Hadronic form factors for rare semileptonic $B$ decays

We discuss first results for the computation of short distance contributions to semileptonic form factors for the rare $B$ decays $B\to K^{\ast }{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ and $B_s\to \varphi {\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$. Our simulations are based on RBC/UKQCD’s $N_f=2+1$ ensembles with domain wall light quarks and the Iwasaki gauge action. For the valence $b$-quark we chose the relativistic heavy quark action.