Forward di-jet production in dilute-dense collisions

Abstract

We derive a factorization formula for forward production of two jets in dilutedense collisions that is valid for an arbitrary value of the momentum imbalance of the jets, kt. This generalizes the transverse momentum dependent (TMD) factorization formula that has been derived before by Dominguez et al. Their formula is valid only for small values of the transverse momentum of the small-x gluon from the target; it has kt dependent TMD gluon distributions, but on-shell hard matrix elements. We extend the TMD formula to all ranges of kt by including off-shell matrix elements. We also add finite Nc corrections. The new formula encompasses both, the TMD factorization for small kt on the order of the saturation scale, and the High Energy Factorization (HEF) for large kt on the order of the momentum of the jets. The TMD and HEF factorizations can be derived from the Color Glass Condensate (CGC) formula for forward di-jet production in the appropriate limits. We show explicitly the equivalence of HEF and CGC in the dilute target approximation.