Study on the possible molecular state composed of within the Bethe-Salpeter framework *

Abstract

Abstract Recently, a vector charmonium-like state was observed in the portal of . This intrigues an active discussion on the structure of the resonance because it has obvious significance for gaining a better understanding on its hadronic structure that contains suitable inner constituents. Therefore, this observation concerns the general theoretical framework about possible structures of exotic states. Since the mass of is slightly above the production threshold of whereas it is below that of with the same quark contents as that of , it is natural to conjecture that is a molecular state of , as suggested in the literature. Confirming or negating this allegation would shed light on the goal we are concerned with. We calculate the mass spectrum of a system composed of a vector meson and an axial vector i.e., within the framework of the Bethe-Salpeter equations. Our numerical results show that the dimensionless parameter in the form factor, which is phenomenologically introduced to every vertex, is far beyond the reasonable range for inducing even a very small binding energy . It implies that the system cannot exist in the nature as a hadronic molecule in this model. Therefore, we may not be able to assume the resonance to be a bound state of and instead, it could be attributed to something else, such as a tetraquark.