Running Coupling Corrections to High Energy Inclusive Gluon Production
W. A. Horowitz, Yuri V. Kovchegov
TL;DR
The paper computes running coupling corrections to the leading-order high-energy inclusive gluon production cross section using the BLM scale-setting method. It analyzes both bremsstrahlung and triple-gluon-vertex diagrams to derive a seven-running-coupling (septumvirate) structure, with two complex-conjugate momentum scales that ensure a real cross section. The authors present an exact running-coupling expression for the gluon production cross section and propose a running-coupling generalization of kt-factorization within the CGC framework, supported by a MV-model discussion. They also explore implications for gluon multiplicity dN/dy and centrality dependence, concluding that running-coupling effects alone are insufficient to describe RHIC data and that incorporating small-x evolution is essential. Overall, the work provides RG-improved predictions for high-energy hadronic and nuclear collisions and outlines a concrete path to include running couplings in the kt-factorization formalism.
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.