Spin-taste representation of minimally doubled fermions from first principles: Karsten-Wilczek fermions

TL;DR

This paper derives the spin-taste representation of Karsten-Wilczek fermions from first principles, enabling construction of hadron operators and understanding taste-symmetry breaking effects in lattice QCD.

Contribution

It provides the first-principles derivation of spin-taste representation for minimally doubled fermions, clarifying operator construction and cutoff effects.

Findings

Derived the correct spin-taste representation from first principles.

Classified all meson, diquark, and baryon operators with taste considerations.

Predicted taste-symmetry breaking effects and validated with numerical results.

Abstract

Minimally doubled fermions realize one pair of Dirac fermions on the lattice. Similarities to Kogut-Susskind fermions exist, namely, spin and taste degrees of freedom become intertwined, and a peculiar non-singlet chiral symmetry and ultralocality are maintained. However, charge conjugation, some space-time reflection symmetries and isotropy are broken by the cutoff. We address the most simple variant, Karsten-Wilczek fermions, in its parallel and in its perpendicular version. We derive the correct spin-taste representation from first principles. The spin-taste representation on the quark level permits construction of local or extended hadron interpolating operators for any spin-taste combination, albeit with contamination by parity partners and taste-symmetry breaking. We classify all interpolating operator for mesons and diquarks, and give examples for baryons. We also discuss the appropriate discretizations for taste-singlet or taste-isovector mass or chemical potential terms. We explain the counterterms in the spin-taste framework, and derive generic constraints on the parametric form and cutoff effects from the KW determinant and hadronic correlation functions. We derive how and why non-perturbative tuning schemes for the counterterms work, and obtain analytic, assumption-free, non-perturbative predictions for taste-symmetry breaking and other hadronic properties from first principles. In particular, we identify the origin and nature of two different types of taste-symmetry breaking cutoff effects. The few available numerical results for KW fermions validate these predictions.