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

We derive the quark mass dependence of $m_{\pi }^2,$ $m_{\mathrm{AWI}},$ and $f_{\pi },$ 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 $N_f=2\mathrm{}$ degenerate quarks. The distinct features of the results are (1) the additive renormalization for the mass parameter $m_q$ in the Lagrangian, (2) $O\left(a\right)\mathrm{}$ corrections to the chiral log ${(m}_q\log m_q)$ term, (3) the existence of a 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 $m_{\mathrm{AWI}}.$ By fitting the mass dependence of $m_{\pi }^2$ and $m_{\mathrm{AWI}},$ obtained by the CP-PACS Collaboration for $N_f=2\mathrm{}$ full QCD simulations, we find that the data are consistently described by the derived formulas. Resumming the most singular terms $\log m_q,$ we also derive modified formulas, which show a better control over the next-to-leading order correction.