QCD QED Potentials, Quantum Field Theoretical Generalization of Yukawa Potential

TL;DR

This paper generalizes Yukawa potentials within quantum field theories to include scale-dependent couplings and dynamical masses, providing insights into quark confinement, deconfinement, and electron-positron interactions.

Contribution

It introduces a quantum field theoretical framework that extends Yukawa potentials to incorporate running coupling constants and dynamical masses, explaining confinement and contact interactions.

Findings

QCD potential predicts quark confinement and deconfinement.

QED potential shows a sharply rising delta function near contact distance.

Dynamical mass emerges in the zero input mass limit through renormalization.

Abstract

Despite the success of quantum field theories, the origin of the mass of elementary particles persists. 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 exists 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 of the quantum fields in the 4-dimensional space when the dimensional regularization method of renormalization is utilized. The complex forms of the QCD and QED interaction potentials are obtained by replacing the fixed mass and coupling constants in the Yukawa potential with the scale-dependent running coupling constant and the corresponding dynamical mass. The derived QCD potential predicts quark confinement and deconfinement, and the QED potential derived by the same method predicts the sharply rising delta function potential near the contact distance between the electron and positron.