A Lattice Computation of the Decay Constants of $B$ and $D$ Mesons

TL;DR

This paper reports a lattice QCD calculation of decay constants for B and D mesons, resolving previous discrepancies and providing new estimates with systematic error analysis.

Contribution

It introduces a method interpolating between static and heavy Wilson fermion approaches, correcting normalization issues, and extrapolates results to zero lattice spacing.

Findings

Calculated decay constants for B, Bs, D, Ds mesons with systematic errors.

Resolved previous discrepancies between static and Wilson fermion methods.

Estimated the ratio f_K/f_π in the quenched approximation.

Abstract

A lattice calculation of the pseudoscalar decay constant of heavy-light mesons is reported. Results are obtained (in the quenched approximation) from lattices at $\beta=6.3$ through a procedure that interpolates between the static approximation of Eichten and the conventional ("heavy" Wilson fermion) method. The previously observed discrepancy between these two approaches has been resolved: we find the scaling quantity $f\sqrt{M}$ to be significantly smaller than previous calculations had indicated ({\it e.g.} at $\beta=6.0$); in addition, we discuss a modification which is required in normalizing the conventional amplitude to correct for large-$am$ lattice errors. This change guarantees that $f\sqrt{M}$ will smoothly approach its value in the static limit. From the numerical interpolation of the static and intermediate-mass results, we find, in units of MeV, $f_B=187(10)\pm34\pm15$, $f_{B_s}=207(9)\pm34\pm22$, $f_D=208(9)\pm35\pm12$ and $f_{D_s}=230(7)\pm30\pm18$, where the first error is statistical and the second two are estimates of systematics due to 1) fitting and large-$am$ effects and 2) scaling. In addition, using lattices at $\beta=6.3$, $\beta=6.0$ and $\beta=5.7$ and extrapolating to the limit of zero lattice spacing, we have computed $f_K/f_\pi = 1.08\pm.03\pm.08$ in the quenched approximation.