kTfactorisation

kTfactorisation, often written as kT-factorisation, is a framework in perturbative quantum chromodynamics (QCD) for describing certain high-energy processes in which the transverse momentum of incoming partons is retained rather than integrated over. In this approach the cross section is expressed as a convolution of unintegrated parton distribution functions (UPDFs) Φa(x, kT^2, μ^2) with off-shell partonic scattering amplitudes, reflecting that the initial-state partons carry transverse momentum kT and virtuality kT^2. Observables are obtained by integrating over the longitudinal momentum fraction x and the transverse momentum kT of the incoming partons.

The UPDFs depend on x, kT, and the factorization scale μ, and they evolve with dynamics that interpolate between DGLAP and BFKL evolution. A commonly used framework for this evolution is the CCFM equation, which reduces to the familiar DGLAP behavior at large x and to BFKL-like behavior at small x. Unlike collinear factorisation, kT-factorisation retains the transverse momentum of the partons, which makes it particularly relevant in regimes where small-x gluon densities and transverse momenta play a crucial role.

Applications of kT-factorisation include forward jet production, heavy-quark production, and other observables in hadron-hadron and lepton-hadron collisions where small-x effects are important. It has been implemented in Monte Carlo event generators such as CASCADE and used to probe proton structure in high-energy experiments.

Limitations include the lack of a fully universal factorization theorem for all processes, scheme and model dependencies in the definition of UPDFs, and the challenge of matching to conventional collinear factorisation. Nevertheless, kT-factorisation remains a valuable tool for exploring high-energy QCD dynamics and small-x phenomena.