The Lattice $\Lambda$ Parameter in Domain Wall QCD

TL;DR

This paper evaluates the ratio of the scale parameter Lambda in domain wall QCD to continuum theory at one loop, highlighting the necessity of Pauli-Villars regulator to remove unphysical modes, with detailed results based on domain wall height M.

Contribution

It provides a detailed one-loop calculation of the Lambda parameter ratio in domain wall QCD, emphasizing the role of Pauli-Villars regulator for accurate results.

Findings

The ratio of Lambda in domain wall QCD to continuum varies with domain wall height M.

Pauli-Villars regulator is essential to subtract unphysical massive fermion modes.

Results are presented as a function of the domain wall height M.

Abstract

We evaluate the ratio of the scale parameter $\Lambda$ in domain wall QCD to the one in the continuum theory at one loop level incorporating the effect of massless quarks. We show that the Pauli-Villars regulator is required to subtract the unphysical massive fermion modes which emerge in the fermion loop contributions to the gluon self energy. Detailed results are presented as a function of the domain wall height $M$.