QCD QED Potentials, Quark Confinement

Theoretical Generalization of Yukawa Potential

Abstract

One of the enduring puzzles in high energy particle physics is why quarks do not exist independently ‎despite their existence inside the hadron as quarks have never been found in isolation. This problem may ‎be solved by formulating a QCD potential for the entire range of interaction distances of the quarks. The ‎mystery could be related to the fundamental origin of the mass of elementary particles despite the success ‎of the quantum field theories to the highest level of accuracy. The renormalization program is an essential ‎part of the calculation of the scattering amplitudes, where the infinities of the calculated masses of the ‎elementary particles are subtracted for the progressive calculation of the higher-order perturbative terms. ‎The mathematical structure of the mass term from quantum field theories expressed in the form of infinities ‎suggests that there may exist a finite dynamical mass in the limit when the input mass parameter ‎approaches zero. The Lagrangian recovers symmetry at the same time as the input mass becomes zero, ‎whereas the self-energy diagrams acquire a finite dynamical mass in the 4-dimensional space when the ‎dimensional regularization method of renormalization is utilized. We report a new finding that using the ‎mathematical expression of the self-energy(mass) for photons and gluons calculated from this method, the ‎complex form of the QCD and QED interaction potentials can be obtained by replacing the fixed ‎interaction mediating particle’s mass and coupling constants in Yukawa potential with the scale-‎dependent running coupling constant and the corresponding dynamical mass. The derived QCD QED ‎potentials predict the behavior of the related elementary particles exactly as verified by experimental ‎observation.‎