF Seminar at Fermi National Accelerator Laboratory Gavril Giurgiu Carnegie Mellon University August 16, 2005

2. Gavril Giurgiu, Carnegie Mellon 2 Outline Introduction B mixing phenomenology CDF detector and B Physics triggers B mixing analysis overview –semileptonic and hadronic B s signals –decay time –B s lifetime –flavor tagging –B 0 mixing and tagging calibration –B s semileptonic and hadronic amplitude scans Conclusions and outlook

3. Gavril Giurgiu, Carnegie Mellon 3 Introduction In the Standard Model, the charged current interactions of quarks are described by the Lagrangean: The weak eigenstates d’, s’ and b’ are linear combinations of the mass eigenstates d, s and b and the quark mixing is given by the CKM matrix: The Standard Model does not predict the values of CKM elements. We have to measure them. B 0 and B s oscillations provide information on V td and V ts

4. Gavril Giurgiu, Carnegie Mellon 4 B Mixing Phenomenology Neutral B system: Mass eigenstates: Oscillation frequency of B q mesons given by  m q = M H - M L Width (lifetime) difference    H  L Neglecting , mixing probability after time t is give by: Asymmetry:

5. Gavril Giurgiu, Carnegie Mellon 5 B Mixing Phenomenology (cont) Although  m d is well measured (0.502  0.007 ps -1 ) determination of V td is affected by ~20% error due to large uncertainties on different parameters In the ratio between  m d and  m s many common parameters cancel B 0 /B s oscillations are described by top quark exchange box diagrams  m q and V tq (q=d,s) are related by known parameters

6. Gavril Giurgiu, Carnegie Mellon 6 Unitarity Triangle Knowledge of both B d and B s mixing frequencies would provide better constraints on one side of unitarity triangle: In the complex plane, the unitarity relation is represented by a triangle Re Im B → J/ψ K s b → u decays B 0 /B s mixing The CKM matrix is unitary: One of the six unitarity relations:

7. Gavril Giurgiu, Carnegie Mellon 7 Current B s Status B s mixing not observed yet B s oscillates more than 30 times faster than B d  experimental challenge At 95% C.L. lower limit  m s > 14.4 ps -1 with sensitivity of 17.8 ps -1 CKM triangle global fit:

8. Gavril Giurgiu, Carnegie Mellon 8 CDF Detector

9. Gavril Giurgiu, Carnegie Mellon 9 CDF Detector – Schematic View Plug Calorimeter 1.3 < |  | < 3.5 Central Tracker (COT) |  | < 1.0 dE/dx for PID Time of Flight for K/p separation placed before 1.4 Tesla Solenoid Electromagnetic and Hadronic calorimeters Silicon Detector |  | < 2.0 Muon Detectors |  | < 1.0

10. Gavril Giurgiu, Carnegie Mellon 10 B Physics at the Tevatron The b cross section is 10 3 times larger than at the e + e - machines B s mesons are only produced at Tevatron The total inelastic cross section is about 60 mb while the b production cross section in the central region is:  b, |y|<0.6  b Need triggers to select the b events

11. Gavril Giurgiu, Carnegie Mellon 11 Silicon Vertex Trigger (SVT) Silicon Vertex Trigger is designed to select b events - Implemented at Level 2 -Uses silicon detector information and beamline position to determine the track impact parameter -Good impact parameter resolution ~ 47  m: ~33  m beam size  ~30  m intrinsic SVT resolution -Trigger on displaced track

12. Gavril Giurgiu, Carnegie Mellon 12 SVT Triggers for B Physics Semileptonic (partially reconstructed) decays: B s  lepton D s X - large number of events - decay time resolution degraded due to missing neutrino - triggered by 4 GeV lepton and displaced track with impact parameter |d 0 |>120  m and |d 0 |<1 mm Hadronic (fully reconstructed) decays: B s   D s - smaller number of events - good decay time resolution - triggered by two displaced tracks with impact parameter |d 0 |>120  m and |d 0 |<1 mm d0d0 d0d0 d0d0

13. Gavril Giurgiu, Carnegie Mellon 13 Mixing Analysis Overview Mixing analysis ingredients: - Signal reconstruction - Decay time - B flavor at decay - B flavor at production inferred through flavor tagging: - lepton tags - jet charge tags Statistical significance of  m s measurement: Tagging Signal Reconstruction Decay time resolution Sig

14. Gavril Giurgiu, Carnegie Mellon 14 Semileptonic B s Signals Missing neutrino  cannot see B s mass peak Use D s mass peak and (lepton, D s ) charge correlation: l + D - - right sign combination l - D - - wrong sign combination Decay modes: D s    ( 4355  94 ) D s  K*K ( 1750  83 ) D s  3  ( 1573  88 ) Total of 7000 B s candidates but ~18% come from “Physics backgrounds”

