The inevitable quark three-body force and its implications for exotic states

Abstract

Three-body nuclear forces are essential for explaining the properties of light nuclei with a nucleon number greater than three. Building on insights from nuclear physics, we extract the form of quark three-body interactions and demonstrate that these terms are crucial for extending the quark model fit of the meson spectrum to include baryons using the same parameter set. We then discuss the implications of our findings for exotic configurations involving more than three quarks, such as the $T_{cc}$ and ${\chi }_{c1}\left(3872\right)$. We find that the quark three-body interactions, which are valid at short ranges typical of a compact hadron, provide additional repulsion of more than 10 MeV for the compact configurations of both the $T_{cc}$ and ${\chi }_{c1}\left(3872\right)$. Since most of the previous quark model calculations based on two-body quark interactions do not find the energies of compact configurations for the $T_{cc}$ and ${\chi }_{c1}\left(3872\right)$ to be as attractive as 10 MeV below the threshold, our results strongly suggest that these tetraquark states are unlikely to be compact states, leaving the molecular configuration as the likely viable option.