2025/12/02 by Lin-Qing Song, Song, Lin-Qing, Hai-Qing Zhou +1
Physics and Astronomy · #Quantum Chromodynamics and Particle Interactions #High-Energy Particle Collisions Research #Cold Atom Physics and Bose-Einstein Condensates
paper · pdf · doi:10.48550/arxiv.2512.02524
This study presents a systematic estimation of the relativistic correction to the binding energies of two-body hadronic molecular states by comparing the numerical solutions of the three-dimensional (3D) Schrödinger, 3D Salpeter, and fully relativistic four-dimensional (4D) Bethe-Salpeter (BS) equations derived from the same underlying interaction. The numerical results reveal a counter-intuitive property: for hadronic molecular states whose binding energies are in the MeV range, the relativistic correction is unexpectedly large. This finding contradicts the conventional expectation that a heavier exchanged mass in the interaction implies suppressed relativistic effects. Specifically, we first benchmark the results using the Wick-Cutkosky model with a one-boson-exchange (OBE) interaction of mass mex, and then extend the analysis to the physical DD system. We find within the 1∼ 50 MeV binding energy region, the relativistic correction is substantial, amounting to -90% ∼ -70% of the non-relativistic result. Such a significant correction strongly suggests that analyses based solely on the 3D Schrödinger or 3D Salpeter equations for hadronic molecular states should be treated with caution.