Lambda-nucleon force from lattice QCD

Abstract

We study the $\Lambda$-nucleon ($\Lambda N$) force by using lattice QCD. The Bethe-Salpeter amplitude is calculated for the lowest scattering state of the $\Lambda N$ so as to obtain the $\Lambda N$ potential. The numerical calculation is twofold: (i) Full lattice QCD by using 2+1 flavor PACS-CS gauge configurations with, $\beta=1.9$, corresponding to the lattice spacing of $a=0.0907(13)$ fm, on a $32^3\times 64$ lattice. A set of parameter $(\kappa_{ud},\kappa_s)=(0.13770,0.13640)$ is used, which corresponds to $m_\pi\approx 300$ MeV and $m_K\approx 594$ MeV. The spatial lattice volume corresponds to (2.86 fm)$^3$. (ii) Quenched lattice QCD with $\beta=5.7$, the lattice spacing of $a=0.1416(9)$ fm, on the $32^3\times48$ lattice. Two sets of hopping parameters $(\kappa_{ud},\kappa_s)=(0.1665,0.1643),(0.1670,0.1643)$ are used. The spatial lattice volume is (4.5 fm)$^3$. For the full QCD, we find that the $\Lambda p$ has a relatively strong (weak) repulsive core in the $^1S_0$ ($^3S_1$) channel at short distance, while the potential has slight attractive region at medium distance. The lowest scattering energy in the finite lattice volume is calculated; Slightly negative values obtained in both spin channels. For the quenched QCD, we find that the results are qualitatively in agreement with those in the full QCD calculation.