Inseparability of charged quasirelativistic scalar mesons
Phys. Rev. D 113, 116029 – Published 17 June, 2026
DOI: https://doi.org/10.1103/mkfr-fvxl
Abstract
We study the Duan-Giedke-Cirac-Zoller continuous-variable inseparability criterion in a weakly relativistic, single-pair Klein-Gordon model of two charged scalar mesons. We implement a nonrelativistic inseparability criterion to quasirelativistic Klein–Gordon bound states, evaluated in the relativistic center-of-mass frame, where canonical position and momentum operators remain meaningful approximate observables. We assumed that the distance between the mesons exceeds the radius of the short-range strong interaction, which is of the order of 2-3 femtometers. Therefore, the dominant interaction in the system is a central-symmetric Coulomb potential. In particular, we utilized the sufficient criterion for separability and the necessary condition of inseparability to calculate the total variance of two operators in the weakly relativistic and nonrelativistic cases. In the weakly relativistic case, we used the solution of the Klein-Gordon equation. In contrast, in the nonrelativistic case, we used the solution of the Schrödinger equation obtained for the same central-symmetric potential. Within this regime, the Klein-Gordon states considered show a stronger violation of the separability bound than the corresponding Schrödinger states.
