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 $D{D}^{\ast }$ 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.

Comments: 13 pages; 3 figures