Effective field theories for QCD with rooted staggered fermions

TL;DR

This paper develops an effective field theory framework for rooted staggered fermions in lattice QCD, clarifying how taste violations and the rooting trick influence continuum extrapolation and chiral perturbation theory.

Contribution

It extends the Symanzik effective theory to include rooted staggered fermions, linking renormalization-group methods with rooted staggered chiral perturbation theory.

Findings

Rooted staggered chiral perturbation theory is validated as the correct low-energy effective theory.

A theoretical connection is established between the continuum limit and numerical success of rooted staggered simulations.

The approach clarifies how taste violations are incorporated into effective field theories.

Abstract

Even highly improved variants of lattice QCD with staggered fermions show significant violations of taste symmetry at currently accessible lattice spacings. In addition, the "rooting trick" is used in order to simulate with the correct number of light sea quarks, and this makes the lattice theory nonlocal, even though there is good reason to believe that the continuum limit is in the correct universality class. In order to understand scaling violations, it is thus necessary to extend the construction of the Symanzik effective theory to include rooted staggered fermions. We show how this can be done, starting from a generalization of the renormalization-group approach to rooted staggered fermions recently developed by one of us. We then explain how the chiral effective theory follows from the Symanzik action, and show that it leads to "rooted" staggered chiral perturbation theory as the correct chiral theory for QCD with rooted staggered fermions. We thus establish a direct link between the renormalization-group based arguments for the correctness of the continuum limit and the success of rooted staggered chiral perturbation theory in fitting numerical results obtained with the rooting trick. In order to develop our argument, we need to assume the existence of a standard partially-quenched chiral effective theory for any local partially-quenched theory. Other technical, but standard, assumptions are also required.