Nucleon Mass Sum Rule Violation in QCD and Confinement

TL;DR

This paper demonstrates that in QCD, the nucleon mass sum rule is violated when quarks are in motion and a linearly rising confinement potential energy exists, due to chromo-magnetic fields inside the nucleon.

Contribution

It reveals the violation of the nucleon mass sum rule in the presence of chromo-magnetic fields and linear confinement potential energy in QCD.

Findings

Mass of the nucleon is not equal to the sum of constituent energies under certain conditions.

Chromo-magnetic fields inside the nucleon affect the mass-energy relationship.

Linear or faster rising confinement potential leads to sum rule violation.

Abstract

In this paper we show that for a nucleon at rest if the quarks and/or antiquarks are in motion inside the nucleon producing chromo-magnetic field then the mass sum rule in QCD is violated when the confinement potential energy at large distance $r$ rises linearly with $r$ (or faster). Hence we find that the mass of the nucleon at rest is not equal to the mass-energy of all the quarks plus antiquarks plus gluons inside the nucleon if there exists chromo-magnetic field inside the nucleon and the confinement potential energy at large distance $r$ rises linearly with $r$ (or faster).