B s  J/ update Lifetime Difference & Mixing phase

1. Bs J/ update Lifetime Difference & Mixing phase for the CDF and DØ collaborations Avdhesh Chandra Beauty 2006 University of Oxford, UK

2. Unitary Triangle for Bs In SM quark mixing (Q2/3 Q-1/3) is given by CKM matrix Unitarity triangle equation for b-quark ‘Bd’ (The unitary triangle) Large effort in B physics Mainly at B factories ’Bs’ (A ‘squashed’ unitary triangle) bbs; bs(or 12 or ) small in SM Checking if bs is small is as important as measuring the sides and angles of The unitary triangle Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

3. Bs System (Mixing) b b Schrödinger Equation: s s • M12 stems from the real part of the box diagram, dominated by top • G12 stems from the imaginary part, dominated by charm Diagonalization gives two physically observed “Light” and “Heavy” mass eigenstates CP even CP odd New Physics can alter CP violating phase 12 significantly from its SM prediction of 0.3 Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

4. Scalar  Vector Vector • Bs  V1 + V2 (J/+ ) i.e. Spin 0  1+1 L= 0,1,2 • L = 0 and 2 corresponds to CP even; L=1 CP odd • Angular distribution can be written in terms of helicity • Most suitable coordinate bases:Transversity basis • Transversity basis is convenient for separation of CP-even and CP-odd components of the decay amplitude • Polar coordinates in this basis are defined in “J/ rest frame” and “ rest frame” cos=transversity Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

5. Angular Distribution Decay amplitude •  CP-violating weak phase ; in SM ~0.3 • 1 2 CP-conserving strong phase ; ~ || and 0 • A0(0) , A||(0) CP-even linear polarization amplitude at t=0 • A(0) CP-odd linear polarization amplitude at t=0 Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

6. Angular Distribution Decay amplitude •  CP-violating weak phase ; in SM ~0.3 • 1 2 CP-conserving strong phase ; ~ || and 0 • A0(0) , A||(0) CP-even linear polarization amplitude at t=0 • A(0) CP-odd linear polarization amplitude at t=0 CDF:  approximated to 0 Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

7. Chicago  DØ CDF p Booster Tevatron p p source Main Injector & Recycler The CDF & DØ Detector Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

8. The CDF & DØ Detector • Excellent tracking & mass resolution • Silicon || < 2 , 90 cm long • 96 layer drift chamber 44 to 132 cm • Triggered Muon coverage • pT > 1.5 GeV, || < 1 • Low pT Muon identification • pT > 1.5 GeV, || < 2 • High tracking efficiency: • 95% || < 3 (Silicon disks) Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

9. Bs J/(m+ m-) (K+ K-) Event topology Transverse decay length Proper decay length Dimuon triggered events are selected which don't have Impact Parameter trigger to unbias proper decay length measurement Tight kinematics cuts are required to select the Bs candidates Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

10. Likelihood Fit Maximum likelihood fit functions has Signal PDF and background PDF for observables Mass, Proper decay length & three decay angles with detector acceptance Detector acceptance are different due to different kinematics cuts Parameterization multiplied to the decay amplitude equation and final PDF is again normalized Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

11. Fit Results 2nd line for each observable: (Bs) = (Bd)  = 1.53 ps Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

12. Fit Projections Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

13. Fit Results 2nd line for each observable: (Bs) = (Bd)  = 1.53 ps Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

14. Fit Projections Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

15.  vs  and are correlated observables best displayed in following 2D graph Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

16.  vs Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

17.  vs Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

18.  vs Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

19.  vs Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

20.  vs   and  are also correlated observables with theory relation Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

21. Semileptonic charge asymmetry constrain Charge asymmetry of semileptonic Bs decays depends on CP violating weak phase by following relation (hep-ph/0406300) • ASL is measured in two independent way at DØ • Indirectly from time-integrated di-muon charge asymmetry gives ▬0.0076  0.0102 • Directly from time-integrated charge asymmetry from Bs Ds▬0.0245  0.0193 • Combining above two measurement ▬0.0006  0.0090 Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

22.  vs  Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

23.  vs  Semileptonic charge asymmetry band provide an independent constrain and hence more precise measurement of CP violation phase Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

24.  vs  Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

25. Sign Ambiguity For almost all theoretical models solution 1 is the most favorable solution from data set we have used to measure the observables BUT We have three more equally probable solutions from the same data set depends what choice you make for 1 2 &  Due to Angular distribution equation 1 3 2 4 Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

26. Likelihood Scans Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

27. Results Free  fit  fixed to 0 (CP conserved) DØ DØ Semileptonic charge asymmetry constrain DØ CDF Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

28. Combining the results of Bs system Measurement of , and  together can be displayed on the real and imaginary axis on a following 2D graph Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

29. Combining the results of Bs system Till last Friday Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

30. Combining the results of Bs system Under assumption 1 & 20 Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

31. Combining the results of Bs system Under assumption 1 & 20 Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

32. Summary • First direct measurement of CP-violating phase in the Bs system (DØ only)  = -0.79 +0.53 -0.60 0.01 • With the additional constraint from the new DØ measurement of the charge asymmetry in the Bs semileptonic decays (DØ only)  = -0.56 +0.44 -0.41 0.01 • Other measurement of observables of Bs system from CDF and DØ are also consistent with SM prediction. Under assumption 1 & 20 Bs J/ update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

33. BACKUP SLIDES

34. Bs System Weak decay constant Bag parameter Large uncertainty cancels out un