LATTICE COMPUTATION OF THE DECAY CONSTANTS OF B-MESONS AND D-MESONS

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 square-root M to be significantly smaller than previous calculations had indicated (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 square-root 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)+/-34+/-15, f(Bs)=207(9)+/-34+/-22, f(D)=208(9)+/-35+/-12, and f(Ds)=230(7)+/-30+/-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. The ratios are better determined: f(D)/f(Ds), f(B)/f(Bs), f(B)/f(D), and f(Bs)/f(Ds) are all 0.90 within a total error of less than 0.05. The purely static values are f(B)stat=235(20)+/-21 MeV, f(Bs)stat=259(19)+/-19 MeV, and f(B)stat/f(Bs)stat=0.90(2)+/-0.02. Finally, 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+/-0.03+/-0.08 in the quenched approximation, where the first error includes statistical and fitting errors, and the second is an estimate of the error in extrapolation to the continuum limit.