Chiral perturbation theory with Wilson-type fermions includinga2effects:Nf=2degenerate case

Abstract

We derive the quark mass dependence of ${m}_{\ensuremath{\pi}}^{2},$ ${m}_{\mathrm{AWI}},$ and ${f}_{\ensuremath{\pi}},$ using chiral perturbation theory, which includes the ${a}^{2}$ effect associated with the explicit chiral symmetry breaking of the Wilson-type fermions, in the case of the ${N}_{f}=2$ degenerate quarks. The distinct features of the results are (1) the additive renormalization for the mass parameter ${m}_{q}$ in the Lagrangian, (2) $O(a)$ corrections to the chiral log ${(m}_{q}\mathrm{log}{m}_{q})$ term, (3) the existence of a more singular term $\mathrm{log}{m}_{q}$ generated by ${a}^{2}$ contributions, and (4) the existence of both ${m}_{q}\mathrm{log}{m}_{q}$ and $\mathrm{log}{m}_{q}$ terms in the quark mass from the axial Ward-Takahashi identity ${m}_{\mathrm{AWI}}.$ By fitting the mass dependence of ${m}_{\ensuremath{\pi}}^{2}$ and ${m}_{\mathrm{AWI}},$ obtained by the CP-PACS Collaboration for ${N}_{f}=2$ full QCD simulations, we find that the data are consistently described by the derived formulas. Resumming the most singular terms $\mathrm{log}{m}_{q},$ we also derive modified formulas, which show a better control over the next-to-leading order correction.