1. G.P. Di Giovanni LPNHE - Univ. “Pierre et Marie Curie” - IN2P3/CNRS XLIIId Rencontres de Moriond EWK, 2008 B s Mixing,  s & CP Violation

2. Synopsis G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS Theoretical Introduction Neutral B s Meson System: B s Oscillation Frequency Lifetime Difference and CP Violation Phase in B s  J/  Charge Asymmetry in B s Semileptonic Decays Charge Asymmetry in B +  J/  K + Summary

3. Neutral B s System G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 1 Flavor eigenstates: ( ) Pure B s and B s at production : Mass eigeinstates are (|p| 2 +|q| 2 =1):  Different Masses: defines the Mixing Oscillation Frequency  Different Lifetimes: CPV: Small Phase expected in SM

4. B s Mixing Oscillation G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 2 CDF: World First Observation (5  ) Integrated Luminosity: 1 fb -1 D  : Evidence (3  ) Integrated Luminosity: 2.4 fb -1 First D  measurement using a hadronic mode Consistent with CDF result

5. CP Violation in B s System G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 3 B s mixing oscillation observed by CDF: is well measured Precisely determines in good agreement with the Standard Model Phase of the mixing amplitude is instead poorly determined Both are needed to constrain New Physics: M SM M NP M SM +M NP Re Im Large value of CP Violation phase  M is a clear sign of New Physics!

6. CP in B s  J/   Decays G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 4 CP Violation arises from the interference between mixing and decay: Unitarity Triangle in B s System: ss CP violation phase  s in SM is predicted to be very small: Same New Physics affects the CPV phases as If NP phase dominates 

7. Phenomenology of B s  J/   G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 5 Nice experimental signature for B physics at hadron machines Decays into an admixture of CP even (~75%) and CP odd (~25%)  Mass and CP states are very close C-even  Different Parity  Separate CP contributions decays leads to three different angular momentum final states: L=0 (S-wave), L=2 (D-wave)  P-even L=1 (P-wave)  P-odd Angular Analysis to separate the different parity contributions Transversity Basis Sensitivity to and CP-Violation phase (also in untagged sample due to CP-even/CP-odd interference) 

8. Signal PDF for B s  J/   G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 6 General decay rate formula: Untagged analysis are insensitive to  s and  s signs  4-fold ambiguity Terms with  m s dependence flip sign for initial B s flavor In the Transversity basis the vector meson polarization w.r.t the direction of motion is: Longitudinal  A 0 [CP even] Transverse and parallel to each other  A || [CP even] Transverse and perpendicular to each other  A   [CP odd] Strong phases: B s decays into mixture of CP eigeinstates: interference terms in general decay rate formula

9. B s Lifetime and Decay Width G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 7 Lifetime: Sizeable  s  CP-even and CP-odd contributions of the signal can be distinguished CDF: ~2500 signal events (1.7 fb -1 ) D  : ~1040 signal events (1.1 fb -1 ) Decay Width: World Best  s Measurements (arXiv: 0712.2348) PRL 98, 121801 (2007) B 0  J/  K *0 : CDF validates treatment of detector acceptance!  Results compatible and competitive with B Factories (back-up slides) Results assuming no  CP violation   s =0

10. CP in Untagged B s  J/   G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 8 Allowing CP violation phase  s to float in the fitter Symmetry in the likelihood 4-fold ambiguity D  quotes a point estimate:  CDF observes irregular likelihood and biases in fit  Feldman-Cousins confidence region: SM probability p value =22% (1.2  ) --- 1  contour (39% CL) arXiv:0712.2348PRL 98, 121801 (2007) Standard Model expectations:  s =0.096  0.039 ps -1 2  s = 0.04  0.01 rad (arXiv:hep-ph/0612167)

11. Flavor Tagging Effect G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 9 Tagging improves sensitivity to CP violation phase  s Exact symmetry present in signal probability distribution Two minima in the likelihood Check  s -  s likelihood profile with Toy MC to understand tagging effect Likelihood: with tagging, gain sensitivity to both |cos(2  s )| and sin(2  s ), rather than only |cos(2  s )| and |sin(2  s )| (note absolute value)  s  -  s is no longer a likelihood symmetry:  4-fold ambiguity reduced to 2-fold  allowed region for  s is reduced to half 2  ln L = 2.31 (68% CL) 2  ln L = 5.99 (95% CL) 2  s -  s likelihood profile Untagged Tagged

