Twisted-mass QCD, O(a) improvement and Wilson chiral perturbation theory

TL;DR

This paper identifies a limitation in the proof of automatic O(a) improvement in twisted mass lattice QCD at maximal twist and proposes a new definition of the twist angle to ensure consistent improvement across quark masses.

Contribution

It introduces a revised definition of the twist angle that guarantees automatic O(a) improvement without restrictions on quark mass in twisted mass lattice QCD.

Findings

The original twist angle definition can fail to ensure O(a) improvement at small quark masses.

A new twist angle definition maintains O(a) improvement regardless of quark mass size.

Explicit calculations of pion mass demonstrate the presence or absence of O(a) effects depending on the twist angle definition.

Abstract

We point out a caveat in the proof for automatic O(a) improvement in twisted mass lattice QCD at maximal twist angle. With the definition for the twist angle previously given by Frezzotti and Rossi, automatic O(a) improvement can fail unless the quark mass satisfies m_q >> a^2 Lambda_QCD^3. We propose a different definition for the twist angle which does not require a restriction on the quark mass for automatic O(a) improvement. In order to illustrate explicitly automatic O(a) improvement we compute the pion mass in the corresponding chiral effective theory. We consider different definitions for maximal twist and show explicitly the absence or presence of the leading O(a) effect, depending on the size of the quark mass.