Meson-Baryon Scattering Lengths from Mixed-Action Lattice QCD

The ${\pi }^{+}{\mathrm{\Sigma }}^{+}$, ${\pi }^{+}{\mathrm{\Xi }}^0$, $K^{+}p$, $K^{+}n$, 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 $a_{{\pi }^{+}{\mathrm{\Sigma }}^{+}}=-0.197\pm 0.017$ fm, and $a_{{\pi }^{+}{\mathrm{\Xi }}^0}=-0.098\pm 0.017$ fm, where the comprehensive error includes statistical and systematic uncertainties.