 from untagged B s samples at the (5S)

1.  from untagged Bs samples at the (5S) Sibylle Petrak, SLAC     

2. Introduction We will explore the consequences of a non-zero lifetime difference y = /2 of Bs mesons and derive the resulting possibilities to measure the CP angle . This was first studied by Dunietz (Phys. Rev. D52 (1995) 3048) for incoherent Bs production. In the following we will apply these techniques to the (5S).

3. Kaons: B: Bs:     s J/L   (1 - cos(2) y) (J/)=Ds+Ds-   (1 -y)     L J/s   (1 + cos(2) y) )   (1 - cos(2) y) Ds+K-)   (1 - || cos() y) z measures differences in the average lifetimes of state 1 and 2. If state 1 is a CP eigenstate and state 2 is of average lifetime then the z mean value scales like cos (CP phase) y

4. First consider (4S) P(f,)  exp(-||) { (1+|| ) cosh( y  )- 2 Re() sinh( y  ) } only cosh( y  )term,  mean value = zero Flavor states:  = 0 CP eigenstates: | |= 1 both cosh( y  )andsinh( y  )terms, sinh(y  )is dominant, non-zero  mean value and States with interfering amplitudes: | | 1 J/ Kmeasures cos(2) y and “zero” is calibrated with J/ K*, K*  K 

5. Monte Carlo study Data: Results: 2000 J/s events Is J/*, y.1a measure of J/s, y ? YES. Calibrate with 1000 J/* events Measured :z = ( -18  39 ) m Expected : z = 0 Two parameter points: Does the observed shift of J/s between y and y.1 agree with the expected bias? 1) y YES. Measured :z = ( 46  7 ) m Expected : z = 52 m 2) cos(2) 1 ; y =  = . 1 z   c ()B cos(2) 

6. Estimation of accuracy Statistical uncertainty from  fit to J/ Ksample. Systematic uncertainty described as statistical uncertainty of J/ K*, K*  K  sample.

7. Now extend to (5S) C= -1 state is the same as (4S). But now also C= +1 possible. For C= +1: P(f,)  exp(-||) { (1+|| - y [2 Re()]) cosh( y ||)(y [ 1+||] - 2 Re()) sinh( y | |) } only || dependence, always symmetric  distributions C=-1 C=+1

8.  dependent modes Ds K , Ds* K , Ds K* , Ds* K* |Vub Vcs| |Vcb Vus| ||=

9. Sensitivity to  y=-0.5, ||=0.5

10. Inclusive Reconstruction at (4S) B D*  with Dnot reconstructed D*  D D*  D

11. The Path 1) Measurey = /2with J/, DsDs 2) MeasureR= f(C=-1)/(f(C=-1) + f(C=+1))= B((5S)Bs Bs)+B((5S)Bs* Bs*) / B((5S) all BsBs) 3) Measure||via B(Bs  Ds* K) / B(Bs  Ds* )  (1+ | |)

12. Parameter Ranges Present known parameter ranges: 0.04 < y < 0.14 (Beneke, Buchalla, Dunietz) 0 <R < 1 (contradicting predictions), 0.9 <R < 1 (model analysis of cross section CUSB) 0.24 < ||< 0.47 (CKM ratio)

13. Resolution on y 3 years with 3 1 error of a measurement with central value y=0.1 B((5S)Bs Bs) =  B((4S)B B)

14. Resolution on  3 years with 3 1 error of a measurement with central value  = 90. Besides parameter varied other parameters are fixed to y=0.1, R=0.5,||=0.3.

15. Resolution on  3 years with 3 1 error of a measurement with central value  = 90. Besides parameter varied other parameters are fixed to y=0.1, R=0.5,||=0.3.

16. Conclusions Untagged Bs D*s K samples are a promising possibility to measure the CP angle . With 3 cms a statistical resolution of < 10 is within reach. More dedicated work is needed on experimental ((5S) Monte Carlo) and theoretical (factorization) side. There is also a possibility of testing the SM prediction “No CP violation in Bs J/”.