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

Abstract

We perform the analytical next-to-leading order calculation of the process p + A γ∗ + jet + X, at forward rapidities and low x. These kinematics justify a hybrid approach, where a quark from the ‘projectile’ proton scatters off the gluon distribution of the ‘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 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.