ππscattering in twisted mass chiral perturbation theory

Abstract

In this report we describe both $I=2$ and $I=0$ $\ensuremath{\pi}\ensuremath{\pi}$ 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 $I=2$, ${I}_{3}=\ifmmode\pm\else\textpm\fi{}2$ channels (${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$), the leading scaling violations of $\ensuremath{\pi}\ensuremath{\pi}$ scattering at maximal twist begin at $\mathcal{O}({m}_{\ensuremath{\pi}}^{2}{b}^{2})$. This is not the case in any other isospin channel, for which the scaling violations at maximal twist begin at $\mathcal{O}({b}^{2})$. 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.