Understanding the Structure of Doubly-Heavy Tetraquarks based on the Diquark Model

TL;DR

This paper studies the structure of doubly-heavy tetraquarks using a diquark model and Schrödinger equation solutions, revealing an unexpected hierarchy in excitation energies due to centrifugal forces, with implications for exotic hadron dynamics.

Contribution

It introduces a novel analysis of tetraquark excitation energies showing an inversion in mass hierarchy caused by centrifugal effects, applicable across multiple heavy hadron systems.

Findings

Excitation energy between heavy diquark and light antidiquark is larger than between light anti-quarks.

Inversion of mass hierarchy explained by centrifugal force on light degrees of freedom.

The mechanism is consistent across different heavy hadron systems.

Abstract

We investigate the $T_{cc}$ tetraquark, treating it as a bound state of a heavy diquark and a light antidiquark. Using the Silvestre-Brac potential and solving the Schr\"odinger equation via the Gaussian Expansion Method, we find that the excitation energy between the heavy diquark and light antidiquark is unexpectedly larger than that between the two light anti-quarks within the anti-diquark -- contrary to the naive expectation where the former is smaller than the latter. We trace this inversion of the mass hierarchy to the centrifugal force acting on the light degree of freedom. Applying the same framework to other systems ($T_{bb}, \Lambda_b, \Lambda_c$) yields qualitatively identical behavior, demonstrating the robustness of the mechanism. These results provide new insights into diquark dynamics and the mass structure of exotic hadrons.