A Lattice QCD study of $p-\Lambda$ scattering in continuum and chiral limits

Abstract

We present a first systematic study of $I=1/2$ proton-$\Lambda$ ($p$-$\Lambda$) scattering from lattice QCD, using seven sets of $(2+1)$-flavor lattice ensembles with pion masses spanning 135-317 MeV and three lattice spacings with $a=(0.052,0.077, 0.105)$ fm. Using L\"uscher's finite-volume method, effective range expansion and chiral/continuum extrapolations, we obtain the inverse of scattering length and effective range for the $^1S_0$ channel as 0.177(83) GeV and 2.9(1.4) fm, and for the $^3S_1$ channel as 0.016(76) GeV and 1.8(1.1) fm. From the derived S-wave phase shifts, we provide an estimate of the $p-\Lambda$ scattering cross section. Our results for scattering length, effective range and cross sections are in good agreement with available experimental measurements. We also find that the $p-\Lambda$ system sustains attractive interactions. These results provide critical input for the unification of nuclear force theories and the construction of neutron star equations of state.