Determination of 2 β s in B 0 s → J / ψ K + K − Decays in the Presence of a K + K − S - Wave Contribution

We present the complete differential decay rates for the process Bs → J/ψK+K− including S-wave and P-wave angular momentum states for the K+K− meson pair. We examine the effect of an S-wave component on the determination of the CP violating phase 2βs. Data from the B-factories indicate that an S-wave component of about 10% may be expected in the φ(1020) resonance region. We find that if this contribution is ignored in the analysis it could cause a bias in the measured value of 2βs towards zero of the order of 10%. When including the K+K− S-wave component we observe an increase in the statistical error on 2βs by less than 15%. We also point out the possibility of measuring the sign of cos 2βs by using the interference between the K +K− S-wave and P-wave amplitudes to resolve the strong phase ambiguity. We conclude that the S-wave component can be properly taken into account in the analysis. †[email protected] ar X iv :0 90 8. 36 27 v1 [ he pph ] 2 5 A ug 2 00 9