Lattice calculation of weak amplitudes of D and B mesons

A lattice calculation of the pseudoscalar decay constants and the [(flavor)=2] mixing matrix elements for D and B mesons is reported. Calculations are done (in the quenched approximation) with =6.1 on a 123×33 lattice; results from =5.7 on a 163×25 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 fbd=1051730 MeV, fbs=1553148 MeV, fcd=1742646 MeV, fcs=2344655 MeV (with normalization such that f=132 MeV). The ratios of these quantities have considerably smaller errors: fbd/fcd=0.600.010.03, fbs/fcs=0.660.0040.09, fbs/fbd=1.47 0.070.30, and fcs/fcd=1.350.070.21. For the lattice B parameters we find BLLlatt=1.010.060.18 and BLRlatt=1.160.010.11 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.