Extracting Scattering Phase-Shifts in Higher Partial-Waves from Lattice QCD Calculations

TL;DR

This paper extends L"uscher's method to extract higher partial-wave scattering phase-shifts (up to l=9) from Lattice QCD calculations, addressing formalism, symmetry considerations, and signal challenges.

Contribution

It develops the formalism and expressions needed to determine higher partial-wave phase-shifts from lattice QCD, beyond the s-wave case.

Findings

Derived expressions for phase-shifts with l<=6 and l=9.

Analyzed the impact of cubic symmetry on phase-shift extraction.

Discussed strategies and challenges for higher partial-wave signals.

Abstract

L\"uscher's method is routinely used to determine meson-meson, meson-baryon and baryon-baryon s-wave scattering amplitudes below inelastic thresholds from Lattice QCD calculations - presently at unphysical light-quark masses. In this work we review the formalism and develop the requisite expressions to extract phase-shifts describing meson-meson scattering in partial-waves with angular-momentum l<=6 and l=9. The implications of the underlying cubic symmetry, and strategies for extracting the phase-shifts from Lattice QCD calculations, are presented, along with a discussion of the signal-to-noise problem that afflicts the higher partial-waves.