1. ICFP 2005, Taiwan Colin Gay, Yale University B Mixing and Lifetimes from CDF Colin Gay, Yale University for the CDF II Collaboration

2. ICFP 2005, Taiwan Colin Gay, Yale University Outline Status of B lifetimes Bs “lifetime” and lifetime difference Bs mixing

3. ICFP 2005, Taiwan Colin Gay, Yale University State of Lifetime Heavy Quark Expansion predicts B +, B 0 in ok shape  b a bit below expectation B s on edge More on this later  /(B 0 ) Expt/(B 0 ) Theory B0 1.528 ± 0.009 ps B+ 1.643 ± 0.010 ps 1.076 ± 0.0081.06±0.02 Bs 1.405 ± 0.045 ps 0.920 ± 0.0301.00±0.01 BB 1.232 ± 0.072 ps 0.806 ± 0.0470.86±0.05

4. ICFP 2005, Taiwan Colin Gay, Yale University Lifetime/Mixing samples SemileptonicHadronic Easy to trigger () 100s–1000s events Eg High pt lepton Missing complicates ~2k-100k evts Eg Low pt lepton + displaced track ~8k events Eg Two displaced tracks ~500-10k events Eg lifetime Unbiased trigger lifetime biased trigger Mixing

5. ICFP 2005, Taiwan Colin Gay, Yale University Measuring Lifetime For fully reconstructed (hadronic) modes Vertex resolution (~constant) Momentum resolution (proportional to ct) For semileptonic modes, missing neutrino causes => Resolution poor at large decay time Important effect for Bs mixing Flight distance Boost proper decay length

6. ICFP 2005, Taiwan Colin Gay, Yale University Fully Reconstructed J/ X Easy to trigger on, large samples, unbiased in lifetime Fully reconstructed modes Excellent vertex and momentum resolution CDF Fully reconstructs J/+ B +  J/K + B 0  J/K*, J/K s B s  J/  b  J/ For example: See summary following for detailed results 1155 § 39 signal

7. ICFP 2005, Taiwan Colin Gay, Yale University Lifetimes from hadronic decays To get large samples of fully reconstructed hadronic decays, we use events recorded via the Secondary Vertex Trigger Requires 2 tracks with impact parameters between 120m and 1mm Trigger has intrinsic lifetime bias Events have excellent momentum and vertex resolutions Final states reconstructed: B ±  D 0  ± (D 0  K) N=8380 evts B 0  D ±   D ±  K) N=5280 evts  D ± 3(D ±  K)N=4173evts Bs  Ds  ± (Ds  ) N=465 evts  Ds 3 (Ds  ) N=133 evts B - ct-efficiency B- D0-B- D0- Larger statistics than J/ modes Larger systematics due to Trigger Efficiency curve Larger backgrounds

8. ICFP 2005, Taiwan Colin Gay, Yale University Lifetimes from hadronic decays B+B+ BsBs BsBs  (B + ) = 1.661±0.027±0.013 ps  (B s ) = 1.598±0.097±0.017 ps  (B 0 ) = 1.511±0.023±0.013 ps

9. ICFP 2005, Taiwan Colin Gay, Yale University Lifetime with high-pt Semileptonic sample Trigger on 8 GeV lepton Reconstruct High statistics, but missing neutrino -> “K” factor  (B + ) = 1.653±0.029±0.032 ps  (B s ) = 1.381±0.055±0.046 ps  (B 0 ) = 1.473±0.036±0.054 ps

10. ICFP 2005, Taiwan Colin Gay, Yale University B Mass & Lifetime Difference Second order weak diagram gives non-zero matrix element In basis have a non-diagonal Hamiltonian Recall Eigenstates are:

11. ICFP 2005, Taiwan Colin Gay, Yale University B s “lifetime” meaning E.g. lifetime measured in SL decays dominates the average Unphysical value => most likely With the constraint (HQE says equal to 1%) When a significant  exists, lifetime measurements are sample composition dependent Measured lifetime is where = fraction of light state

