Twisted-mass QCD, O(a) improvement and Wilson chiral perturbation theory

We point out a caveat in the proof for automatic O(a) improvement in twisted mass lattice QCD at maximal twist angle. With the definition for the twist angle previously given by Frezzotti and Rossi, automatic O(a) improvement can fail unless the quark mass satisfies m_q >> a^2 Lambda_QCD^3. We propose a different definition for the twist angle which does not require a restriction on the quark mass for automatic O(a) improvement. In order to illustrate explicitly automatic O(a) improvement we compute the pion mass in the corresponding chiral effective theory. We consider different definitions for maximal twist and show explicitly the absence or presence of the leading O(a) effect, depending on the size of the quark mass.