Chiral Lagrangian for Karsten-Wilczek Minimally Doubled Fermions

TL;DR

This paper develops a lattice chiral perturbation theory framework for Karsten-Wilczek fermions, addressing their symmetries, effective actions, and chiral Lagrangians, including the treatment of fermion doublers.

Contribution

It introduces a novel chiral Lagrangian formulation for Karsten-Wilczek minimally doubled fermions, extending the analysis to include fermion doublers and their symmetries.

Findings

Constructed Symanzik effective actions up to five-dimensional operators.

Established the symmetry and spurion structure for single and doubled fermions.

Developed chiral Lagrangians using spurion analysis for Karsten-Wilczek fermions.

Abstract

Lattice chiral perturbation theory is developed for Karsten-Wilczek fermions, a variant of minimally doubled fermions. As a first step, we consider the n\"aive fermionic field on lattice without its doubler. Once the symmetries of the action, the Symanzik effective theory and the spurion structure are established for the single fermion, we extend our study to include the doubler. Symanzik effective actions are considered up to five-dimensional operators in both cases. The two fermionic tastes are realized by point-splitting the quark wavefunction in the coordinate space. Spurion analysis is used to construct the chiral lagrangians for Karsten-Wilczek fermions from the Symanzik actions. In this work, we have not included a pion that is massive in the continuum limit.