12. ICFP 2005, Taiwan Colin Gay, Yale University Extracting both B s lifetimes In previous cases, the sample composition, and hence relation of depends upon the unknown In the case of the hadronic decays, there is the additional effect that the trigger turn-on affects the short-lived component of the B s more than the long-lived There is a decay in which one can measure, simultaneously, the light- heavy sample composition AND each components’ lifetime: S,D wave amplitudes = Parity Even, (CP Even) P wave amplitude = Parity Odd, (CP Odd) Since the mass eigenstates of the B s system are Disentangle different L-components of decay amplitudes => isolate two B states See D0 talk for details

13. ICFP 2005, Taiwan Colin Gay, Yale University Two Lifetimes CP-odd fraction ( ) ~ 22% + Recent D0:

14. ICFP 2005, Taiwan Colin Gay, Yale University The two Lifetimes Constraint helps low statistics  H Note that

15. ICFP 2005, Taiwan Colin Gay, Yale University Experiments vs. Theory Flavor-specific “lifetime” (SL) CDF D0 Theory Preferred Theory:

16. ICFP 2005, Taiwan Colin Gay, Yale University Combined CDF/D0 Fit

17. ICFP 2005, Taiwan Colin Gay, Yale University Lifetimes: CDF Summary J/  modes Hadronic modesSemileptonic modesHFAG 2005 B0 1.539±0.051±0.0081.511±0.023±0.0131.473±0.036±0.0541.528 ± 0.009 B+ 1.662 ± 0.033±0.0081.661 ± 0.027±0.0131.653±0.029±0.0321.643 ± 0.010 Bs 1.369±0.100±0.0091.598±0.097±0.017 1.381±0.055±0.0461.405 ± 0.045 BB 1.25±0.26±0.10 1.232 ± 0.072

18. ICFP 2005, Taiwan Colin Gay, Yale University Mixing Analysis Strategy Just like a lifetime measurement, but look for change of B particle to antiparticle Mixing B s or B s at production? Initial state flavor tagging (calibrated on B 0 ) Tagging dilution D=1-2w, w=mistag prob. Effective sample N D 2 (D 2 ~1%) B s or B s at decay? Decays are self-tagging (eg ) Reconstruct proper decay time Kaon Fit Asymmetry (N unmixed -N mixed )/ N to D*A*cos(m t) at fixed m Expect A=1 for m ~ m s Limit (95% CL): m such that A+1.645 A = 1

19. ICFP 2005, Taiwan Colin Gay, Yale University Flavor Tagging + Signals Opposite side tagging Use the other B in the event Semileptonic decay (b  l - ) (1) Muon, (2) Electron Use jet charge (Q b = -1/3) (3) Jet has 2ndary vertex (4) Jet contains displaced track (5) Highest momentum Jet Calibrated on B 0 Opposite side B Reconstructed B Fragmentation track   K K Hadronic (eg ): Less signal yield Excellent p T resolution Good sensitivity at higherm s Semileptonic (eg ): Higher signal yield Poor p T resolution Good sensitivity at lower m s.

20. ICFP 2005, Taiwan Colin Gay, Yale University CDF Limit (Semileptonic Mode) B s ! D s l X l=e/(360 pb -1 ) D s !    Opposite side: e,  tag Jet Charge 7800 events  D 2 = (1.43 § 0.09)%

21. ICFP 2005, Taiwan Colin Gay, Yale University CDF Limit (Hadronic mode) B s ! D s  (360 pb -1 ) D s !    Opposite side: e,  tag Jet Charge ~900 events  D 2 = (1.13 § 0.08)%

22. ICFP 2005, Taiwan Colin Gay, Yale University Potential Improvements Increase statistics Additional Decay Modes, More Data Increase tagging power Same Side Kaon Tagging increase  D 2 by 1-3% Lifetime resolution improve 10-20% Statistics Resolution Statistics

23. ICFP 2005, Taiwan Colin Gay, Yale University Conclusion Bs mixing search at the Tevatron is an ongoing affair Expect improvements in technique and statistics Observation likely still some time away Lifetime ratios in reasonable agreement with theory Bs the exception? Lifetime difference observed. Higher than predicted, but errors still large In addition, the mean width differs by ~2.7 from prediction Could it really be that Will repeat J/  analysis with x4 data Both CDF and D0 are statistics limited