Unintegrated parton distributions and inclusive jet production at HERA

TL;DR

The paper develops a framework to derive unintegrated parton densities from conventional PDFs using a refined last-step evolution and angular ordering, and introduces doubly-unintegrated distributions f_a(x,z,k_t^2,μ^2) within a generalized (z,k_t)-factorisation. This approach extends kt-factorisation and recovers collinear factorisation in appropriate limits, enabling more accurate treatment of kinematics in DIS jet production. At leading order, the method reproduces standard LO QCD results with exact kinematics, while a simplified NLO analysis shows sizable, but controllable, corrections, particularly in forward regions. Comparisons with HERA data (ZEUS and H1) show generally good agreement, validating the approach and motivating further exploration toward NNLO and wider applications.

Abstract

We describe how unintegrated parton distributions can be calculated from conventional integrated distributions. We extend and improve the 'last-step' evolution approach, and explain why doubly-unintegrated parton distributions are necessary. We generalise k_t-factorisation to (z,k_t)-factorisation. We apply the formalism to inclusive jet production in deep-inelastic scattering, mainly at leading-order, but we also study the extension to next-to-leading order. We compare the predictions with recent HERA data.

Figures (11)

• Figure 1: A schematic diagram of inclusive jet production in DIS at LO which shows the approximate equality between, on the left-hand-side (a), the formalism based on the doubly-unintegrated quark distribution, and on the right-hand-side (b), the conventional QCD approach using integrated parton densities, $a(x,\mu^2)$.
• Figure 2: Upper part of the evolution chain.
• Figure 3: Schematic picture of the $k_t$-factorisation formula \ref{['eq:ktfactCCFM']}
• Figure 4: Verification of $(z,k_t)$-factorisation for the doubly-unintegrated quark distribution, $f_q(x,z,k_t^2,\mu^2)$, shown in the final diagram. In the first two diagrams the penultimate parton in the DGLAP evolution chain, with 4-momentum $k_{n-1}=xp/z$, splits into a quark with 4-momentum $k_n\equiv k=x\,p-\beta\,q^\prime+k_\perp$.
• Figure 5: Verification of $(z,k_t)$-factorisation for the doubly-unintegrated gluon distribution, $f_g(x,z,k_t^2,\mu^2)$, shown in the final diagram. In the first two diagrams the penultimate parton in the DGLAP evolution chain, with 4-momentum $k_{n-1}=xp/z$, splits into a gluon with 4-momentum $k_n\equiv k=x\,p-\beta\,q^\prime+k_\perp$.