We present results of a high statistics study of $f_{\pi }$, $f_K$, $f_D$, $f_{D_s}$, and $f_V^{-1\mathrm{}}$ in the quenched approximation using Wilson fermions at $\beta =6.0\mathrm{}$ on ${32}^3$×64 lattices. We find that the various sources of systematic errors (due to setting the quark masses, renormalization constant, and lattice scale) are now larger than the statistical errors. Our best estimates, without extrapolation to the continuum limit, are $f_{\pi }=134\mathrm{}\left(4\right)\mathrm{}$ MeV, $f_K=159\mathrm{}\left(3\right)\mathrm{}$ MeV, $f_D=229\mathrm{}\left(7\right)\mathrm{}$ MeV, $f_{D_s}=260\mathrm{}\left(4\right)\mathrm{}$ MeV, and $f_V^{-1\mathrm{}}\left(m_{\rho }\right)=0.33\mathrm{}\left(1\right)\mathrm{}$, where only statistical errors have been shown. We discuss the extrapolation to the continuum limit by combining our data with those from other collaborations.

• Received 11 December 1995

DOI:https://doi.org/10.1103/PhysRevD.54.1155