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arXiv · 2608.21459

A Hydrogen-Like Model for Pion and Kaon Masses Based on Dirac Quark-Hamiltonians and Numerical Methods

Zhenhua Ning·A. S. Davuluru·H. Raposo·Jong-Ping Hsu
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Abstract

We consider a relativistic hydrogen-like model for meson mass spectra. The model is based on a Lagrangian with a new general Yang-Mills symmetry. The strong interactions involve a fourth-order field equation that generates a linear confining potential. Notably, this model for meson masses requires quarks to carry only a single `confining charge' $f_c$ rather than three color charges. We classify meson mass spectra into sub-spectra defined by isospin, G-parity, total angular momentum and parity. By applying a numerical solver to the Dirac Hamiltonians--incorporating two short-range confining potentials, we obtain energy eigenvalues in natural units. The model has three coupling constants and one parameter. It provides a robust fit of 31 pions and kaons masses (from $\approx 140 MeV$ to $\approx 2,300 MeV$) to within $\approx 18\%$ of relative percentage error. The model suggests that the confining charge $f_c$=0.045/MeV = 8.87 fm plays the role of the basic length in the quark interactions.

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Zhenhua Ning, A. S. Davuluru, H. Raposo, Jong-Ping Hsu. 2026-08-20. A Hydrogen-Like Model for Pion and Kaon Masses Based on Dirac Quark-Hamiltonians and Numerical Methods. https://arxiv.org/abs/2608.21459

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