Exploring the Efimov effect in the $D^{\ast }{D}^{\ast }{D}^{\ast }$ system

Abstract

The emergence of the Efimov effect in the $D^{\ast }{D}^{\ast }{D}^{\ast }$ system is explored under the assumption that the heavy partner of the $T_{cc}^{+}$ exists as a $D^{\ast }{D}^{\ast }$ molecule with $(I)J^P=(0)1^{+}$. The three-to-three relativistic scattering amplitude is obtained from the ladder amplitude formalism, built from an energy-dependent contact two-body potential where the molecular component of the $T_{cc}^{\ast }$ state can be varied. We find that $(I)J^P=(\frac{1}{2})0^{-}$ three-body bound states can be formed, with properties that suggest that the Efimov effect can be realised for reasonable values of the molecular probability and binding energy of the $T_{cc}^{\ast }$.

7 pages, 5 figures, 1 table