Staggered Chiral Perturbation Theory at Next-to-Leading Order

TL;DR

This paper extends staggered chiral perturbation theory to next-to-leading order to analyze taste and rotational symmetry violations in lattice QCD, providing predictions for taste-breaking effects and testing the validity of the rooting trick.

Contribution

It develops the NLO staggered chiral Lagrangian including analytic terms and predicts relationships between taste-breaking quantities, aiding the understanding of lattice artifacts.

Findings

Predicted relationships between taste-breaking splittings in masses and decay constants.

Derived NLO corrections for pseudo-Goldstone boson properties.

Testable predictions for theories with the rooting trick.

Abstract

We study taste and Euclidean rotational symmetry violation for staggered fermions at nonzero lattice spacing using staggered chiral perturbation theory. We extend the staggered chiral Lagrangian to O(a^2 p^2), O(a^4) and O(a^2 m), the orders necessary for a full next-to-leading order calculation of pseudo-Goldstone boson masses and decay constants including analytic terms. We then calculate a number of SO(4) taste-breaking quantities, which involve only a small subset of these NLO operators. We predict relationships between SO(4) taste-breaking splittings in masses, pseudoscalar decay constants, and dispersion relations. We also find predictions for a few quantities that are not SO(4) breaking. All these results hold also for theories in which the fourth-root of the fermionic determinant is taken to reduce the number of quark tastes; testing them will therefore provide evidence for or against the validity of this trick.