Gluon saturation scale from the KGBJS equation

TL;DR

This paper solves the KGBJS equation for gluon densities, compares it with other models, and introduces a new hard-scale-dependent saturation scale, revealing how saturation effects evolve with energy and scale.

Contribution

It provides the first detailed analysis of the KGBJS equation solutions and introduces the hard-scale-related saturation scale P_s, enhancing understanding of gluon saturation dynamics.

Findings

Saturation scale Q_s depends on the hard scale p and energy x.

At high transverse momenta, saturation effects become independent of the hard scale.

The new scale P_s decreases with decreasing x, starting from the gluon's transverse momentum.

Abstract

The CCFM equation and its extended form with a quadratic term (KGBJS equation) are solved with fixed and running coupling constant. The solution of the KGBJS equation is compared to gluon densities resulting from the CCFM and BK equations. As the saturation scale $Q_s$ now becomes available as a function of the hard scale $p$ we observe that low values of $p$ impede its growth with $\frac 1 x$. Also, at values much larger than partons transversal momentum the saturation effects become independent on the hard scale what we call liberation of saturation scale. We also introduce the hard-scale-related saturation scale $P_s$ and investigate its energy dependence. We observe that the new scale as a function of $x$ decreases starting from the value of transversal momentum of gluon.