Perturbative renormalization parameters for heavy quarks ∗

Formulation of the heavy quark on the lattice, such as NRQCD[1] or the Fermilab approach with the Wilson-like relativistic quarks[2], requires perturbative matching with the continuum theory. Since the quark mass in the lattice unit cannot be neglected for these theories, the perturbative calculation is much more involved and have not developed as that for the massless case. We report the current status of our effort to calculate the one-loop coefficients of the perturbative Z-factor ZV and ZA. It is particularly important to calculate the mass dependence of the axial-current Z-factor ZA, which is required for the calculation of the B meson decay constant fB, since the one-loop coefficient in the static limit is known to be very large[3]. The combinations of the heavy and light quark actions we investigate in this report are listed in Table 1. The Wilson and Clover heavy quarks are used with the Fermilab group’s non-relativistic interpretation[2], with which the relativistic actions can be treated in parallel with NRQCD for heavy quarks, since the both methods are based on the small spatial momentum expansion, or equivalently the ΛQCD/M expansion. And in particular the both methods have the identical static limit.