Speaker
Description
Our work focused on studying the scattering length of $J/\psi N$ under gluon exchange via dispersion relations and compared the results with contributions from existing coupled-channel processes. Starting from the SU(3) tree-level chiral amplitudes of $N\bar{N}\to\pi\pi/K\bar{K}$, we obtained the $S$-wave amplitude considering the final state interactions of the $\pi\pi$-$K\bar{K}$ coupled channels through the Muskhelishvili-Omn`es representation. Using the amplitudes for the $J/\psi J/\psi\to\pi\pi/K\bar{K}$ processes from the literature and the crossing relations, we calculated the scattering length of $J/\psi N$ without considering the rescattering effects. Finally, by applying the Schwartz inequality satisfied by the chromopolarizability, we further refined this result, providing that the product of the scattering lengths of $J/\psi N$ and $\psi(2S) N$ satisfies $a^{J/\psi N}a^{\psi(2S) N}\geq 0.06\ {\rm{ fm}}^2$. Furthermore, both of these $S$-wave scattering lengths are spin-independent. Given that the coupled-channel mechanism yields a $J/\psi N$ scattering length of less than 10 am, we can conclude that the contribution from gluon exchange is qualitatively much larger than that from the coupled channels.
