Lattice QCD with the Overlap-Dirac Operator: Its $\Lambda$ Parameter, and One-Loop Renormalization of Fermionic Currents

TL;DR

This paper calculates the relationship between lattice and MS-bar scales in lattice QCD with the overlap-Dirac operator, and determines one-loop renormalization factors for fermionic currents, improving precision with resummation techniques.

Contribution

It provides the first one-loop relation between the lattice and MS-bar b3b5 scales for overlap fermions and computes renormalization constants for fermionic operators using advanced perturbative methods.

Findings

Derived the ratio b3b5_L / b3b5_MS-bar at one-loop.

Calculated the one-loop renormalization constants Z_b3 for fermionic currents.

Improved estimates of Z_b3 using cactus resummation and mean field theory.

Abstract

We compute the ratio between the scale $\Lambda_L$ associated with a lattice formulation of QCD using the overlap-Dirac operator, and $\Lambda_{MS-bar}$. To this end, the one-loop relation between the lattice coupling $g_0$ and the coupling renormalized in the MS-bar scheme is calculated, using the lattice background field technique. We also compute the one-loop renormalization $Z_\Gamma$ of the two-quark operators $\bar{\psi} \Gamma \psi$, where $\Gamma$ denotes a generic Dirac matrix. Furthermore, we study the renormalization of quark bilinears which are more extended and have better chiral properties. Finally, we present improved estimates of $Z_\Gamma$, coming from cactus resummation and from mean field perturbation theory.