No abstract

We point out a caveat in the proof for automatic Oa improvement in twisted mass lattice QCD at maximal twist angle. With the definition for the twist angle previously given by Frezzotti and Rossi, automatic Oa improvement can fail unless the quark mass satisfies m q a 2 3 QCD . We propose a different definition for the twist angle which does not require a restriction on the quark mass for automatic Oa improvement. In order to illustrate explicitly automatic Oa 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 Oa effect, depending on the size of the quark mass.

We compute the scattering amplitude for pion scattering in Wilson chiral perturbation theory for two degenerate quark flavors. We consider two different regimes where the quark mass m is of order (i) aà 2 QCD and (ii) a 2 à 3 QCD . Analytic expressions for the scattering lengths in all three isospin channels are given. As a result of the Oða 2 Þ terms the I ¼ 0 and I ¼ 2 scattering lengths do not vanish in the chiral limit. Moreover, additional chiral logarithms proportional to a 2 lnM 2 are present in the one-loop results for regime (ii). These contributions significantly modify the familiar results from continuum chiral perturbation theory.

We study lattice QCD with staggered sea and Ginsparg-Wilson valence quarks. The Symanzik effective action for this mixed lattice theory, including the lattice spacing contributions of O(a 2 ), is derived. Using this effective theory we construct the leading order chiral Lagrangian. The masses and decay constants of pseudoscalars containing two Ginsparg-Wilson valence quarks are computed at one loop order.

We discuss simulations with different lattice Dirac operators for sea and valence quarks. A goal of such a ''mixed'' action approach is to probe deeper the chiral regime of QCD by enabling simulations with light valence quarks. This is achieved by using chiral fermions as valence quarks while computationally inexpensive fermions are used in the sea sector. Specifically, we consider Wilson sea quarks and Ginsparg-Wilson valence quarks. The local Symanzik action for this mixed theory is derived to O(a), and the appropriate low energy chiral effective Lagrangian is constructed, including the leading O(a) contributions. Using this Lagrangian one can calculate expressions for physical observables and determine the Gasser-Leutwyler coefficients by fitting them to the lattice data.