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

The $B_s^0\to J\mathrm{/}\psi \varphi$ and $B_s^0\to J\mathrm{/}\psi f_0(980)$ decays are analyzed within generalized QCD factorization including all leading-order corrections in $\text{alphas}$. We point out that the ratio of our calculated widths, $\Gamma (B_s^0\to J/\psi f_0(980), f_0(980)\to \pi^+\pi^-)/ \Gamma(B_s^0 \to J/\psi \phi,\phi\to K^+K^-)$,stronglyindicatesthat$S$-waveeffectsinthe$f_0(980)${}^{\mathrm{\prime }}sdaughterpionsorkaonscannotbeignoredintheextractionofthe$B_s-\bar{B}_s$mixingangle,$-2\beta_s$,fromthe$B_s^0 \to \phi J/\psi$ decay amplitudes.