Attractive $N$-$\phi$ Interaction and Two-Pion Tail from Lattice QCD near Physical Point

TL;DR

This study uses lattice QCD simulations to investigate the attractive interaction between the nucleon and phi meson, revealing a potential with both short-range attraction and a long-range tail consistent with two-pion exchange.

Contribution

First lattice QCD analysis of N-phi interaction near physical quark masses, identifying a potential with a long-range tail from two-pion exchange.

Findings

The N-phi potential has a short-range attractive core and a long-range tail.

The scattering length and effective range are quantified at near physical pion mass.

The long-range tail from two-pion exchange influences the scattering properties.

Abstract

First results on the interaction between the $\phi$-meson and the nucleon ($N$) are presented based on the ($2+1$)-flavor lattice QCD simulations with nearly physical quark masses. Using the HAL QCD method, the spacetime correlation of the $N$-$\phi$ system in the spin 3/2 channel is converted into the $N$-$\phi$ scattering phase shift through the interaction potential. The $N$-$\phi$ potential appears to be a combination of a short-range attractive core and a long-range attractive tail. The latter is found to be consistent with the two-pion exchange (TPE) obtained from the interaction between a color-dipole and the nucleon. The resultant scattering length and effective range for $m_{\pi}=$ 146.4 MeV are $ a^{(3/2)}_0=-1.43(23)_{\rm stat.}\left(^{+36}_{-06}\right)_{\rm syst.} {\rm fm}$ and $ r^{(3/2)}_{\rm eff}=2.36(10)_{\rm stat.}\left(^{+02}_{-48}\right)_{\rm syst.} {\rm fm}$, respectively. The magnitude of the scattering length is shown to have nontrivial dependence of $m_{\pi}$ and is sensitive to the existence of the long-range tail from TPE.