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

Abstract

We point out a caveat in the proof for automatic $\mathrm{O}(a)$ improvement in twisted mass lattice QCD at maximal twist angle. With the definition for the twist angle previously given by Frezzotti and Rossi, automatic $\mathrm{O}(a)$ improvement can fail unless the quark mass satisfies ${m}_{q}\ensuremath{\gg}{a}^{2}{\ensuremath{\Lambda}}_{\mathrm{Q}\mathrm{C}\mathrm{D}}^{3}$. We propose a different definition for the twist angle which does not require a restriction on the quark mass for automatic $\mathrm{O}(a)$ improvement. In order to illustrate explicitly automatic $\mathrm{O}(a)$ 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 $\mathrm{O}(a)$ effect, depending on the size of the quark mass.