Meson-Baryon Scattering Parameters from Lattice QCD with an Isospin Chemical Potential

TL;DR

This paper proposes a lattice QCD method using an isospin chemical potential to extract meson-baryon scattering parameters without the need for costly annihilation diagrams, leveraging pion condensates to determine low-energy constants.

Contribution

It introduces a novel approach to determine meson-baryon scattering parameters via lattice QCD with an isospin chemical potential, avoiding the sign problem and costly diagrams.

Findings

Method enables extraction of scattering parameters from baryon mass shifts.

Pion condensate formation occurs above a critical isospin chemical potential.

Specific low-energy constants are identified through baryon chiral perturbation theory.

Abstract

The extraction of meson-baryon scattering parameters from lattice QCD is complicated by the necessity, in some channels, of including annihilation diagrams. We consider a strategy to avoid the need for these extremely costly and noisy contributions. The strategy is based on simulations with an isospin chemical potential which, contrary to a baryon chemical potential, has no sign problem. When the isospin chemical potential is larger than a critical value, a charged pion condensate forms. Baryons propagating in the pion condensate will have their masses modified by pion-baryon scattering parameters. Consequently these parameters can be extracted from lattice QCD simulations in an isospin chemical potential, and we detail precisely which low-energy constants using baryon chiral perturbation theory.