15. Gavril Giurgiu, Carnegie Mellon 15 Semileptonic B s Signals (cont) D s  K*K ( 1750  83 )D s  3  ( 1573  88 )

16. Gavril Giurgiu, Carnegie Mellon 16 Physics Backgrounds Originates from real B decays: B 0/+  D s D (~13%) B s  D s  (~2%) (D /  / D (s)  lepton X) B s  D s D (s) (~3%) In each case we observe the same decay signature as in B s  D s lepton The decay time distributions and the reconstruction efficiencies are obtained from MC Each decay time distribution is weighted in the maximum likelihood fit using the measured branching fractions and reconstruction efficiencies

17. Gavril Giurgiu, Carnegie Mellon 17 Hadronic B s Signals All final state particles reconstructed  observe B s mass peak Decay modes: D s    ( 526  33 ) D s  K*K ( 254  21 ) D s  3  ( 116  18 ) Total of 900 B s candidates Satellite peak: B s  D s *  (D s *  D s X)

18. Gavril Giurgiu, Carnegie Mellon 18 Hadronic B s Signals (cont) D s  K*K ( 254  21 )D s  3  ( 116  18 )

19. Gavril Giurgiu, Carnegie Mellon 19 Decay Time Decay time: In semileptonic modes missing neutrino is statistically corrected by: Hadronic decays do not need momentum correction

20. Gavril Giurgiu, Carnegie Mellon 20 To resolve the fast B s oscillations we need excellent decay time resolution Hadronic decays Semileptonic decays (fully reconstructed): (partially reconstructed): Decay Time Resolution

21. Gavril Giurgiu, Carnegie Mellon 21 Decay Time Bias Because: (1) In both hadronic and semileptonic decays the triggers require displaced tracks (2) B s events are selected based on decay distance cuts the B s decay time distribution is biased Efficiency as function of decay time obtained from Monte Carlo:

22. Gavril Giurgiu, Carnegie Mellon 22 Lifetime Measurement As a cross check of analysis framework measure B s lifetime Lifetime fit projections in both hadronic and semileptonic modes Semileptonic: c  (B s ) = 443  10 (stat)  xxx (syst)  m Hadronic: c  (B s ) = 479  29 (stat)  5 (syst)  m Good agreement with PDG 2004: c  (B s ) = 438  17  m

23. Gavril Giurgiu, Carnegie Mellon 23 Flavor Tagging For B s mixing analysis at CDF we used 5 opposite side flavor taggers Tag inferred from opposite side B in event: - muon and electron tag (semileptonic decay of opposite B) - three jet charge tag types: - displaced vertex - displaced tracks - high p T Tagging power given by  D 2 where  is the tagging efficiency and D = 1 – 2 P mistag is the tagging dilution P mistag – mistag probability Large dilution (D) means high tagging power Knowledge of the dilution dependence on different quantities enhances tagging power Trigger B meson

24. Gavril Giurgiu, Carnegie Mellon 24 Lepton Identification Combine different quantities in a global likelihood function which gives the probability that a lepton is real Example: for muon identification we use five quantities: 3 matching variables between extrapolated track and muon stub (  X, ,  Z) 2 calorimeter variables (electromagnetic and hadronic energies) Obtain real muon templates from J/ψ→  and fake muon templates from  →p  where the proton matches to a muon stub  X: Hadronic energy: Likelihood:

25. Gavril Giurgiu, Carnegie Mellon 25 Lepton Tagging We use an inclusive lepton-SVT sample to determine the dilution of muon and electron taggers as function of: - lepton likelihood (probability that lepton is real) - (transverse momentum of lepton w.r.t jet axis) Electron tag Muon tag

26. Gavril Giurgiu, Carnegie Mellon 26 Dilution of jet charge tagger is calculated as function of - the jet charge: d i - displacement of track i w.r.t the primary vertex - three jet charge tag types: displaced vertex, displaced track and high momentum Jet Charge Tagging Combined tagging power of all five opposite side taggers (lepton + jet charge):  D 2  1.6 % calculated on inclusive lepton-SVT sample

27. Gavril Giurgiu, Carnegie Mellon 27 Measurement of  m d and Tagger Calibration Perform measurement of  m d Since we observe B 0 oscillations, we can also measure tag dilutions Analyze hadronic and semileptonic decays of B 0 and B + : B 0  D +   B +  D 0   B 0  J/  K *0 B +  J/  K + B 0 /+  D - l + X B 0 /+  D -* l + X B + /0  D 0 l + X Event by event predicted dilution (D) Fit the dilution calibration factor (S) for each of 5 tag types Dilution calibration factors are used for the B s mixing analysis Dilution Calibration Factor Event by event dilution

