Low-energy $Nφ$ scattering from a pole-enhanced triangle diagram

Abstract: We investigate low-energy $Nφ$ scattering driven by a pole-enhanced triangle diagram, in which the two-kaon-exchange contribution is promoted by the near-threshold $Λ(1405)$ pole in the $N\bar K$ subsystem. Using an unphysical kaon mass motivated by lattice simulations, we evaluate the $Nφ$ scattering length and find that this mechanism generates an attractive interaction with a magnitude of $-1.5$ 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-diagram amplitude and show that the scattering length performs a characteristic power-law dependence on the parameter $\tildeδ$, defined as the mass difference between the $K\bar K$ threshold and the $φ$ meson. This threshold-driven behavior 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 diagram in shaping the near-threshold $Nφ$ interaction.