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

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

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

4 Scalar  Vector Vector  B s  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 B s  J/  update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

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

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

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

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

9 B s  J/  (        (      Event topology Transverse decay length Proper decay length Tight kinematics cuts are required to select the B s candidates Dimuon triggered events are selected which don't have Impact Parameter trigger to unbias proper decay length measurement p T of J/  p T of  p T of B s Constrain J/  mass > 1.5 GeV > 2.0 GeV > 6.0 GeV PDG value B s  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 B s  J/  update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

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

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

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

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

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

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

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

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

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

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

21 Semileptonic charge asymmetry constrain Charge asymmetry of semileptonic B s decays depends on CP violating weak phase by following relation (hep-ph/ )  A SL is measured in two independent way at DØ 1)Indirectly from time-integrated di-muon charge asymmetry gives ▬  )Directly from time-integrated charge asymmetry from B s   D s ▬   Combining above two measurement ▬  B s  J/  update ; Lifetime Difference & Mixing phase Avdhesh Chandra (UCR)

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

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

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

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

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

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

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

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

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

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

33 BACKUP SLIDES

34 un Large uncertainty cancels out Bag parameter Weak decay constant B s System