Phase structure with nonzero $\Theta_{\rm QCD}$ and twisted mass fermions

TL;DR

This paper explores the phase diagram and chiral properties of lattice QCD with twisted-mass fermions under nonzero $ heta_{ m QCD}$, revealing a primarily first-order transition structure with specific second-order points.

Contribution

It provides the first detailed analysis of the phase structure of twisted-mass lattice QCD with nonzero $ heta_{ m QCD}$, including effects of nondegenerate quarks and discretization errors.

Findings

Main phase transition is a finite-length first-order line.

Pion masses are nonzero except at endpoints of the first-order line.

Second-order transitions occur only at extremal twist angles and $ heta_{ m QCD}$ values.

Abstract

We determine the phase diagram and chiral condensate for lattice QCD with two flavors of twisted-mass fermions in the presence of nondegenerate up and down quarks, discretization errors and a nonzero value of $\Theta_{\rm QCD}$. Although such a theory has a complex action and cannot, at present, be simulated, the results are needed to understand how to tune to maximal twist in the presence of electromagnetism, a topic discussed in a companion paper. We find that, in general, the only phase structure is a first-order transition of finite length. Pion masses are nonvanishing throughout the phase plane except at the endpoints of the first-order line. Only for extremal values of the twist angle and $\Theta_{\rm QCD}$ ($\omega=0$ or $\pi/2$ and $\Theta_{\rm QCD}=0$ or $\pi$) are there second-order transitions.