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Abstract
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A theoretical search is conducted to determine the mass spectra and wave functions of the higher di-molecular type of meson states 𝑋(3872), 𝑌(4140), 𝑍(4430), 𝑋(5568) in the Hellmann potential, with relativistic effects and corrections. Femtoscopic J/ψ bound states have essential concepts in high-energy physics, especially in creating two-point correlation functions for the hadronic molecule channels that build the 𝑇𝑐𝑐 state. We analytically calculated the radial part of the Schrödinger equation using the transformation to relativistic space using the normal ordering operators. The excited states of eigenenergy are obtained. The constituent mass of the di-molecular type of mesons was determined, which appears due to relativistic effects. It is informative to describe strong interactions and bound states mechanisms using quantum field theory ideas and quantum mechanics. At the conclusion of this research, we will provide advancements in the higher meson states mass spectra in the relativistic limit. The results provide satisfaction in comparison with experimental data and the work of other researchers.
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