Forward production of a Drell-Yan pair and a jet at small $x$ at next-to-leading order

TL;DR

This paper presents a next-to-leading order calculation of forward Drell-Yan pair and jet production at small x, incorporating dense gluon distributions via the Color Glass Condensate framework and resumming high-energy logarithms with BK-JIMWLK evolution.

Contribution

It provides the first complete NLO calculation for this process at small x using the CGC approach, including the treatment of divergences and the resummation of high-energy logarithms.

Findings

Ultraviolet divergences cancel in the calculation.

High-energy divergences are absorbed into BK-JIMWLK evolution.

The resulting cross section is finite and expressed with a minimal set of color operators.

Abstract

We perform the analytical next-to-leading order calculation of the process $p+A\to \gamma^{*}+\mathrm{jet}+X$, at forward rapidities and low $x$. These kinematics justify a hybrid approach, where a quark from the \textquoteleft projectile' proton scatters off the gluon distribution of the \textquoteleft target', which can be a nucleus or a highly boosted proton. By using the Color Glass Condensate effective theory approach, this gluon distribution is allowed to be so dense that the quark undergoes multiple scattering. Moreover, large high-energy logarithms in the ratio of the hard scale and the center-of-mass energy are resummed by the Balitsky, Kovchegov, Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner or BK-JIMWLK evolution equations. We demonstrate that all ultraviolet divergences encountered in the calculation cancel, while the high-energy divergences are absorbed into BK-JIMWLK. The remaining singularities are collinear in nature and can be either absorbed into the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution of the incoming quark, when they stem from initial-state radiation, or else can be treated by introduction of a jet function in case they are caused by final-state emissions. The resulting cross section is completely finite and expressed in function of only a small set of color operators.