Running Coupling Corrections to High Energy Inclusive Gluon Production

TL;DR

This paper derives running coupling corrections for high energy gluon production cross sections, replacing fixed couplings with a complex 'septumvirate' of running couplings, and discusses implications for small-x evolution.

Contribution

It introduces a novel 'septumvirate' of running couplings in gluon production calculations, extending previous 'triumvirate' concepts to include complex momentum scales.

Findings

Replaced three fixed couplings with seven running couplings in the cross section

Identified complex conjugate momentum scales for the denominator couplings

Provided a conjecture for incorporating running couplings into full kT-factorization formulas

Abstract

We calculate running coupling corrections for the lowest-order gluon production cross section in high energy hadronic and nuclear scattering using the BLM scale-setting prescription. In the final answer for the cross section the three powers of fixed coupling are replaced by seven factors of running coupling, five in the numerator and two in the denominator, forming a 'septumvirate' of running couplings, analogous to the 'triumvirate' of running couplings found earlier for the small-x BFKL/BK/JIMWLK evolution equations. It is interesting to note that the two running couplings in the denominator of the 'septumvirate' run with complex-valued momentum scales, which are complex conjugates of each other, such that the production cross section is indeed real. We use our lowest-order result to conjecture how running coupling corrections may enter the full fixed-coupling kT-factorization formula for gluon production which includes non-linear small-x evolution.