Chiral perturbation theory with Wilson-type fermions including $a^2$ effects: $N_f=2$ degenerate case

Sinya Aoki

doi:10.1103/PhysRevD.68.054508

paper

Chiral perturbation theory with Wilson-type fermions including $a^{2}$ effects: $N_{f} = 2$ degenerate case

arXiv:hep-lat/0306027 · doi:10.1103/PhysRevD.68.054508

Abstract

We have derived the quark mass dependence of $m_{π}^{2}$ , $m_{AWI}$ and $f_{π}$ , using the 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. 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 ( $m_{q} lo g m_{q}$ ) term, (3) the existence of more singular term, $lo g m_{q}$ , generated by $a^{2}$ contributions, and (4) the existence of both $m_{q} lo g m_{q}$ and $lo g m_{q}$ terms in the quark mass from the axial Ward-Takahashi identity, $m_{AWI}$ . By fitting the mass dependence of $m_{π}^{2}$ and $m_{AWI}$ , obtained by the CP-PACS collaboration for $N_{f} = 2$ full QCD simulations, we have found that the data are consistently described by the derived formulae. Resumming the most singular terms $lo g m_{q}$ , we have also derived the modified formulae, which show a better control over the next-to-leading order correction.

21 pages, 4 figures (10 eps files), Revtex4, some discussions and references added, the final version to appear in PRD

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Chiral perturbation theory with Wilson-type fermions including a2 effects: Nf​=2 degenerate case

Abstract

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Chiral perturbation theory with Wilson-type fermions including $a^{2}$ effects: $N_{f} = 2$ degenerate case