Extraction of $B_s\to D_s^{(\ast )}$ form factors from $N_f=2$ lattice QCD

Abstract

We report on a two-flavour lattice QCD study of the $B_s\to D_s$ and $B_s\to D_s^{\ast }$ transitions parameterized, in the heavy quark limit, by the form factors $\mathcal{G}$, and $h_{A_1}$, $h_{A_2}$ and $h_{A_3}$, respectively. In the search for New Physics through tests of lepton flavour universality, $B_s$ decay channels are complementary to the $B$ decays widely studied at $B$ factories and LHCb, while on the theory side they can be better controlled than the $B_c$ and $\hat{I}{›}_b$ decays. The purpose of this exploratory two-flavour study is, in preparation for future analyses of lattice QCD simulations with $N_f>2$ and physical quark-masses, to gain experience on a suitable method for a lattice extraction of form factors associated with $b\to c$ currents that may yield tighter control over systematic effects like contamination from excited states and cut-off effects. We obtain the zero-recoil values ${\mathcal{G}}^{B_s\to D_s}(1)=1.03(14)$ and $h^{B_s\to D_s^{\ast }}(1)=0.85(16)$.