Precision lattice QCD computation of the $B^{\ast }B\pi$ coupling

Abstract

The static $B^{\ast }B\pi$ coupling, ${\hat{g}}_{\chi }$, a low energy constant in the leading order heavy meson chiral Lagrangian, is determined using $N_{\mathrm{f}}=2$ lattice QCD. We use CLS ensembles with lattice spacings and pion masses down to $a=0.05\mathrm{fm}$ and $m_{\pi }=270\mathrm{MeV}$, and perform combined continuum and chiral extrapolations of our results which have a much better accuracy than previous numbers in the literature. As a by-product, we determine the coupling between the first radial excitations in the $B$ and $B^{\ast }$ channels (${\hat{g}}_{22}$). Accounting for all uncertainties, which are dominated by the chiral extrapolation, we obtain ${\hat{g}}_{\chi }=0.492(29)$, while ${\hat{g}}_{22}$ is somewhat smaller. The comparison to a precise quenched computation suggests that there is little influence by the sea quarks and ${\hat{g}}_{\chi }$ will not change much when a dynamical strange quark is included.

Comments: 14 pages, all included