Towards a lattice determination of the $B^{\ast }B\ddot{I}€$ coupling

Abstract

The coupling $g_{B^{\ast }B\ddot{I}€}$ is related to the form factor at zero momentum of the axial current between $B^{\ast }$- and $B$-states. This form factor is evaluated on the lattice using static heavy quarks and light quark propagators determined by a stochastic inversion of the fermionic bilinear. The $\gBBP$ coupling is related to the coupling $g$ between heavy mesons and low-momentum pions in the effective heavy meson chiral lagrangian. The coupling of the effective theory can therefore be computed by numerical simulations. We find the value $g=0.42(4)(8)$. Besides its theoretical interest, the phenomenological implications of such a determination are discussed.

20 pages, 6 figures