Low-energy $N\phi$ scattering from a pole-enhanced triangle diagram

We investigate low-energy $N\phi$ scattering driven by a pole-enhanced triangle-like diagram, in which the two-Kaon-exchange contribution is promoted by the near-threshold $\Lambda(1405)$ pole in the $N\bar K$ subsystem. Using an unphysical Kaon mass motivated by lattice simulations, we evaluate the $N\phi$ scattering length and find that this mechanism generates an attractive interaction with a magnitude of $-1.1$ to $-0.5\, \rm{fm}$. Spin-dependent effects are not treated explicitly and are expected to provide subleading corrections in the near-threshold region. We further analyze the low-energy behavior of the triangle-like diagram amplitude and show that the scattering length depends on the parameter $\delta$, defined as the mass difference between the $K\bar K$ threshold and the $\phi$ meson, and the pole position of $\Lambda(1405)$, where the $\Lambda(1405)$ plays a crucial role to understand $N\phi$ interaction. Furthermore, by employing physical hadron masses, our calculated scattering length is found to be consistent with current experimental data, providing a unified description across both unphysical and physical mass regimes. This type of interaction differs from that associated with van der Waals-type forces or the long-range tail of two-pion exchange, highlighting the role of three-body dynamics encoded in the pole-enhanced triangle-like diagram in shaping the near-threshold $N\phi$ interaction.