Two meson systems with Ginsparg-Wilson valence quarks

Unphysical effects associated with finite lattice spacing and partialquenching may lead to the presence of unphysical terms in chiral extrapolationformulae. These unphysical terms must then be removed during data analysisbefore physical predictions can be made. In this work, we show that throughnext-to-leading order, there are no unphysical counterterms in theextrapolation formulae, expressed in lattice-physical parameters, for mesonscattering lengths in theories with Ginsparg-Wilson valence quarks. Our workapplies to most sea quark discretization, provided that chiral perturbationtheory is a valid approximation. We demonstrate our results with explicitcomputations and show that, in favorable circumstances, the extrapolationformulae do not depend on the unknown constant C_Mix appearing at lowest orderin the mixed action chiral Lagrangian. We show that the I=1 KK scatteringlength does not depend on C_Mix in contrast to the I=3/2 K-pi scatteringlength. In addition, we show that these observables combined with f_K / f_piand the I=2 pi-pi scattering length share only two linearly independent sets ofcounterterms, providing a means to test the mixed action theory at one latticespacing. We therefore make a prediction for the I=1 KK scattering length.Comment: 21 pages, 2 figures, 2 tables. Version to be published in PRD. Improved discussion in Sec. III B. Added reference