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

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.