A Monte Carlo study of double logarithms in the small x region

TL;DR

This study uses Monte Carlo simulations to analyze how resumming collinear double logarithms in the BFKL framework improves convergence, reduces cross section growth, and affects gluon diffusion and mini-jet production at small x.

Contribution

It introduces a Monte Carlo implementation of resummed collinear double logarithms in the BFKL gluon Green function, enhancing theoretical predictions at small x.

Findings

Improved collinear convergence of BFKL calculations.

Reduced asymptotic growth of cross sections with energy.

Decreased mini-jet multiplicity and gluon diffusion into infrared and ultraviolet scales.

Abstract

We investigate the effect of the resummation of collinear double logarithms in the BFKL gluon Green function using the Monte Carlo event generator BFKLex. The resummed collinear terms in transverse momentum space were calculated in Ref. [1] and correspond to the addition to the NLO BFKL kernel of a Bessel function of the first kind whose argument contains the strong coupling and a double logarithm of the ratio of the squared transverse momenta of the reggeized gluons. We discuss how these additional terms improve the collinear convergence of the whole approach and reduce the asymptotic growth with energy of cross sections. Taking advantage of the Monte Carlo implementation, we show how the new results reduce the diffusion of the gluon ladder into infrared and ultraviolet transverse momentum scales, while strongly affecting final state configurations by reducing the mini-jet multiplicity.