12. CP in Tagged B s  J/   G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 10 First tagged analysis of B s → J/ΨΦ decay CDF: ~2000 B s events with 1.35 fb -1 Tagging power  OST:  =(96  1)% = (11  2)%  SST:  =(50  1)% = (27  4)% Irregular likelihood does not allow quoting point estimate: Feldman-Cousins likelihood ratio ordering strong phases can separate the two minima Standard Model p value = 15% (1.5  ) Standard Model expectations:  s =0.096  0.039 ps -1 2  s = 0.04  0.01 rad arXiv: 0712.2397 (arXiv:hep-ph/0612167)

13. G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 11 1. Without External Constraints: 2  s in [0.32, 2.82] at the 68% C.L. 2.  s is theoretically constrained: Input  s = 2|  12 |cos  s  2|  12 |cos(2  s ): (  12 =0.048  0.018 ): 2  s in [0.24, 1.36] U [1.78, 2.90] at 68% C.L. 3. Strong phases from B d  J/  K *0 [ PRD 71, 032005 (2005) ], B s lifetime from B d [ PDG ] and  s  2|  12 |cos(2  s ): 2  s in [0.40, 1.20] at 68% C.L. 1-dim Feldman-Cousins procedure on CP violation phase  s 0  2s2s 0  2s2s 0  2s2s CP in Tagged B s  J/  

14. G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 12 Tagged analysis of B s → J/ΨΦ decay from D  D  : ~2000 B s events with 2.8 fb -1 Combined Tagging Power   D 2 = (4.68  0.54)% Quoting point estimate: Standard Model p value = 6.6% arXiv: 0802.2255 FIT inputs:  m s fixed to 17.77 ps -1 Gaussian constraint on Strong phases:    || =-0.46  (  )   =+2.92  (  /5)  CDF  B Factories Standard Model expectations: 2  s = 0.04  0.01 rad (arXiv:hep-ph/0612167) 90% C.L. contours: CDF 68% CL: Constraining lifetime, strong phases and  12

15. Charge Asymmetry G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 13 CDF: 1.6 fb -1 of data collected (di-muon charge asymmetry): (http://www-cdf.fnal.gov/physics/new/bottom/070816.blessed-acp-bsemil/) D  : 1.0 fb -1 of data collected (di-muon charge asymmetry): D  : 1.3 fb -1 of data collected (B s semileptonic decays): PRL 98, 151801 (2007) PRD 74, 092001 (2006) if  CP Violation in mixing Combine these results with B s  J/  measurements to constrain phase  s

16. Constraints on  s G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 14 New Physics in B s mixing: (http://www.utfit.org/) UTfit Group  m s =C Bs *  m s SM : Lattice-QCD dominated uncertainty  s =  s SM -  Bs : Experimentally dominated uncertainty CDF 68% CL: Constraining lifetime, strong phases and  12 D  Result: UTfit combination CDF input: Tagged B s  J/  analysis reduces ambiguities B Factories input: Assuming SU(3) symmetry negative  s solution excluded UT fit inputs:  m s measurement (CDF) Lifetime  s (CDF and D  )  s (CDF on 200 pb -1 )  s and  s (D  on 1.1 fb -1 ) Semileptonic A SL (D  )

17. Direct CP in B +  J/  K + G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 15 Charge asymmetry Direct CP violation due to interference between direct and annihilation amplitudes: In SM A CP (B   J/  K  ) predicted to be of the level of 1% D  : ~40K signal events on 2.8 fb -1 Consistent with the PDG-2007 world average A CP (B   J/  K  )=0.015  0.017 Factor 2 better precision Most stringent bound on NP model predicting large A CP (B +  J/  K + ) A CP (B +  J/  + )= -0.09  0.08 (stat)  0.03 (syst) arXiv:0802.3299

18. Conclusions G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS Tevatron has a very active program in B Physics, with relevance to the B s sector Complementary and competitive with B Factories 16 CDF and D  search for CP violation effects: Direct CP violation (B +  J/  K + ) CP Violation in Mixing: precise measurement CP Violation in the interference between mixing and decay: FIRST sin(2  s ) measurement Interesting sin(2  s ) fluctuation at Tevatron experiments: Exclude large negative values Both experiments, CDF and D  In the same direction of A SL Almost 3.5 fb -1 of data delivered New results with larger dataset coming soon!

