Factorization for forward dijets in dilute-dense collisions

TL;DR

This paper introduces a unified factorization formula for forward dijet production in dilute-dense collisions, bridging the gap between TMD and HEF approaches across all momentum imbalance ranges.

Contribution

It extends existing factorization formulas to finite N_c and all k_t ranges, including off-shell effects and new analytical expressions for gluon distributions.

Findings

Unified factorization formula applicable for all k_t values.

Extended TMD formula to finite N_c and off-shell effects.

Derived analytical expressions for gluon distributions in specific models.

Abstract

We propose a factorization formula for the cross section for forward dijet production in dilute-dense collisions. The new formula is applicable for an arbitrary value of the momentum imbalance of the two jets, $k_t$. It unifies the previously derived transverse momentum dependent (TMD) factorization for small $k_t$ (of the order of the saturation scale), and the High Energy Factorization (HEF) for large $k_t$ (of the order of the momentum of the jets). We extend the previous TMD formula, first to finite $N_c$, and then to all ranges of $k_t$ by including off-shell matrix elements. We present previously unpublished analytical expressions for the TMD gluon distributions in the Golec-Biernat-Wusthoff model, and their perturbative behaviour in the McLerran-Venugopalan model. In addition, we show directly the equivalence of the HEF and the color glass condensate formulae in the dilute target approximation.