Two Meson Systems with Ginsparg-Wilson Valence Quarks

TL;DR

This paper proves that, up to next-to-leading order, meson scattering length extrapolation formulae in theories with Ginsparg-Wilson valence quarks are free of unphysical counterterms, aiding lattice QCD data analysis.

Contribution

It demonstrates the absence of unphysical counterterms in chiral extrapolation formulae for meson scattering lengths with Ginsparg-Wilson valence quarks at next-to-leading order.

Findings

No unphysical counterterms in extrapolation formulae at NLO.

The I=1 KK scattering length is independent of C_Mix.

The observables share only two independent counterterm sets.

Abstract

Unphysical effects associated with finite lattice spacing and partial quenching may lead to the presence of unphysical terms in chiral extrapolation formulae. These unphysical terms must then be removed during data analysis before physical predictions can be made. In this work, we show that through next-to-leading order, there are no unphysical counterterms in the extrapolation formulae, expressed in lattice-physical parameters, for meson scattering lengths in theories with Ginsparg-Wilson valence quarks. Our work applies to most sea quark discretization, provided that chiral perturbation theory is a valid approximation. We demonstrate our results with explicit computations and show that, in favorable circumstances, the extrapolation formulae do not depend on the unknown constant C_Mix appearing at lowest order in the mixed action chiral Lagrangian. We show that the I=1 KK scattering length does not depend on C_Mix in contrast to the I=3/2 K-pi scattering length. In addition, we show that these observables combined with f_K / f_pi and the I=2 pi-pi scattering length share only two linearly independent sets of counterterms, providing a means to test the mixed action theory at one lattice spacing. We therefore make a prediction for the I=1 KK scattering length.