B and D meson decay constants in lattice QCD

This paper uses lattice QCD to calculate the decay constants of B and D mesons using an O(a)-improved action that takes light quark actions as a starting point, tuned so that it can be directly applied at the physical masses of the b and c quarks. The B meson decay constant f B is of particular phenomenological interest, since it is responsible for most of the uncertainty in current determinations of the CabibboKobayashi-Maskawa matrix element Vtd from BB̄ mixing. Recent calculations of the decay constants of B mesons give much lower values than the earliest calculations done in the static approximation because of several effects, all of which happened to be negative. Perturbative corrections turn out to be large and negative. The static approximation has larger statistical errors than methods with propagating quarks. This led to contamination from excited states, which raised the estimate of f B . The use of smeared sources and propagating quark methods mitigate this problem. The O(a) finite lattice spacing corrections likewise turned out to be large and negative. Conversely, the earliest results for lighter quarks tended to be too low. They were done using naive light quark methods with an incorrect and singular quark field normalization which forced f MAM→0 in the heavy quark limit. The combination of a too high f BAM B from the static approximation and a too low f DAM D from light quark methods led to very large estimates of the 1/M corrections to f MAM in the static limit. With more recent results, including those presented here, the 1/M corrections are much reduced. References @1,2# contain reviews of some of the early work. Currently, convenient inverse lattice spacings are no larger than a'2 or 3 GeV. Therefore, discretization errors that go like the quark mass in lattice units ma to a power are unpleasantly large for the c quark and completely out of control for the b quark. This means that standard light quark formulations for lattice fermion actions cannot be used unaltered for the b quark. There are several ways of approximating heavy quarks in lattice QCD calculations with control over discretization errors. These include nonrelativistic QCD @3,4,5# ~NRQCD!,