Attractive N−ϕ interaction and two-pion tail from lattice QCD near physical point

Abstract

First results on the interaction between the $\ensuremath{\phi}$-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 $N\text{\ensuremath{-}}\ensuremath{\phi}$ system in the spin $3/2$ channel is converted into the $N\text{\ensuremath{-}}\ensuremath{\phi}$ scattering phase shift through the interaction potential. The $N\text{\ensuremath{-}}\ensuremath{\phi}$ 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 ${m}_{\ensuremath{\pi}}=146.4\text{ }\text{ }\mathrm{MeV}$ are ${a}_{0}^{(3/2)}=\ensuremath{-}1.43(23{)}_{\mathrm{stat}}({{\text{ }}_{\ensuremath{-}06}^{+36})}_{\mathrm{syst}}\text{ }\text{ }\mathrm{fm}$ and ${r}_{\mathrm{eff}}^{(3/2)}=2.36(10{)}_{\mathrm{stat}}{({\text{ }}_{\ensuremath{-}48}^{+02})}_{\mathrm{syst}}\text{ }\text{ }\mathrm{fm}$, respectively. The magnitude of the scattering length is shown to have nontrivial dependence of ${m}_{\ensuremath{\pi}}$ and is sensitive to the existence of the long-range tail from TPE.