Evolution of genuine states to molecular ones: The $T_{cc}(3875)$ case

TL;DR

This paper explores how genuine nonmolecular states can evolve into molecular states through meson coupling, emphasizing that binding energy alone doesn't determine compositeness but scattering parameters do, with specific analysis on the $T_{cc}(3875)$.

Contribution

It demonstrates that the compositeness of hadronic states depends on scattering parameters and coupling, not solely on binding energy, providing a generalized framework for hadronic systems.

Findings

Genuine states can become molecular through meson coupling near threshold.

Scattering length and effective range are key to determining compositeness.

Including direct meson interactions increases the molecular component.

Abstract

We address the issue of the compositeness of hadronic states and demonstrate that starting with a genuine state of nonmolecular nature, but which couples to some meson-meson component to be observable in that channel, if that state is blamed for a bound state appearing below the meson-meson threshold it gets dressed with a meson cloud and it becomes pure molecular in the limit case of zero binding. We discuss the issue of the scales, and see that if the genuine state has a mass very close to threshold, the theorem holds, but the molecular probability goes to unity in a very narrow range of energies close to threshold. The conclusion is that the value of the binding does not determine the compositeness of a state. However, in such extreme cases we see that the scattering length gets progressively smaller and the effective range grows indefinitely. In other words, the binding energy does not determine the compositeness of a state, but the additional information of the scattering length and effective range can provide an answer. We also show that the consideration of a direct attractive interaction between the mesons in addition to having a genuine component, increases the compositeness of the state. Explicit calculations are done for the $T_{cc}(3875)$ state, but are easily generalized to any hadronic system.