$B_s\to f_0(980)$ 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 ${\cal O}(10^{-7})$ ($B_s\to f_0(980)\ell^+\ell^-$, with $\ell=e,\mu$), ${\cal O}(10^{-8})$ ($B_s\to f_0(980)\tau^+\tau^-$) and ${\cal O}(10^{-6})$($B_s\to f_0(980)\nu\bar\nu$). 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 $B_s \to J/\psi \phi$. As a last application, we consider $D_s \to f_0$ form factors, providing a determination of the branching ratio of $D_s \to f_0 e^+ \nu_e$.