Lattice results for the decay constant of heavy-light vector mesons

We compute the leptonic decay constants of heavy-light vector mesons in the quenched approximation. The reliability of lattice computations for heavy quarks is checked by comparing the ratio of vector to pseudoscalar decay constant with the prediction of heavy quark effective theory in the limit of an infinitely heavy quark mass. Good agreement is found. We then calculate the decay constant ratio for B mesons: $f_{B^{*}}{/f}_B{=1.01\mathrm{}\left(0.01\right)(}_{-0.01}^{+0.04\mathrm{}}).\mathrm{}$ We also quote quenched $f_{B^{*}}=177\mathrm{}\left(6\right)\mathrm{}\left(17\right)\mathrm{}\hspace{0.5em}\mathrm{MeV}.$