Lattice Determination of the $B^{\ast }B\pi$ Coupling

The coupling $g_{B^{\ast }B\pi }$ is related to the form factor at zero momentum of the axial current between $B^{\ast }$ and $B$ states. Moreover it is related to the effective coupling between heavy mesons and pions that appear the heavy meson chiral Lagrangian. This coupling has been evaluated on the lattice using static heavy quarks and light quark propagators determined by a stochastic inversion of the fermionic bilinear. We found the value $g=0.42(4)(8)$. Beside its theoretical interest, this quantity has phenomenological implications in $B\to \pi +\bar{l}l$ decays.