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

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

2003-06-23

arxiv.org/abs/hep-lat/0306027v2

Phys.Rev.D68:054508,2003

Physics

High Energy Physics

High Energy Physics - Lattice

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

Scientific paper

10.1103/PhysRevD.68.054508

We have derived the quark mass dependence of $m_{\pi}^2$, $m_{\rm AWI}$ and $f_{\pi}$, 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 ($m_q\log m_q$) term, (3) the existence of more singular term, $\log m_q$, generated by $a^2$ contributions, and (4) the existence of both $m_q\log m_q$ and $\log m_q$ terms in the quark mass from the axial Ward-Takahashi identity, $m_{\rm AWI}$. By fitting the mass dependence of $m_\pi^2$ and $m_{\rm AWI}$, 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 $\log m_q$, we have also derived the modified formulae, which show a better control over the next-to-leading order correction.

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