Universality of Mixed Action Extrapolation Formulae

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.Comment: 36 pages, appendix on twisted mass sea fermions added, expanded discussion of NLO operators, version published in JHEP; typographical errors corrected in Eqs. (68) and (69