Phase diagram of non-degenerate twisted mass fermions

TL;DR

This paper maps the phase diagram and pion spectrum for Wilson and twisted-mass fermions considering non-degenerate quarks and lattice discretization effects, revealing connections between continuum and lattice phases.

Contribution

It provides a detailed analysis of the phase structure of non-degenerate twisted-mass fermions using chiral perturbation theory, highlighting the impact of discretization errors.

Findings

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

Discretization effects can shift physical masses towards different phases

Physical-point simulations may enter non-physical phases at large lattice spacings

Abstract

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, using Wilson and twisted-mass chiral perturbation theory. 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 of the lattice theory with degenerate quarks. We show that discretization effects can, in some cases, push simulations with physical masses closer to either the CP-violating phase or another phase not present in the continuum, so that at sufficiently large lattice spacings physical-point simulations could lie in one of these phases.