Automatic O(a) improvement for twisted-mass QCD in the presence of spontaneous symmetry breaking

TL;DR

This paper proves that twisted-mass lattice QCD at maximal twist automatically eliminates O(a) discretization errors using symmetry arguments, clarifies the dynamic determination of the twist angle, and compares different maximal twist definitions.

Contribution

It provides a symmetry-based proof of automatic O(a) improvement at maximal twist and analyzes the twist angle definition within Wilson Chiral Perturbation Theory.

Findings

Scaling violations are even in the lattice spacing a for quantities with non-zero continuum limit.

The twist angle is dynamically determined by vacuum expectation values in the Symanzik theory.

Comparison of different maximal twist definitions shows their implications in simulations.

Abstract

In this paper we present a proof for automatic O(a) improvement in twisted mass lattice QCD at maximal twist, which uses only the symmetries of the leading part in the Symanzik effective action. In the process of the proof we clarify that the twist angle is dynamically determined by vacuum expectation values in the Symanzik theory. For maximal twist according to this definition, we show that scaling violations of all quantities which have non-zero values in the continuum limit are even in a. In addition, using Wilson Chiral Perturbation Theory (WChPT), we investigate this definition for maximal twist and compare it to other definitions which were already employed in actual simulations.