Phase diagram of non-degenerate Wilson and twisted mass fermions

TL;DR

This paper explores the phase diagram and pion spectrum of Wilson and twisted-mass fermions considering non-degeneracy and discretization errors, revealing connections between continuum and lattice phases.

Contribution

It provides a detailed analysis of the phase structure and pion spectrum for non-degenerate Wilson and twisted-mass fermions, linking continuum CP-violating phases to lattice Aoki phases.

Findings

CP-violating phase connects to Aoki phase in non-degenerate case

Critical surface with massless pions identified in phase diagram

Competition between non-degeneracy and discretization effects in pion spectrum

Abstract

In this talk we determine the phase diagram and pion spectrum for Wilson and twisted-mass fermions in the presence of non-degeneracy between the up and down quark and discretization errors. We find that the CP-violating phase of the continuum theory, which occurs for sufficiently large non-degeneracy, is continuously connected to the Aoki phase found in the lattice theory with degenerate quarks. Both for the Aoki and first-order scenarios, this results in a critical surface along which at least one of the pions is massless. In the pion spectrum, we focus mainly on the untwisted case, where there is competition between the effects of non-degeneracy and discretization errors. A more extensive analysis can be found in our recent paper [11].