pi-pi Scattering in Twisted Mass Chiral Perturbation Theory

TL;DR

This paper analyzes pi-pi scattering in twisted mass lattice QCD, highlighting lattice spacing effects, isospin symmetry breaking, and the challenges in computing the I=0 channel due to channel mixing.

Contribution

It provides a next-to-leading order chiral perturbation theory analysis of pi-pi scattering, revealing lattice artifacts and isospin mixing effects specific to twisted mass formulations.

Findings

Leading scaling violations in I=2, I_3=±2 channels start at O(m_pi^2 b^2).

Isospin symmetry breaking causes significant mixing between I=2, I_3=0 and I=0 channels.

The I=0 channel computation is likely impractical due to large mixing effects.

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.