Scalar resonance effects on the B_s - \bar B_s mixing angle

Abstract

The $B_s^0\to J/\ddot{I}ˆ\ddot{I}•$ and $B_s^0\to J/\ddot{I}ˆf_0(980)$ decays are analyzed within generalized QCD factorization including all leading-order corrections in $\alphas$. We point out that the ratio of our calculated widths, $\hat{I}“(B_s^0\to J/\ddot{I}ˆf_0(980),f_0(980)\to \ddot{I}{€}^{+}\ddot{I}{€}^{-})/\hat{I}“(B_s^0\to J/\ddot{I}ˆ\ddot{I}•,\ddot{I}•\to K^{+}{K}^{-})$, strongly indicates that $S$-wave effects in the $f_0(980)$'s daughter pions or kaons cannot be ignored in the extraction of the $B_s-{\bar{B}}_s$ mixing angle, $-2{\hat{I}}_s^2$, from the $B_s^0\to \ddot{I}•J/\ddot{I}ˆ$ decay amplitudes.

16 pages and 3 figures; revised version due to erroneous discussion of annihilation contribution which led to their over-estimation. Main conclusions are not altered, yet Fig. 2-3 changed; one additional table (Table IX) compares theoretical values to data for branching fractions, asymmetries as well as polarizations. New paragraph about f_0(980) decay constant on page 14. Accepted in PRD