Revisiting Single Inclusive Jet Production: Timelike Factorization and Reciprocity

TL;DR

This paper revisits the factorization theorems for single inclusive jet production, identifies inconsistencies in previous formulas, and derives a new all-order factorization theorem that enhances precision in jet substructure analysis.

Contribution

It presents a new all-order factorization theorem for inclusive jet production, correcting previous inconsistencies and extending the formalism to jet substructure observables.

Findings

Explicit two-loop calculations in QCD and $ ext{N}=4$ SYM confirm the new factorization structure.

Identified inconsistency in previous semi-inclusive jet factorization formula.

Derived a convolution-based factorization theorem maintaining universality of the hard function.

Abstract

Factorization theorems for single inclusive jet production play a crucial role in the study of jets and their substructure. In the case of small radius jets, the dynamics of the jet clustering can be factorized from both the hard production dynamics, and the dynamics of the low scale jet substructure measurement, and is described by a matching coefficient that can be computed in perturbative Quantum Chromodynamics (QCD). A proposed factorization formula describing this process has been previously presented in the literature, and is referred to as the semi-inclusive, or fragmenting jets formalism. By performing an explicit two-loop calculation, we show the inconsistency of this factorization formula, in agreement with another recent result in the literature. Building on recent progress in the factorization of single logarithmic observables, and the understanding of reciprocity, we then derive a new all-order factorization theorem for inclusive jet production. Our factorization involves a non-trivial convolution structure, that maintains the universality of the hard function from inclusive fragmentation. We perform an explicit two-loop calculation of the jet function in both $\mathcal{N}=4$ super Yang-Mills (SYM), and for all color channels in QCD, finding exact agreement with the structure derived from our renormalization group equations. In addition, we derive several new results, including an extension of our factorization formula to jet substructure observables, a jet algorithm definition of a generating function for the energy correlators, and new results for exclusive jet functions. Our results are a key ingredient for achieving precision jet substructure at colliders.