A lattice calculation of the pseudoscalar decay constants and the [Δ(flavor)=2] mixing matrix elements for D and B mesons is reported. Calculations are done (in the quenched approximation) with β=6.1 on a ${12}^3$×33 lattice; results from β=5.7 on a ${16}^3$×25 lattice contribute to our estimate of the systematic errors. An extrapolation to large meson mass is required in order to treat the B meson. We find $f_{\mathrm{bd}}$=105±17±30 MeV, $f_{\mathrm{bs}}$=155±31±48 MeV, $f_{\mathrm{cd}}$=174±26±46 MeV, $f_{\mathrm{cs}}$=234±46±55 MeV (with normalization such that $f_{\pi }$=132 MeV). The ratios of these quantities have considerably smaller errors: $f_{\mathrm{bd}}$/$f_{\mathrm{cd}}$=0.60±0.01±0.03, $f_{\mathrm{bs}}$/$f_{\mathrm{cs}}$=0.66±0.004±0.09, $f_{\mathrm{bs}}$/$f_{\mathrm{bd}}$=1.47 ±0.07±0.30, and $f_{\mathrm{cs}}$/$f_{\mathrm{cd}}$=1.35±0.07±0.21. For the lattice B parameters we find $B_{\mathrm{LL}}^{\mathrm{latt}=1.01\mathrm{}\pm 0.06\pm 0.18}$ and $B_{\mathrm{LR}}^{\mathrm{latt}=1.16\mathrm{}\pm 0.01\pm 0.11}$ for the bd system, with quite similar values for the cu and bs systems. These B parameters are defined slightly differently than in the continuum and are effectively renormalization-group invariant. The first error in each of our results is statistical; the second is an estimate of the systematic errors due to scale-breaking, finite-size, extrapolation and operator-renormalization effects.

• Received 27 June 1988

DOI:https://doi.org/10.1103/PhysRevD.38.3540