The hadronic potential at short distance

TL;DR

This paper offers new physical insights into the short-distance behavior of gauge theories and the potential energy in QCD and QED, highlighting the impact of regularization choices on Coulomb potential modifications.

Contribution

It introduces the role of cut-off functions and their parameters in shaping the short-distance potential, emphasizing the importance of keeping the cut-off scale finite in renormalization.

Findings

Cut-off functions can significantly modify Coulomb potential at small distances.

The regularization parameters should remain finite, not tend to infinity.

General aspects of short-distance gauge theory potentials are discussed.

Abstract

A fictitious discussion is taken as a point of origin to present novel physical insight into the nature of gauge theory and the potential energy of QCD and QED at short distance. Emphasized is the considerable freedom in the cut-off function which eventually can modify the Coulomb potential of two charges at sufficiently small distances. Emphasized is also that the parameters of the regularization function (the ``cut-off scale'') should not be driven to infinity but kept constant in line with the modern interpretation of renormalization theory. The paper restricts to general aspects. The technical paraphernalia and the comparison with experiment are shifted to a sequence of 4 subsequent stand-alone and sufficiently small papers to be published immediatelely hereafter.