Correlation functions with Karsten-Wilczek fermions

TL;DR

This paper investigates the symmetry properties and correlation functions of Karsten-Wilczek fermions, revealing how residual symmetries influence mesonic correlations, oscillations, and the emergence of additional pseudoscalar states.

Contribution

It provides a detailed analysis of symmetry breaking, correlation functions, and non-perturbative tuning conditions specific to Karsten-Wilczek fermions, including the effects of the second fermion.

Findings

Residual symmetries explain absence of time-reflection symmetry breaking.

Oscillating contributions from the second fermion are identified in correlation functions.

Mass splittings of additional pseudoscalar states vanish as a0a^2.

Abstract

The Karsten-Wilczek action describes two chiral fermions but breaks the symmetries under both charge conjugation ($ \widehat{C}) $ and time reflection ($ \widehat{\Theta} $) explicitly, though invariance under $ \widehat{C\Theta} $ and a mirror fermion symmetry $ \widehat{T\Theta} $ are maintained. These proceedings outline how the action's symmetries and the presence of the second fermion emerge in mesonic correlation functions. The residual symmetries explain the non-observation of broken time-reflection symmetry in a class of mesonic correlation functions. Time-reflection symmetry is enforced for correlation functions that are manifestly invariant under $ \widehat{C} $ or $ \widehat{T} $. Due to contributions from the second fermion, oscillating contributions arise in some mesonic correlation functions. A second condition for non-perturbative tuning of the relevant counterterm is obtained from these oscillations. Both non-perturbative tuning conditions are independent and agree within errors. Due to contributions from the second fermion, additional pseudoscalar states are observed in non-standard channels. Mass splittings between these additional states and the Goldstone boson vanish as $ \mathcal{O}(a^2) $.