Flavor symmetry breaking in lattice QCD with a mixed action

TL;DR

This paper analyzes the phase structure of mixed-action lattice QCD, demonstrating that spontaneous symmetry breaking occurs only in the sea sector, thus ruling out mixed condensates and constraining low-energy constants.

Contribution

It provides a proof that flavor symmetry breaking cannot occur in the valence sector, refining the understanding of phase structure in mixed-action QCD.

Findings

Spontaneous symmetry breaking occurs only in the sea sector.

Mixed condensates involving valence and sea quarks are ruled out.

Constraints are derived on the low-energy constants of the effective theory.

Abstract

We study the phase structure of mixed-action QCD with two Wilson sea quarks and any number of chiral valence quarks (and ghosts), starting from the chiral lagrangian. A priori, the effective theory allows for a rich phase structure, including a phase with a condensate made of sea and valence quarks. In such a phase, mass eigenstates would become admixtures of sea and valence fields, and pure-sea correlation functions would depend on the parameters of the valence sector, in contradiction with the actual setup of mixed-action simulations. Using that the spectrum of the chiral Dirac operator has a gap for nonzero quark mass we prove that spontaneous symmetry breaking of the flavor symmetries can only occur within the sea sector. This rules out a mixed condensate, and implies restrictions on the low-energy constants of the effective theory.