Momentum Sum Rule Violation in QCD at High Energy Colliders and Confinement

TL;DR

This paper demonstrates that the momentum sum rule in QCD is violated at high energy colliders due to the nature of confinement potential energy, especially when considering infinite or finite hadron sizes.

Contribution

It shows that the commonly assumed momentum sum rule in QCD does not hold under realistic confinement potential energy behaviors at high energies.

Findings

Momentum sum rule is violated for infinite hadron size.

Violation occurs for any confinement potential energy form at finite hadron size.

Confinement potential energy at large distances must grow slower than ln(r) to preserve the sum rule.

Abstract

Momentum sum rule in QCD is widely used at high energy colliders. Although the exact form of the confinement potential energy is not known but the confinement potential energy at large distance $r$ can not rise slower than ${\rm ln}(r)$. In this paper we find that if the confinement potential energy at large distance $r$ rises linearly with $r$ (or faster) then the momentum sum rule in QCD is violated at the high energy colliders if we consider the hadron size as infinite. For finite size hadron we find that the momentum sum rule in QCD is violated at the high energy colliders for any form of the confinement potential energy.