Quenched Chiral Corrections to Heavy-Light Decay Constants at Order 1/M

Quenched chiral perturbation is used to study the decay constants for heavy-light mesons beyond the leading order in 1/M. The results are used to estimate the error in quenched lattice calculations of the decay constants. For the double ratio $R_1=(f_{D_s}\mathrm{/}{f}_D)\mathrm{/}(f_{B_s}\mathrm{/}{f}_B)$ we find that the error is small, conservatively 6%, but likely smaller. We also find that quenching decreases the ratio $f_{D_s}\mathrm{/}{f}_D$ relative to the unquenched theory.