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

Abstract

First results on the interaction between the $\varphi$-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 $N$-$\varphi$ system in the spin 3/2 channel is converted into the $N$-$\varphi$ scattering phase shift through the interaction potential. The $N$-$\varphi$ 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 $a_0^{(3/2)}=-1.43(23{)}_{stat.}{\left({}_{-06}^{+36}\right)}_{syst.}\mathrm{fm}$ and $r_{\mathrm{eff}}^{(3/2)}=2.36(10{)}_{stat.}{\left({}_{-48}^{+02}\right)}_{syst.}\mathrm{fm}$, 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.

Comments: 8 pages, 6 figures, matches version published in PRD