Central and tensor Lambda-nucleon potentials from lattice QCD

TL;DR

This study uses lattice QCD to calculate Lambda-Nucleon interactions, revealing the nature of the potentials and scattering lengths across different quark masses, with implications for understanding hyperon-nucleon forces.

Contribution

The paper provides the first detailed lattice QCD calculations of both central and tensor Lambda-Nucleon potentials, including their quark mass dependence, in both full and quenched QCD.

Findings

LN potential has a strong repulsive core in the ^1S_0 channel

LN potential has a weak repulsive core in the ^3S_1 channel

The interaction is overall attractive, as indicated by negative energy shifts

Abstract

We present our latest study of Lambda-Nucleon (LN) interaction by using lattice QCD, following up on our report at LATTICE 2008. We have calculated not only the scattering lengths but also the central and tensor potentials, which are obtained from the Bethe-Salpeter (BS) amplitude measured in lattice QCD. For these calculations, we employ two different types of gauge configurations: (i) 2+1 flavor full QCD configurations generated by the PACS-CS collaboration at $\beta=1.9$ ($a=0.0907(13)$ fm) on a $32^3\times 64$ lattice, whose spatial volume is (2.90 fm)$^3$, with the quark masses corresponding to $(m_\pi,m_K)\approx (301,592)$, $(414,637)$, $(570,724)$ and $(699,787)$ (in units of MeV). (ii) Quenched QCD configurations at $\beta=5.7$ ($a=0.1416(9)$ fm) on a $32^3\times48$ lattice, whose spatial volume is (4.5 fm)$^3$, with the quark masses corresponding to $(m_\pi,m_K)\approx (512,606)$, $(464, 586)$ and $(407,565)$. The following qualitative features are found: The LN potential 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 tensor potential is found to be weaker than the $NN$ case. These results hold in both full and quenched QCD. The energy of the ground state on the finite lattice volume is calculated: In both spin channels, energy shift due to the finite volume, from which we extract the scattering length via the L\"{u}scher's formula, is found to be negative at all values of quark masses, suggesting that the LN interaction is attractive. We have also discussed the quark mass dependences of the potentials and the scattering lengths.