Minimally doubled fermions at one loop

TL;DR

This paper analyzes the one-loop renormalization properties of minimally doubled fermions in lattice QCD, focusing on hyper-cubic symmetry breaking effects and their impact on quark self-energy and current renormalization.

Contribution

It provides the first one-loop perturbative study of minimally doubled fermions, including renormalization factors and conserved currents, highlighting hyper-cubic symmetry breaking effects.

Findings

Quark self-energy exhibits linearly divergent momentum renormalization.

Renormalization factors for vector and axial-vector currents are equal to one at one loop.

Hyper-cubic symmetry breaking affects the renormalization properties of the fermions.

Abstract

Minimally doubled fermions have been proposed as a cost-effective realization of chiral symmetry at non-zero lattice spacing. Using lattice perturbation theory at one loop, we study their renormalization properties. Specifically, we investigate the consequences of the breaking of hyper-cubic symmetry, which is a typical feature of this class of fermionic discretizations. Our results for the quark self-energy indicate that the four-momentum undergoes a renormalization which contains a linearly divergent piece. We also compute renormalization factors for quark bilinears, construct the conserved vector and axial-vector currents and verify that at one loop the renormalization factors of the latter are equal to one.