Non-linear evolution of unintegrated gluon density at large values of coupling constant

TL;DR

This paper introduces a new evolution equation for unintegrated gluon densities applicable at large QCD coupling constants, incorporating non-linear effects and supported by AdS/CFT and perturbative arguments, with numerical solutions revealing the saturation scale.

Contribution

It generalizes the linear resummation model to include non-linear terms for strong coupling regimes in gluon density evolution.

Findings

Numerical solutions of the evolution equation show the behavior of the saturation scale at strong coupling.

The model's validity is supported by AdS/CFT and perturbative considerations.

Comparison with weak coupling results highlights differences in gluon saturation dynamics.

Abstract

We propose an evolution equation for unintegrated gluon densities that is valid for large values of the QCD coupling constant $\bar{\alpha} _s$. Our approach is based on the linear resummation model introduced by Sta\'{s}to. We generalize the model including a non-linear term in the diffusive regime. The validity of the diffusive evolution at strong coupling is supported by the AdS/CFT consideration, as well as perturbative arguments. We solve the evolution equation numerically and extract the saturation scale, which we compare with the weak coupling counterpart.