The static $B^{ *}B\pi$ 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 $B^{ *}$ 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.
Categories: hep-lat