The chaotic effects in a nonlinear QCD evolution equation

TL;DR

This paper investigates nonlinear QCD evolution equations, revealing chaotic solutions that cause a new shadowing effect at small x, potentially impacting future collider experiments and our understanding of gluon dynamics.

Contribution

It introduces a new nonlinear QCD evolution equation exhibiting chaos, expanding the understanding of gluon saturation and shadowing effects beyond existing models.

Findings

The new evolution equation exhibits chaos with positive Lyapunov exponents.

Chaos induces a shadowing effect blocking QCD evolution at small x.

Potential implications for collider experiments and gluon saturation theories.

Abstract

The corrections of gluon fusion to the DGLAP and BFKL equations are discussed in a united partonic framework. The resulting nonlinear evolution equations are the well-known GLR-MQ-ZRS equation and a new evolution equation. Using the available saturation models as input, we find that the new evolution equation has the chaos solution with positive Lyaponov exponents in the perturbative range. We predict a new kind of shadowing caused by chaos, which blocks the QCD evolution in a critical small $x$ range. The blocking effect in the evolution equation may explain the Abelian gluon assumption and even influence our expectations to the projected Large Hadron Electron Collider (LHeC), Very Large Hadron Collider (VLHC) and the upgrade (CppC) in a circular $e^+e^-$ collider (SppC).