Universality of Mixed Action Extrapolation Formulae

TL;DR

The paper addresses how to reliably extrapolate mixed action lattice QCD results, using chirally symmetric valence fermions, to physical observables across different sea quark discretizations. By deriving a mixed action EFT from the Symanzik action and performing a spurion analysis with a controlled power counting, the authors prove a universality: the valence-sector Lagrangian and one-loop extrapolation formulae share a continuum-like form across sea discretizations, differing only by lattice-spacing induced mass shifts embodied in a single mixing parameter, DeltaMix, and related counterterms. They provide a concrete prescription to convert partially quenched chiral perturbation theory extrapolations into mixed action extrapolations for a wide range of observables, with explicit examples for neutron EDM, nucleon twist-2 matrix elements, and nucleon-nucleon scattering, while noting the neutron EDM as an exception due to its theta-term dependence. The framework leverages the universality of the leading mixed action operator and the preservation of valence chiral symmetry, enabling practical, accurate extrapolations using lattice-physical parameters and known mass shifts; this greatly facilitates cross-action analyses and the interpretation of MA lattice QCD results in hadronic physics.

Abstract

Mixed action theories with chirally symmetric valence fermions exhibit very desirable features both at the level of the lattice calculations as well as in the construction and implementation of the low energy mixed action effective field theory. In this work we show that when such a mixed action effective field theory is projected onto the valence sector, both the Lagrangian and the extrapolation formulae become universal in form through next to leading order, for all variants of discretization methods used for the sea fermions. Our conclusion relies on the chiral nature of the valence quarks. The result implies that for all sea quark methods which are in the same universality class as QCD, the numerical values of the physical coefficients in the various mixed action chiral Lagrangians will be the same up to lattice spacing dependent corrections. This allows us to construct a prescription to determine the mixed action extrapolation formulae for a large class of hadronic correlation functions computed in partially quenched chiral perturbation theory at the one-loop level. For specific examples, we apply this prescription to the nucleon twist--2 matrix elements and the nucleon--nucleon system. In addition, we determine the mixed action extrapolation formula for the neutron EDM as this provides a nice example of a theta-dependent observable; these observables are exceptions to our prescription.