Lattice QCD calculation of form factors describing the rare decays $B\to K^{\ast }{\ell }^{+}{\ell }^{-}$ and $B_s\to \varphi {\ell }^{+}{\ell }^{-}$

Abstract

The rare decays $B^0\to K^{\ast 0}{\mu }^{+}{\mu }^{-}$ and $B_s\to \varphi {\mu }^{+}{\mu }^{-}$ are now being observed with enough precision to test Standard Model predictions. A full understanding of these decays requires accurate determinations of the corresponding hadronic form factors. Here we present results of lattice QCD calculations of the $B\to K^{\ast }$ and $B_s\to \varphi$ form factors; we also determine the form factors relevant for the tree-level decays $B_s\to K^{\ast }\ell \nu$. We use full-QCD configurations including 2+1 flavors of sea quarks using an improved staggered action, and we employ lattice non-relativistic QCD to describe the bottom quark.

Comments: 23 pages. Version 3 (accepted to Phys. Rev. D) includes interpolations to the physical strange quark mass. Central values shift by less than 1 sigma. Tables and figures updated accordingly