19. Backup Slides

20. CKM Matrix G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 17 In Standard Model Mixing and CP Violation effects are described within the CKM mechanism: Unitarity condition for CKM matrix: V † V=1 Expanded in terms of =sin(  c )~0.23 Phase  responsible for CP Violation Unitarity Triangle: Standard Model does not predict values Experimental Input is crucial Large CPVSuppressed CPV

21. The Tevatron G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 18 collisions at 1.96 TeV Excellent Performance Peak Initial Luminosity: 3 x 10 32 cm -2 s -1 Challenge for Detectors, Triggers and Reconstructions B physics benefits from more data The analyses presented in this talk span from 1.0 to 2.8 fb -1 Currently on tape ~3 fb -1

22. Tevatron Detectors G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 19 CDF II Detector Tracker: - Silicon Vertex Detector - Drift Chambers Excellent Momentum Resolution Particle ID: TOF and dE/dx Triggered Muon Coverage D  Detector New L00 installed in 2006! Solenoid: 2T, weekly reversed polarity Excellent Calorimetry and electron ID Triggered Muon Coverage

23. Transversity Analysis: B 0  J/  K *0 G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 20 Validation sample for the angular analysis on B s  J/  Measurements of amplitudes and strong phases using transversity basis CDF: ~7800 signal events on 1.35 fb -1 Correct treatment of detector acceptance Results comparable and competitive with BaBar [ Phys. Rev. D 76, 031102,(2007) ] ParameterCDFBaBar |A 0 | 2 0.569 ± 0.009 ± 0.0090.556 ± 0.009 ± 0.010 |A || | 2 0.211 ± 0.012 ± 0.006 0.211 ± 0.010 ± 0.006  || -  0 -2.96 ± 0.08 ± 0.03-2.93 ± 0.08 ± 0.04 -0-0 2.97 ± 0.06 ± 0.01 2.91 ± 0.05 ± 0.03

24. Untagged Analysis: Bias G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 21 Biases Non-Gaussian estimates in pseudo-experiments Strong dependence on true values for biases on some fit parameters Fits on simulated samples generated with SM inputs for  s and  s  Dependence on one parameter in the likelihood vanishes for some values of other parameters: Likelihood looses degrees of freedom e.g., if ΔΓ=0, δ ┴ is undetermined:

25. Constraints on Tagged B s  J/   G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 22 SU(3) flavor symmetry suggests that B s and B 0 have similar lifetimes and strong phases Likelihood profiles with external constraints from B factories Underestimated confidence regions when using 2  ln L = 2.31 (5.99) to approximate 68% (95%) C.L. regions  External constraints on strong phases remove residual 2-fold ambiguity constrain strong phases constrain lifetime and strong phases

26. Charge Asymmetry (I) G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 23 PRL 98, 151801 (2007) Detector asymmetries highly reduced by D  regular change of magnet polarity D  : ~27k signal events (1.3 fb -1 ) Semileptonic decay B s   D s -  X, D s -     K + K: if  Sensitivity to phase : NP does not take much to modify the SM prediction If NP dominates Can combine this result with the measurement from B s  J/  to constrain the phase  s Additional statistics and new decay modes will improve the result PRL 98, 151801 (2007)

27. Charge Asymmetry (II) G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 24 Inclusive dimuon charge asymmetry D  : 1.0 fb -1 of data collected by Tevatron f q is the production rate of B q mesons in the hadronization of the b quark Using world averages for f q, the semileptonic asymmetry for B d from B factories and the measured parameters  m q and  q : PRD 74, 092001 (2006) CDF: 1.6 fb -1 of data collected by Tevatron (http://www-cdf.fnal.gov/physics/new/bottom/070816.blessed-acp-bsemil/) Related to : additional constraint on  s

28. Magnet Polarity Inversion G.P. Di Giovanni, Univ. “Pierre et Marie Curie” - IN2P3/CNRS 25 D  performs a regular change of magnet polarity: Reduce artificial asymmetry in the detector Systematics effects in charge asymmentry analyses cancel out Methodology described in Phys. Rev. D 74, 092001 (2006): 1. Divide the sample in 8 subsamples corresponding to all possible combination of toroid polarity  =  1, pseudorapidity sign of the system considered  =  1 and charge of the muon particle q =  1 2. Solve the system of equations:   is the fraction of integrated luminosity with toroid polarity  (    - =1) A is the integrated charge asymmetry to be measured A fb is the forward-backward asymmetry A det is the detector asymmetry for particles emitted in fwd and bwd directions A ro is the range out asymmetry: muons acceptance changes if muons bends towards or bend away the beam line A q    is the detector asymmetry which accounts for muons reconstruction efficiency when toroid polarity is reversed A  is the detector related asymmetry fwd-bwd remaining after toroid polarity flip N is the total number of events