S and D-wave phase shifts in isospin-2 pi pi scattering from lattice QCD

TL;DR

This paper uses lattice QCD to analyze S- and D-wave phase shifts in isospin-2 pion-pion scattering, providing detailed phase shift data and demonstrating a new operator construction method for multi-hadron systems.

Contribution

It introduces a general operator construction respecting multi-hadron symmetries and applies variational analysis to extract scattering phase shifts at multiple kinematic points.

Findings

Elastic scattering well described by a scattering length parameterization

Phase shifts determined at various energies in the elastic region

Method successfully applied at a pion mass of 396 MeV

Abstract

The isospin-2 pi pi system provides a useful testing ground for determining elastic hadron scattering parameters from finite-volume spectra obtained using lattice QCD computations. A reliable determination of the excited state spectrum of two pions in a cubic box follows from variational analysis of correlator matrices constructed using a large basis of operators. A general operator construction is presented which respects the symmetries of a multi-hadron system in flight. This is applied to the case of pi pi and allows for the determination of the scattering phase-shifts at a large number of kinematic points, in both S-wave and D-wave, within the elastic region. The technique is demonstrated with a calculation at a pion mass of 396 MeV, where the elastic scattering is found to be well described by a scattering length parameterisation.