Broader validity of collinear factorization

Establish whether collinear factorization applies beyond the processes for which it has been rigorously proven, thereby determining the scope of its use in hadronic cross-section calculations.

Background

The paper explains that hadronic cross sections are conventionally decomposed into universal long-distance factors, namely parton distribution functions and fragmentation functions, and perturbatively calculable partonic cross sections. Although collinear factorization has been proven only for certain classes of processes, its broader applicability underlies the theoretical treatment of simultaneous W-boson and charmed-hadron production analyzed in the paper. The authors identify this broader validity as a conjectural issue supported empirically by agreement with data across many processes.

References

A factorisation theorem to NLO has been established for the case of incoming longitudinally polarised photons, while no general proof exists for transversely polarised photons.

— Observables in exclusive heavy quarkonium electroproduction at NLO and prospects for the EIC  (2609.12652 - Flett, 11 Sep 2026) in Section 1, “Introduction and set up”

For the $\gamma N\to\gamma\pi0N$ process, the Glauber obstruction in the gluon GPD channel breaks the standard collinear factorization rather than causing a mere endpoint subtlety, and whether a modified factorization formula involving additional nonperturbative functions/effects beyond GPDs and DAs can restore predictability remains an open question.

— Generalized parton distributions: Theory meets experiment  (2609.19544 - Guo et al., 17 Sep 2026) in Section 3, “Hard exclusive 2→3 processes”

At present, however, no general proof of collinear factorization has been established to all orders in the $1/Q$ expansion for observables involving two or more identified hadrons. Beyond the first subleading power, the number of independent multiparton correlation functions increases rapidly, while long-distance soft interactions and more intricate color correlations considerably complicate the factorization analysis.

— Higher twists in QCD  (2609.19620 - Melnitchouk, 17 Sep 2026) in Section 2.4, Diagrammatic Approach

Although it has only been proven for certain processes, it is conjectured to apply more broadly -- something that is supported by agreement with experimental data in the case of many processes.

— Simultaneous production of a $W$ boson and a charmed hadron at the LHC in general-mass variable-flavour-number scheme  (2608.14268 - Alanko et al., 14 Aug 2026) in Section 1, Introduction