The epsilon regime with twisted mass Wilson fermions

TL;DR

This paper extends the chiral epsilon expansion to twisted mass Wilson fermions, analyzing lattice spacing effects on mesonic correlators and providing formulas to match lattice data for physical insights.

Contribution

It generalizes the epsilon expansion to twisted mass Wilson fermions, explicitly computes leading lattice artifacts, and offers formulas for data analysis at arbitrary twist angles.

Findings

Leading O(a^2) corrections computed at NLO in GSM* regime.

Explicit suppression of chiral symmetry breaking effects at maximal twist.

Formulas provided for matching lattice data to extract low energy constants.

Abstract

We investigate the leading lattice spacing effects in mesonic two-point correlators computed with twisted mass Wilson fermions in the epsilon-regime. By generalizing the procedure already introduced for the untwisted Wilson chiral effective theory, we extend the continuum chiral epsilon expansion to twisted mass WChPT. We define different regimes, depending on the relative power counting for the quark masses and the lattice spacing. We explicitly compute, for arbitrary twist angle, the leading O(a^2) corrections appearing at NLO in the so-called GSM^* regime. As in untwisted WChPT, we find that in this situation the impact of explicit chiral symmetry breaking due to lattice artefacts is strongly suppressed. Of particular interest is the case of maximal twist, which corresponds to the setup usually adopted in lattice simulations with twisted mass Wilson fermions. The formulae we obtain can be matched to lattice data to extract physical low energy couplings, and to estimate systematic uncertainties coming from discretization errors.