28. Gavril Giurgiu, Carnegie Mellon 28 B 0 /B + Semileptonic Signals B mesons are identified by vertexing the trajectory of a D meson with a lepton track Each lepton-D signature is a mixture of B 0 and B + B → l + D 0 X, D 0 → K +  - B → l + D -, D - → K +  -  - B → l + D* -, D* - → D 0  - ~100000 events ~52000 events ~25000 events B 0 /B + ~ 20/80 B 0 /B + ~ 85/15 B 0 /B + ~ 85/15

29. Gavril Giurgiu, Carnegie Mellon 29 B 0 /B + Hadronic Signals B 0 → D -  +, D - → K +  -  - B + → D 0  +, D 0 → K +  - ~6200 events ~5600 events The “double horn” structures on the low mass sidebands comes from partially reconstructed B mesons. Example: B + → D* 0  +, D* 0 → D 0  0

30. Gavril Giurgiu, Carnegie Mellon 30  m d Results Hadronic:  m d = (0.503±0.063±0.015) ps - 1 Dilution calibration factors: S(muon) = 0.83±0.10±0.03 S(electron) = 0.79±0.14±0.04 S(vertex) = 0.78±0.19±0.05 S(track) = 0.76±0.21±0.03 S(high p T ) = 1.35±0.26±0.02 Total  D 2 ~ 1.1% Semileptonic:  m d = (0.498±0.028±0.015) ps -1 Dilution calibration factors: S(muon) = 0.93±0.04±0.03 S(electron) = 0.98±0.06±0.03 S(vertex) = 0.97±0.06±0.04 S(track) = 0.90±0.08±0.05 S(high p T ) = 1.08±0.09±0.09 Total  D 2 ~ 1.4% Muon Tags World average:  m d = 0.502  0.007 ps -1

31. Gavril Giurgiu, Carnegie Mellon 31 Amplitude Scan Method Introduce Fourier coefficient A (amplitude) Fix  m s at different test values and fit for A: (Moser et.al., NIMA 384 491) A  1 for true value of  m s A  0 away from true value Toy MC test with  m s = 10 ps -1 and simulated sample 10x larger than real data - points: A  1  - yellow band: A  1.645  - dotted line: 1.645  - yellow band bellow 1  exclusion at 95% CL

32. Gavril Giurgiu, Carnegie Mellon 32 B s Analysis Performed “blind” analysis by randomizing the tag decision: tag = tag  (-1) event number Evaluate sensitivity and systematic uncertainties from “blind” analysis Systematic errors evaluated using pseudo-experiments: - include all variables and distributions determined from data - fit the toy sample with different Likelihood configurations - use variations in Amplitude (  A) and statistical error (  A ) to derive the systematic error:

33. Gavril Giurgiu, Carnegie Mellon 33 Semileptonic Amplitude Scan Measurement is statistics dominated Main systematic uncertainties from prompt background and from Physics background Sensitivity: 7.4 ps -1 Limit:  m s > 7.7 ps -1 at 95% C.L.

34. Gavril Giurgiu, Carnegie Mellon 34 Hadronic Amplitude Scan Measurement is statistics dominated Main systematic errors come from tagger calibration Sensitivity: 0.4 ps -1 Limit:  m s > 0.0 ps -1 at 95% C.L.

35. Gavril Giurgiu, Carnegie Mellon 35 Combined CDF result on  m s After combining semileptonic and hadronic modes: Sensitivity: 8.4 ps -1 Limit:  m s > 7.9 ps -1 With full B s momentum reconstruction, hadronic mode will dominate the measurement at high  m s

36. Gavril Giurgiu, Carnegie Mellon 36 Conclusions 95% C.L.  m s limits from CDF: Semileptonic: 7.4 ps -1 Hadronic: 0.0 ps -1 (will become important at high  m s with more statistics) Combined limit: 7.9 ps -1, sensitivity: 8.4 ps -1 Results will substantially improve soon: - Same side Kaon tagger - Improve decay time resolution in hadronic modes - Add more data Updated analyses expected soon

37. Gavril Giurgiu, Carnegie Mellon 37 Sensitivity Projections Use analytical formula to predict sensitivity as a function of B s yield current: no improvement, baseline: +1%  D 2 and 10% improvement in decay time resolution stretched: +3%  D 2 and 20% improvement in decay time resolution 25ps -1 only in semileptonic case

38. Gavril Giurgiu, Carnegie Mellon 38 Amplitude Scan Method (cont) Test amplitude method on B 0 oscillations by scanning for  m d in hadronic modes zoom in