O(a)-improved quark action on anisotropic lattices and perturbative renormalization of heavy-light currents

TL;DR

This paper explores the improvement of Wilson quark actions on anisotropic lattices, focusing on perturbative renormalization of heavy-light currents, and demonstrates how to achieve tree-level and $O(m_0a_\tau)$ improvements.

Contribution

It presents a method for Symanzik improvement of Wilson quark actions on anisotropic lattices, including calculations of renormalization factors at one-loop order.

Findings

Tree-level improvement of the action is achievable.

$O(m_0a_\tau)$ improvement is possible with a specific spatial Wilson coupling.

Renormalization factors for heavy-light operators are computed perturbatively.

Abstract

We investigate the Symanzik improvement of the Wilson quark action on anisotropic lattices. Taking first a general action with nearest-neighbor and clover interactions, we study the mass dependence of the ratio of the hopping parameters, the clover coefficients, and an improvement coefficient for heavy-light vector and axial vector currents. We show how tree-level improvement can be achieved. For a particular choice of the spatial Wilson coupling, the results simplify, and $O(m_0a_\tau)$ improvement is possible. (Here $m_0$ is the bare quark mass and $a_\tau$ the temporal lattice spacing.) With this choice we calculate the renormalization factors of heavy-light bilinear operators at one-loop order of perturbation theory employing the standard plaquette gauge action.