Coupled $\pi\pi, K\overline{K}$ scattering in $P$-wave and the $\rho$ resonance from lattice QCD

TL;DR

This study uses lattice QCD to analyze coupled $ ho$ resonance scattering in $ ho$ and $Kar{K}$ channels, providing detailed phase shifts and revealing weak channel coupling at near-physical pion mass.

Contribution

First lattice QCD calculation of coupled-channel $ ho$ resonance scattering including $Kar{K}$, with detailed phase shift analysis at near-physical pion mass.

Findings

Identified $ ho$ resonance parameters from phase shifts.

Extended analysis into coupled $Kar{K}$ channel for the first time.

Found small coupling between $ ho$ and $Kar{K}$ channels.

Abstract

We determine elastic and coupled-channel amplitudes for isospin-1 meson-meson scattering in $P$-wave, by calculating correlation functions using lattice QCD with light quark masses such that $m_\pi = 236$ MeV in a cubic volume of $\sim (4 \,\mathrm{fm})^3$. Variational analyses of large matrices of correlation functions computed using operator constructions resembling $\pi\pi$, $K\overline{K}$ and $q\bar{q}$, in several moving frames and several lattice irreducible representations, leads to discrete energy spectra from which scattering amplitudes are extracted. In the elastic $\pi\pi$ scattering region we obtain a detailed energy-dependence for the phase-shift, corresponding to a $\rho$ resonance, and we extend the analysis into the coupled-channel $K\overline{K}$ region for the first time, finding a small coupling between the channels.