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

TL;DR

This paper calculates mass-dependent renormalization and improvement coefficients for heavy-light vector and axial-vector currents using perturbation theory, ensuring more accurate lattice QCD simulations involving heavy and light quarks.

Contribution

It provides the first perturbative determination of these coefficients for relativistic heavy and domain-wall light quarks, including multiple gauge actions, at one-loop level.

Findings

Renormalization and improvement coefficients of vector and axial-vector currents are identical due to chiral symmetry.

Results vary with heavy quark mass and domain-wall height across different gauge actions.

The calculations reduce systematic errors in lattice QCD involving heavy-light systems.

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 $O(\alpha_s (am_Q)^n a\p)$ as well as $O(\alpha_s (am_Q)^n)$ ($n\ge$0), where $\p$ 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.