Hadron interactions from lattice QCD

TL;DR

This paper reviews lattice QCD studies of hadron interactions, including scattering lengths, phase shifts, and potentials, highlighting recent results that align with experimental data and phenomenological models.

Contribution

It provides a comprehensive overview of recent lattice QCD calculations of hadron interactions, including novel methods for defining potentials and extracting scattering parameters.

Findings

Lattice QCD results for $\pi\pi$ scattering lengths agree with other estimates.

The $P$-wave $\pi\pi$ phase shift calculation yields a $ ho$ meson decay width consistent with experiments.

Qualitative features of the nucleon-nucleon potential are reproduced using wave function-based methods.

Abstract

Studies on hadron interactions from lattice QCD are reviewed. The $S$-wave $\pi\pi$ scattering lengths of the I=0 and I=2 channels are extracted from various lattice determinations of low energy constants in $N_f=2$ chiral perturbation theory. The results agree with each other and agree also with other non-lattice estimates. Recently the $P$-wave $\pi\pi$ scattering phase shift for the I=1 channel has been calculated. A preliminary estimate of the $\rho$ meson decay width from the phase shift is consistent with the experimental value. Two approaches to potentials between hadrons are discussed. One is a method using static quarks to define the distance between two hadrons. The other is a method to define a potential from a wave function of two hadrons. An application of the latter to the nucleon-nucleon ($NN$) potential turns out to reproduce qualitative features of the phenomenological $NN$ potential such as attraction at long distance and repulsion at short distance. Theoretical issues of this approach are also discussed.