The phase diagram of twisted mass lattice QCD

TL;DR

This paper analyzes the phase diagram of two-flavor twisted mass lattice QCD using effective chiral Lagrangian techniques, revealing how different signs of a key coefficient lead to distinct phase structures including Aoki phases and first order transitions.

Contribution

It extends previous work by including discretization effects up to NLO and explores the phase structure in the twisted mass plane, identifying conditions for phase transitions and crossover behaviors.

Findings

Two possible phase diagrams depending on a coefficient sign.

Identification of Aoki phase and first order transition scenarios.

Graphs of condensate and pion masses illustrating phase behavior.

Abstract

We use the effective chiral Lagrangian to analyze the phase diagram of two-flavor twisted mass lattice QCD as a function of the normal and twisted masses, generalizing previous work for the untwisted theory. We first determine the chiral Lagrangian including discretization effects up to next-to-leading order (NLO) in a combined expansion in which m_\pi^2/(4\pi f_\pi)^2 ~ a \Lambda (a being the lattice spacing, and \Lambda = \Lambda_{QCD}). We then focus on the region where m_\pi^2/(4\pi f_\pi)^2 ~ (a \Lambda)^2, in which case competition between leading and NLO terms can lead to phase transitions. As for untwisted Wilson fermions, we find two possible phase diagrams, depending on the sign of a coefficient in the chiral Lagrangian. For one sign, there is an Aoki phase for pure Wilson fermions, with flavor and parity broken, but this is washed out into a crossover if the twisted mass is non-vanishing. For the other sign, there is a first order transition for pure Wilson fermions, and we find that this transition extends into the twisted mass plane, ending with two symmetrical second order points at which the mass of the neutral pion vanishes. We provide graphs of the condensate and pion masses for both scenarios, and note a simple mathematical relation between them. These results may be of importance to numerical simulations.