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Precision lattice QCD computation of the $B^*Bπ$ coupling

The static $B^{*}Bπ$ coupling, $\hat{g}_χ$, 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 $m_π=270\mathrm{MeV}$, 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 $\hat{g}_χ= 0.492(29)$, 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 $\hat{g}_χ$ will not change much when a dynamical strange quark is included.