QCDfaktorisation

QCDfaktorisation, or QCD factorisation, is a framework in quantum chromodynamics that formalizes how certain high-energy hadronic processes can be described by a separation of scales. The central idea is that short-distance, high-momentum transfer physics can be computed perturbatively, while long-distance, non-perturbative physics is encoded in universal quantities extracted from data.

Factorisation theorems express measurable cross sections as convolutions of universal non-perturbative functions with process-dependent, perturbatively calculable coefficients. In collinear factorisation, the cross section for a hadronic process is written as a sum over parton types of integrals of parton distribution functions (and, where relevant, fragmentation functions) times short-distance coefficients. The coefficients depend on the hard scale and the renormalisation and factorisation scales mu_R and mu_F.

Key features include the universality of the long-distance functions (PDFs, FFs), their evolution with scale via the DGLAP equations, and the ability to perform calculations order by order in the strong coupling alpha_s. Variants such as transverse-momentum dependent (TMD) factorisation or k_T-factorisation apply when transverse momenta are relevant. The formalism is complemented by effective theories like soft-collinear effective theory for organizing contributions.

Limitations exist: factorisation can fail in certain processes due to soft Glauber gluons or in some heavy-quarkonium production frameworks where additional non-perturbative dynamics are required. Practically, QCD factorisation underpins global fits of parton distributions, predictions for Higgs and jet production at colliders, and the interpretation of hadronization through fragmentation functions.