Multiplicity-dependent forward jet production in proton–nucleus collisions

A bstract Forward jet production in proton–nucleus collisions probes a dilute projectile scattering from a dense small- x nuclear gluon field, while the charged-particle multiplicity inside the jet probes the final-state cascade in the jet cone. We develop a factorization framework for single-inclusive forward jets with an internal multiplicity measurement by combining the Color Glass Condensate (CGC) description of the production process with soft-collinear effective theory (SCET) semi-inclusive jet functions. At the formal matching level, the construction enforces the inclusive limit through the stated O ( α s ) matching order. When the multiplicity weight vanishes, the measured fixed-order terms reduce to the known inclusive next-to-leading order (NLO) CGC forward-jet cross section. The all-order resummed form is retained as a factorization ansatz. We define the multiplicity-measured jet operator in a CGC background. We then formulate a matching prescription that separates the PDF and BK/JIMWLK sectors from the measured jet evolution. Sudakov, SiJF, and multiplicity radiation are assigned consistently within this prescription. This separation identifies the Wilson-line resolution mechanism through which saturation can modify the internal multiplicity evolution. The resulting framework shows that high-multiplicity forward jets are sensitive both to the production-level quark/gluon mixture and to finite- Q s corrections when an early in-cone splitting is resolved by the target. A baseline numerical implementation tests this construction in a phenomenological nPDF-reweighted per-nucleon setup and illustrates a multiplicity-conditioned nuclear-side diagnostic. The displayed baseline uses LO-like production weights, the accepted diagonal-quark denominator factor, and the local Wilson-line correction to multiplicity evolution. Finite measured hard numerators are defined by the matching construction but are not included in the displayed curves. The numerical diagnostic is not a completed calculation of ∆Γ A – ∆Γ p with separately normalized proton and nuclear dipoles.