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Inclusive Single- and Dijet Rates in Next-to-Leading Order QCD for gamma^*proton and gamma^*gamma Collisions

B. Pötter

TL;DR

This work develops and applies a consistent NLO QCD framework to inclusive jet production in γ^* p and γ^* γ collisions, addressing soft and collinear singularities via phase-space slicing and absorbing the resulting logarithms into photon PDFs with MSbar-like factorization for virtual photons. It integrates LO and NLO partonic cross sections for direct, single-resolved, and double-resolved photon contributions, and systematically studies dependencies on jet kinematics and photon virtuality P^2 using real and virtual photon PDFs (GRS and SaS). The study provides detailed numerical results for single- and dijet cross sections under HERA and LEP2 conditions, demonstrates reduced scale dependence at NLO, and achieves reasonable agreement with ZEUS data for certain P^2 ranges while highlighting areas (e.g., very low P^2) where underlying-event effects may be relevant. The work also lays groundwork for improved virtual-photon PDFs and more precise comparisons with forthcoming jet data, strengthening the use of jet measurements to probe the partonic structure of the virtual photon.

Abstract

We present one- and two-jet inclusive cross sections for gamma*gamma scattering and virtual photoproduction in ep collisions. The hard cross sections are calculated in next-to-leading order QCD. Soft and collinear singularities are extracted using the phase-space-slicing method. The initial state singularity of the virtual photon depends logarithmically its' virtuality. This logarithm is large and has to be absorbed into the parton distribution function of the virtual photon. We define for this purpose an MS-bar factorization scheme similar to the real photon case. We numerically study the dependence of the inclusive cross sections on the transverse energies and rapidities of the outgoing jets and on the photon virtuality. The ratio of the resolved to the direct cross section in ep collisions is compared to ZEUS data.

Inclusive Single- and Dijet Rates in Next-to-Leading Order QCD for gamma^*proton and gamma^*gamma Collisions

TL;DR

This work develops and applies a consistent NLO QCD framework to inclusive jet production in γ^* p and γ^* γ collisions, addressing soft and collinear singularities via phase-space slicing and absorbing the resulting logarithms into photon PDFs with MSbar-like factorization for virtual photons. It integrates LO and NLO partonic cross sections for direct, single-resolved, and double-resolved photon contributions, and systematically studies dependencies on jet kinematics and photon virtuality P^2 using real and virtual photon PDFs (GRS and SaS). The study provides detailed numerical results for single- and dijet cross sections under HERA and LEP2 conditions, demonstrates reduced scale dependence at NLO, and achieves reasonable agreement with ZEUS data for certain P^2 ranges while highlighting areas (e.g., very low P^2) where underlying-event effects may be relevant. The work also lays groundwork for improved virtual-photon PDFs and more precise comparisons with forthcoming jet data, strengthening the use of jet measurements to probe the partonic structure of the virtual photon.

Abstract

We present one- and two-jet inclusive cross sections for gamma*gamma scattering and virtual photoproduction in ep collisions. The hard cross sections are calculated in next-to-leading order QCD. Soft and collinear singularities are extracted using the phase-space-slicing method. The initial state singularity of the virtual photon depends logarithmically its' virtuality. This logarithm is large and has to be absorbed into the parton distribution function of the virtual photon. We define for this purpose an MS-bar factorization scheme similar to the real photon case. We numerically study the dependence of the inclusive cross sections on the transverse energies and rapidities of the outgoing jets and on the photon virtuality. The ratio of the resolved to the direct cross section in ep collisions is compared to ZEUS data.

Paper Structure

This paper contains 39 sections, 118 equations, 24 figures, 3 tables.

Table of Contents

  1. Introduction
  2. General Structure of the Hadronic Cross Sections
  3. Factorization of Hard and Soft Regions
  4. NLO Corrections
  5. Factorization for the Photon
  6. Partonic Cross Sections
  7. Notation
  8. The Two-Body Processes
  9. Phase-Space-Slicing Method
  10. Singularities in the Final and in the Massless Initial State
  11. Singularities in the Initial State of a Virtual Photon
  12. Final State Singularities
  13. Initial State Singularities for Massless Particles
  14. Parton Initial State Singularities in the SR Case
  15. Real Photon Initial State Singularities in the D Case
  16. ...and 24 more sections

Figures (24)

  • Figure 1: Factorization of hard and soft processes in the hadronic cross section.
  • Figure 2: Partonic cross section: Born graph and real gluon emission.
  • Figure 3: The factorization theorem for the singular part of the partonic cross section.
  • Figure 4: Notation of the different processes involving one virtual photon.
  • Figure 5: Separation of the three particle phase space.
  • ...and 19 more figures