Dynamically-coupled partial-waves in $\rho\pi$ isospin-2 scattering from lattice QCD

TL;DR

This paper reports the first lattice QCD calculation of $ ho \, \pi$ isospin-2 scattering, including dynamically-coupled partial waves, providing new insights into meson interactions from first principles.

Contribution

It introduces a novel lattice QCD methodology to analyze dynamically-coupled partial-waves in meson scattering, specifically for the isospin-2 $ ho \, \pi$ system.

Findings

Determined partial-wave amplitudes with $J \le 3$

Quantified dynamical mixing between $S$ and $D$-waves

Validated the approach with multiple lattice volumes and momenta

Abstract

We present the first determination of $\rho \pi$ scattering, incorporating dynamically-coupled partial-waves, using lattice QCD, a first-principles numerical approach to QCD. Considering the case of isospin-2 $\rho \pi$, we calculate partial-wave amplitudes with $J \le 3$ and determine the degree of dynamical mixing between the coupled $S$ and $D$-wave channels with $J^P=1^+$. The analysis makes use of the relationship between scattering amplitudes and the discrete spectrum of states in the finite volume lattice. Constraints on the scattering amplitudes are provided by over one hundred energy levels computed on two lattice volumes at various overall momenta and in several irreducible representations of the relevant symmetry groups. The spectra follow from variational analyses of matrices of correlations functions computed with large bases of meson-meson operators. Calculations are performed with degenerate light and strange quarks tuned to the physical strange quark mass so that $m_\pi \sim 700$ MeV, ensuring that the $\rho$ is stable against strong decay. This work demonstrates the successful application of techniques, opening the door to calculations of scattering processes that incorporate the effects of dynamically-coupled partial-waves, including those involving resonances or bound states.