Minimally doubled fermions at one-loop level

TL;DR

This paper analyzes the one-loop renormalization properties of minimally doubled fermion actions, specifically Borici-Creutz and Karsten-Wilczek, highlighting their differences and similarities in lattice QCD.

Contribution

It provides the first detailed one-loop level renormalization analysis of minimally doubled fermion actions on hyperdiamond lattices.

Findings

Renormalization involves wave-function and momentum adjustments.

Differences in renormalization between Borici-Creutz and Karsten-Wilczek actions.

Explicit symmetry breaking affects operator mixing and renormalization.

Abstract

Single fermionic degrees of freedom together with standard chiral symmetry at finite lattice spacing, correct continuum limit and local interactions only are precluded by the Nielsen-Ninomiya no-go theorem. The class of minimally doubled fermion actions exhibits exactly two chiral modes. Recent interest in these actions has been sparked by the investigation of fermionic actions defined on "hyperdiamond" lattices. Due to the necessity of breaking hypercubic symmetry explicitly, radiative corrections generate operator mixings with relevant and marginal operators that should vanish in continuum QCD. These cannot be avoided and must be taken into account in particular by a peculiar wave-function renormalisation and additive momentum renormalisation. Renormalisation properties at one-loop level of the self-energy, local bilinears and conserved vector and axial-vector currents are presented for Borici-Creutz and Karsten-Wilczek actions. Distinct differences and similarities between both actions are elucidated.