The $X(4500)$ state considered as the mixture of hadronic molecule and diquark-antidiquark within effective field theory

Abstract

In the present work, we construct the Lagrangians including three-meson, meson-diquark-antidiquark vertices, such that the diquark-antidiquark component as well as the molecular component are introduced within the effective field theory. With the obtained effective potentials projecting to spin 0, 1 and 2, we solve the Bethe-Salpeter equation with the on-shell approximation, and find that $X(4500)$ can be explained as the mixture of components $D_s^{\ast +}{D}_s^{\ast -}$, $A_{cq}{\bar{A}}_{cq}$ and $A_{cs}{\bar{A}}_{cs}$ with $I^G(J^{PC})=0^{+}(0^{++})$. In addition, another two resonances with quantum numbers $I^G(J^{PC})=0^{+}(1^{++})$ and $I^G(J^{PC})=0^{+}(2^{++})$ are predicted.

6 pages, 2 figures