Meson-Baryon Scattering Lengths from Mixed-Action Lattice QCD

TL;DR

This paper computes meson-baryon scattering lengths using mixed-action lattice QCD and chiral perturbation theory, providing new numerical results for these fundamental interactions relevant to hadronic physics.

Contribution

It introduces lattice QCD calculations of specific meson-baryon scattering lengths combined with chiral extrapolations, highlighting challenges with three-flavor chiral convergence.

Findings

Calculated pion-hyperon scattering lengths with quantified uncertainties.

Demonstrated issues with three-flavor chiral expansion convergence.

Provided numerical values for scattering lengths relevant to hadronic interactions.

Abstract

The $\pi^+\Sigma^+$, $\pi^+\Xi^0$, $K^+p$, $K^+n$, and $\overline{K}{}^0 \Xi^0$ scattering lengths are calculated in mixed-action Lattice QCD with domain-wall valence quarks on the asqtad-improved coarse MILC configurations at four light-quark masses, and at two light-quark masses on the fine MILC configurations. Heavy Baryon Chiral Perturbation Theory with two and three flavors of light quarks is used to perform the chiral extrapolations. To the order we work in the three-flavor chiral expansion, the kaon-baryon processes that we investigate show no signs of convergence. Using the two-flavor chiral expansion for extrapolation, the pion-hyperon scattering lengths are found to be $a_{\pi^+\Sigma^+}=-0.197\pm0.017$ fm, and $a_{\pi^+\Xi^0}=-0.098\pm0.017$ fm, where the comprehensive error includes statistical and systematic uncertainties.