$k_{\perp}$-Factorization and Perturbative Invariants at Small $x$

TL;DR

The work addresses perturbative QCD at small x by presenting k_perp-factorization as a framework that connects BFKL gluon evolution to observable cross sections and remains compatible with collinear factorization after integrating over transverse momentum. It reviews LL and NLL resummations, derives heavy-flavour DIS coefficient functions to NLL accuracy, and introduces physical anomalous dimensions that are scheme-invariant and relate the scaling violations of different observables. This approach provides a physically meaningful separation between perturbative and non-perturbative inputs and yields invariant quantities like K-factors for robust phenomenology, with direct relevance to HERA data. Overall, it offers a coherent, scheme-robust description of small-x dynamics through physical kernels and cross-observable relations.

Abstract

I review the basic idea of $k_{\perp}$-factorization and its relation to collinear factorization. Theoretical results in resummed perturbation theory are summarized and the example of the heavy-flavour structure functions is explicitly considered. Using these results one can investigate the small-$x$ behaviour of quantities that are independent of the non-perturbative parton densities. In particular, one can introduce physical anomalous dimensions that relate the scaling violations in different hadronic observables.