Perturbative determination of mass dependent renormalization and improvement coefficients for the heavy-light vector and axial-vector currents with relativistic heavy and domain-wall light quarks

Abstract

We determine the mass dependent renormalization as well as improvement coefficients for the heavy-light vector and axial-vector currents consisting of the relativistic heavy and the domain-wall light quarks through the standard matching procedure. The calculation is carried out perturbatively at the one loop level to remove the systematic error of $O({\alpha }_s(a{m}_Q{)}^{n}a\text{p})$ as well as $O({\alpha }_s(a{m}_Q{)}^n)$ ($n\ge$0), where $\text{p}$ is a typical momentum scale in the heavy-light system. We point out that renormalization and improvement coefficients of the heavy-light vector current agree with those of the axial-vector current, thanks to the exact chiral symmetry for the light quark. The results obtained with three different gauge actions, plaquette, Iwasaki and DBW2, are presented as a function of heavy quark mass and domain-wall height.

Comments: 33 pages, 6 figures