A note on the possible bound $D^{(\ast)} D ^{(\ast)}, \bar{B}^{(\ast)} \bar{B}^{(\ast)} $ and $D^{(\ast)} \bar{B}^{(\ast)} $ states

TL;DR

This paper uses Heavy-Meson Effective Theory to analyze the potential for forming deuteron-like bound states among heavy mesons, motivated by the recent observation of the $T_{cc}^+$ tetraquark, and explores conditions for other loosely-bound states.

Contribution

It provides a simplified field-theoretical approach to study possible heavy meson molecules, fixing potentials using experimental data from $T_{cc}^+$ to predict other bound states.

Findings

Potential for other loosely-bound states identified.

Conditions for formation of $D^{(*)} D^{(*)}$, $ar{B}^{(*)} ar{B}^{(*)}$, and $D^{(*)} ar{B}^{(*)}$ molecules analyzed.

Analysis suggests possible existence of additional heavy meson molecules.

Abstract

Motivated by the recently observation of the tetraquark $T_{cc}^+ $ state, in this work I revisit the Heavy-Meson Effective Theory to perform a simplified field-theoretical study of possible deuteron-like $D^{(\ast)} D ^{(\ast)}, \bar{B}^{(\ast)} \bar{B}^{(\ast)} $ and $D^{(\ast)} \bar{B}^{(\ast)} $ molecules. In particular, using the data from $T_{cc}^+ $ as input to fix the potential associated to the shallow-bound $ D D^{*} $ system with $I(J^P) = 1(1^+)$, the conditions for the formation of other loosely-bound states in the doubly charmed sector are analyzed. The other sectors are also discussed.