DEPENDENCE OF THE CURRENT RENORMALISATION CONSTANTS ON THE QUARK MASS

TL;DR

This paper investigates how the renormalisation constants for vector and axial currents depend on quark mass, revealing significant systematic effects and limitations of existing correction methods in Wilson and Clover formulations.

Contribution

It provides a detailed analysis of quark mass dependence of renormalisation constants and evaluates the effectiveness of correction prescriptions in lattice QCD.

Findings

Significant $O(am_q)$ effects in Wilson formulation.

Notable $O(g_0^2 a m_q)$ effects in Clover formulation.

Correction methods are not universally effective.

Abstract

We study the behaviour of the vector and axial current renormalisation constants $Z_V$ and $Z_A$ as a function of the quark mass, $m_q$. We show that sizeable $O(am_q)$ and $O(g_0^2 a m_q)$ systematic effects are present in the Wilson and Clover cases respectively. We find that the prescription of Kronfeld, Lepage and Mackenzie for correcting these artefacts is not always successful.