Properties of minimally doubled fermions

TL;DR

This paper investigates minimally doubled fermions in lattice QCD, analyzing their symmetry properties, operator mixing, and meson spectrum to assess their viability for numerical simulations of two-flavour QCD.

Contribution

It provides a detailed perturbative and non-perturbative analysis of counterterms and symmetry restoration for minimally doubled fermions in lattice QCD.

Findings

Counterterms are necessary for symmetry restoration.

Two non-perturbative methods effectively remove power-law divergences.

The meson spectrum aligns with two-flavour QCD in the continuum limit.

Abstract

Most quark actions in lattice QCD encounter difficulties with chiral symmetry and its spontaneous breakdown. Minimally doubled fermions (MDF) are a category of strictly local chiral lattice fermions, whose continuum limit reproduces two degenerate quark flavours. The two poles of their Dirac operator are aligned such that symmetries under charge conjugation or reflection of one particular direction are explictly broken at finite lattice spacing. Properties of MDF are scrutinised with regard to broken symmetry and meson spectrum to discern their suitability for numerical studies of QCD. Interactions induce anisotropic operator mixing for MDF. Hence, restoration of broken symmetries in the continuum limit requires three counterterms, one of which is power-law divergent. Counterterms and operator mixing are studied perturbatively for two variants of MDF. Two independent non-perturbative procedures for removal of the power-law divergence are developed by means of a numerical study of hadronic observables for one variant of MDF in quenched approximation. Though three out of four pseudoscalar mesons are affected by lattice artefacts, the spectrum's continuum limit is consistent with two-flavour QCD. Thus, suitability of MDF for numerical studies of QCD in the quenched approximation is demonstrated.