pi-pi Scattering in Twisted Mass Chiral Perturbation Theory

Abstract

In this report we describe both I=2 and I=0 pi-pi scattering for twisted mass lattice QCD utilizing twisted mass chiral perturbation theory at next-to-leading order. Focusing on the lattice spacing (b) corrections, we demonstrate that in the exotic I=2, I_3=+-2 channels, the leading scaling violations of pi-pi scattering at maximal twist begin at O(m_pi^2 b^2). This is not the case in any other isospin channel, for which the scaling violations at maximal twist begin at O(b^2). Furthermore, we demonstrate the existence of a mixing between the I=2, I_3 = 0 and I=0 scattering channels due to the breaking of isospin symmetry by the twisted mass term. The mixing term, although formally next-to-leading order, is relatively large, thus necessitating the use of a coupled channel analysis. We argue that this mixing likely renders the computation of the I=0 channel impractical with twisted mass lattice QCD.