Improved TMD factorization for forward dijet production in dilute-dense hadronic collisions

TL;DR

This paper develops a unified factorization formula for forward dijet production in dilute-dense collisions, bridging TMD and high-energy approaches within the Color Glass Condensate framework, applicable across different transverse momentum regimes.

Contribution

It introduces a new, generalized formula for forward dijets that unifies TMD and high-energy factorization, derived through two independent methods.

Findings

Derived a unified factorization formula valid for all transverse momentum imbalances.

Showed the connection between TMD and high-energy factorization within the CGC framework.

Provided two independent derivations using Feynman diagrams and color-ordered amplitudes.

Abstract

We study forward dijet production in dilute-dense hadronic collisions. By considering the appropriate limits, we show that both the transverse-momentum-dependent (TMD) and the high-energy factorization formulas can be derived from the Color Glass Condensate framework. Respectively, this happens when the transverse momentum imbalance of the dijet system, $k_t$, is of the order of either the saturation scale, or the hard jet momenta, the former being always much smaller than the latter. We propose a new formula for forward dijets that encompasses both situations and is therefore applicable regardless of the magnitude of $k_t$. That involves generalizing the TMD factorization formula for dijet production to the case where the incoming small-$x$ gluon is off-shell. The derivation is performed in two independent ways, using either Feynman diagram techniques, or color-ordered amplitudes.