Inverse Excitation Hierarchy in Doubly-Heavy Tetraquarks within the Diquark Model

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.