Chiral perturbation theory for twisted mass QCD at small quark mass

We study the lattice cutoff ($a$) and quark mass dependences of pion masses and decay constants in the $N_f = 2$ twisted mass QCD, using the Wilson chiral perturbation theory to the next leading order (NLO). In order to investigate the region near zero quark mass, we introduce the power counting scheme where $O(a^2, am)$ terms are included in the tree level effective Lagrangian. At the NLO of this power counting scheme, we calculate the charged pion mass and decay constant as a function of the lattice cutoff as well as the twisted quark mass at the maximal twist. In this paper, we adopt two different definitions for the maximal twist. We confirm that the difference between the two appears as the $O(a^2)$ effects so that the automatic $O(a)$ improvement is realized for both definitions.

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