Pion mass splitting and phase structure in Twisted Mass QCD

TL;DR

This paper uses Wilson Chiral Perturbation Theory to analyze how twisted mass terms affect pion masses and vacuum structure in lattice QCD, including lattice artifacts and phase transitions.

Contribution

It provides a next-to-leading order analysis of pion mass splitting and vacuum orientation in Twisted Mass QCD, accounting for lattice artifacts up to O(a^2).

Findings

Lattice artifacts induce pion mass splitting.

O(a^2) terms are crucial for modeling Aoki phases.

The same constant influences both mass splitting and phase structure.

Abstract

In the framework of Wilson Chiral Perturbation Theory, we study the effect induced by a twisted Wilson term, as it appears in Twisted Mass QCD (with 2 degenerate quarks). In particular we consider the vacuum orientation and the pion masses. The computations are done to NLO both in the mass and in the lattice spacing (i.e. to O(a^2)). There are no restrictions on the relative size of lattice artifacts with respect to the physical mass, thus allowing, in principle, to bridge between the physical regime and the unphysical one, where lattice artifacts tend to dominate. The inclusion of O(a^2) lattice artifacts can account for the splitting of degeneracy of the three pion masses. Moreover O(a^2) terms are necessary to model non trivial behaviors of the vacuum orientation such as possible Aoki phases. It turns out that these last two phenomena are determined by the same constant.