Unintegrated parton distributions

Abstract

We develop the theory of parton distributions f(_a)(π, k(^t2), μ(^2), unintegrated with respect to transverse momentum k(_t), from a phenomenological standpoint. In particular, we demonstrate a convenient approximation in which the unintegrated functions are obtained by explicitly performing the last step of parton evolution in perturbative QCD, with single-scale functions a(π, Q(^2) as input. Results are presented in the context of DGLAP and combined BFKL-DGLAP evolution, but with angular ordering imposed in the last step of the evolution. We illustrate the application of these unintegrated distributions to predict cross sections for physical processes at lepton-hadron and hadron-hadron colliders. The use of partons with incoming transverse momentum, based on k(_t)-factorisation, is intended to replace phenomenological "smearing" in the perturbative region k(_t) > k(_o) (k(_o) ≈ 1 GeV), and enables the full kinematics of a process to be included even at leading order. We apply our framework to deep inelastic scattering and the fitting of F(_2)(π, Q(^2), to the transverse momentum spectra of prompt photons in hadroproduction and in photoproduction, and to the topical problem of bb production at HERA. Finally, we address the issue of parton-parton recombination (shadowing) at very low values of π, building on recent work by Kovchegov and others to make predictions for the likely magnitude of shadowing effects at the LHC.