The phase-shift of isospin-2 pi-pi scattering from lattice QCD

TL;DR

This study demonstrates how lattice QCD can be used to extract non-resonant pi-pi scattering phase-shifts in isospin-2 channels, providing insights into scattering behavior at various pion masses and volumes.

Contribution

It presents a novel application of lattice QCD to compute non-resonant phase-shifts for isospin-2 pi-pi scattering using a variational operator basis and multiple volumes.

Findings

Phase-shifts agree with experimental data at low momentum.

No significant quark mass dependence observed.

Method successfully maps energy spectra to phase-shifts.

Abstract

Finite-volume lattice QCD calculations offer the possibility of extracting resonance parameters from the energy-dependent elastic phase-shift computed using the Luescher technique. In this letter, as a trial of the method, we report on the extraction of the non-resonant phase-shift for S and D-wave pi-pi isospin-2 scattering from dynamical lattice QCD computations. We define a variational basis of operators resembling pairs of pions of definite relative momentum and extract a spectrum of excited states that maps to phase-shifts at a set of discrete scattering momenta. Computations are performed with pion masses between 400 and 520 MeV on multiple spatial volumes. We observe no significant quark mass dependence in the phase-shifts extracted which are in reasonable agreement with the available experimental data at low momentum.