On the phase structure of twisted mass lattice QCD

TL;DR

This paper analyzes the phase structure of two-flavor twisted-mass lattice QCD using chiral perturbation theory, accounting for lattice artifacts up to $\mathcal{O}(a^2)$ and a twisted mass term $\mu$. By expressing the chiral potential in terms of vacuum variables $u_0,u_a$ and parameters $c_1,c_2,c_3$, it identifies two main scenarios depending on the sign of $c_2$: an Aoki phase with spontaneous flavor-parity breaking for $c_2>0$ and a normal phase with a first-order transition for $c_2<0$, as well as the possibility of a new $Z_2$-breaking phase when higher-order terms are included. The analysis shows how nonzero twist mass $\mu$ shifts the vacuum, alters phase boundaries, and can wash out certain transitions, with a line of first-order transitions terminating at second-order endpoints and depending on the lattice coupling $\beta$. The results guide lattice QCD simulations by clarifying where lattice artifacts are most pronounced and how to tune parameters to minimize their impact while preserving $\mathcal{O}(a)$ improvement on the transition line.

Abstract

The introduction of a chirally twisted mass term has been proposed as an attractive approach to O(a) improvement of Quantum Chromodynamics with Wilson fermions on a lattice. For numerical simulation projects it is important to know the phase structure of the theory in the region of small quark masses. We study this question in the framework of chiral perturbation theory. Generalizing the analysis of Sharpe and Singleton we find extensions of normal and Aoki phase scenarios and a possible new phase with spontaneous breakdown of chiral symmetry to a discrete $Z_2$.

Figures (6)

• Figure 1: The values of $u_0$ and $u_3$ in the minimum of the potential as a function of $c_1 / 2 |c_2| \propto \tilde{m}$ for $c_3 = c_2$ in the Aoki scenario.
• Figure 2: Phase diagram for the Aoki scenario.
• Figure 3: The values of $u_0$ and $u_3$ in the minimum of the potential as a function of $c_1 / 2 |c_2| \propto \tilde{m}$ for $c_3 = |c_2|$ in the normal scenario.
• Figure 4: Jump of $u_0$ at the phase transition for the normal scenario.
• Figure 5: Phase diagram for the normal scenario.