Exploring Efimov states in $D^{\ast }{D}^{\ast }{D}^{\ast }$ and $D{D}^{\ast }{D}^{\ast }$ three-body systems

Abstract

The Efimov effect is an intriguing three-body quantum phenomenon. Searching for Efimov states within the realms of nuclear and hadronic physics presents a challenge due to the inherent inability of natural physical systems to exhibit adjustable two-body scattering lengths. In this study, we examine the potential existence of Efimov states in the $D^{\ast }{D}^{\ast }{D}^{\ast }$ and $D{D}^{\ast }{D}^{\ast }$ three-hadron systems. Utilizing a pionless effective field theory framework, we determine that the presence of Efimov states in the spectrum of the $D^{\ast }{D}^{\ast }{D}^{\ast }$ system is contingent upon the existence of an $(I,J)=(1,2)$ $D^{\ast }{D}^{\ast }$ two-body bound system. If only the $T_{cc}^{+}$ and its heavy quark spin partner $T_{cc}^{\ast +}$ exist while there is no near-threshold pole in all other $S$-wave $D^{(\ast )}{D}^{\ast }$ scattering amplitudes, no Efimov effect is expected in the $D^{(\ast )}{D}^{\ast }{D}^{\ast }$ systems.

25 pages, 8 figures