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

TL;DR

This paper models the $X(4500)$ state as a mixture of hadronic molecules and diquark-antidiquark components using effective field theory, solving Bethe-Salpeter equations to explain its structure and predict additional resonances.

Contribution

It introduces a novel effective field theory approach combining molecular and diquark-antidiquark components to analyze the $X(4500)$ state and predicts new resonances.

Findings

$X(4500)$ is explained as a mixture of specific molecular and diquark components.

Predicted two additional resonances with different quantum numbers.

Effective potentials successfully reproduce the observed state.

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 $D_{s}^{*+}D_{s}^{*-}$, ${A}_{cq}\bar{A}_{cq}$ 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.