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

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.