Possible Molecular States of $D^{(*)}D^{(*)}$ and $B^{(*)}B^{(*)}$ within the Bethe-Salpeter framework

TL;DR

This paper investigates the molecular structures of heavy meson pairs like $D^{(*)}D^{(*)}$ and $B^{(*)}B^{(*)}$ using the Bethe-Salpeter framework, supporting the interpretation of the $T^+_{cc}$ as a molecular state.

Contribution

It introduces a Bethe-Salpeter approach with a one boson exchange model to identify possible molecular states of heavy meson pairs, including the $T^+_{cc}$.

Findings

The isospin-1 $D^{(*)}D^{(*)}$ state with $J^P=1^+$ can exist.

The isospin-1 $D^{*}D^{*}$ state with $J^P=0^+$ can exist.

Possible molecular states of $B^{(*)}B^{(*)}$ are also identified.

Abstract

Recently the LHCb collaboration reported a new exotic state $T^+_{cc}$ which possesses $cc\bar u\bar d$ flavor structure. Since its mass is very close to the threshold of $D^0D^{*+}$ (or $D^{*0}D^{+}$) and its width is very narrow, it is inclined to conjecture that $T^+_{cc}$ is a molecular state of $D^0D^{*+}$ (or $D^{*0}D^{+}$). In this paper we study the possible molecular structures of $D^{(*)}D^{(*)}$ and $B^{(*)}B^{(*)}$ within the Bethe-Salpeter (B-S) framework. We employ one boson exchange model to stand the interaction kernels in the B-S equations. With reasonable input parameters we find the isospin eigenstate $\frac{1}{\sqrt{2}}(D^0D^{*+}-D^{*0}D^{+})$ ($J^P=1^+$) constitutes a solution, which supports the ansatz of $T^+_{cc}$ being a molecular state of $D^0D^{*+}$ (or $D^{*0}D^{+}$). With the same parameters we also find that the isospin-1 state $\frac{1}{\sqrt{2}}(D^{*0}D^{*+}+D^{*0}D^{*+})$ ($J^P=0^+$) can exist. Moreover, we also study the systems of $B^{(*)}B^{(*)}$ and their counterparts exist as possible molecular states. Consistency of theoretical computations based on such states with the data of the future experiments may consolidate the molecular structure of the exotic state $T^+_{cc}$.