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The rare decays $B^0 \to K^{*0} \mu^+ \mu^-$ and $B_s \to \phi \mu^+ \mu^-$are now being observed with enough precision to test Standard Modelpredictions. A full understanding of these decays requires accuratedeterminations of the corresponding hadronic form factors. Here we presentresults of lattice QCD calculations of the $B \to K^*$ and $B_s \to \phi$ formfactors; we also determine the form factors relevant for the tree-level decays$B_s \to K^* \ell \nu$. We use full-QCD configurations including 2+1 flavors ofsea quarks using an improved staggered action, and we employ latticenon-relativistic QCD to describe the bottom quark.

Lattice QCD calculation of form factors describing the rare decays $B \to K^* \ell^+ \ell^-$ and $B_s \to \phi \ell^+ \ell^-$