Automatic O(a) improvement for twisted-mass QCD in the presence of   spontaneous symmetry breaking
  In this paper we present a proof for automatic O(a) improvement in twisted mass lattice QCD at maximal twist, which uses only the symmetries of the leading part in the Symanzik effective action. In the process of the proof we clarify that the twist angle is dynamically determined by vacuum expectation values in the Symanzik theory. For maximal twist according to this definition, we show that scaling violations of all quantities which have non-zero values in the continuum limit are even in a. In addition, using Wilson Chiral Perturbation Theory (WChPT), we investigate this definition for maximal twist and compare it to other definitions which were already employed in actual simulations. 
Sinya Aoki and Oliver Bar