$B_s\to f_0(980)$ form factors and $B_s$ decays into $f_0(980)$

Abstract

We compute the $B_s\to f_0(980)$ transition form factors using light-cone QCD sum rules at leading order in the strong coupling constant, and also including an estimate of next-to-leading order corrections. We use the results to predict the branching fractions of the rare decay modes $B_s\to f_0{\ell }^{+}{\ell }^{-}$ and $B_s\to f_0\nu \bar{\nu }$, which turn out to be $\mathcal{O}(10^{-7})$ ($B_s\to f_0(980){\ell }^{+}{\ell }^{-}$, with $\ell =e,\mu$), $\mathcal{O}(10^{-8})$ ($B_s\to f_0(980){\tau }^{+}{\tau }^{-}$) and $\mathcal{O}(10^{-6})$($B_s\to f_0(980)\nu \bar{\nu }$). We also predict the branching ratio of $B_s\to J/\psi f_0(980)$ decay under the factorization assumption, and discuss the role of this channel for the determination of the $B_s$ mixing phase compared to the golden mode $B_s\to J/\psi \varphi$. As a last application, we consider $D_s\to f_0$ form factors, providing a determination of the branching ratio of $D_s\to f_0{e}^{+}{\nu }_e$.

Comments: 11 pages, 5 figures