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

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, $f_B=187(10)\pm 34\pm 15$, $f_{B_s}=207(9)\pm 34\pm 22$, $f_D=208(9)\pm 35\pm 12$ and $f_{D_s}=230(7)\pm 30\pm 18$, 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.

Comments: 72 pages (tex file, mtexsis macros and 19 postscript figures bundled by "uufiles"), UW/PT-93-06