Phenomenological exploration of the strong coupling constant in the perturbative and nonperturbative regions

TL;DR

This paper investigates the strong coupling constant in both perturbative and nonperturbative QCD regions using phenomenological models, experimental data, and applies findings to charmonium spectrum analysis.

Contribution

It introduces a continuous phenomenological function for the coupling constant across QCD regions and integrates it into a relativistic model for charmonium.

Findings

Determined a continuous phenomenological function for the coupling constant.

Calculated the finite value of the vector quark self-energy.

Fitted the charmonium spectrum using the developed models.

Abstract

The QCD running coupling costant is studied in the perturbative region, considering the existing experimental data, and also in the nonperurbative region, at low momentum transfer. A continous phenomenological function is determined by means of three different models also calculating the corresponding finite value of the vector quark self-energy. These two quantities are used for the vector interaction of a Dirac relativistic model for the charmonium spectrum. The process required to fit the spectrum is discussed and the relationship with previous models is analyzed.