Theory of Jets in Deep Inelastic Scattering
E. Mirkes
TL;DR
The paper tackles the need for precise, flexible NLO QCD predictions of jet production in deep inelastic scattering at HERA to test QCD, extract $\alpha_s(\mu_R)$ and gluon densities, and explore polarization effects. It develops a fully flexible NLO framework using phase space slicing with universal crossing functions and implements it in the mepjet program to compute 1- and 2-jet cross sections (with NC/CC exchange) and LO 3- and 4-jet results, including analytic formulae. The work analyzes the impact of higher-order corrections on jet observables across jet definitions and discusses implications for forward jet production at low $x$, the polarized gluon distribution $\Delta g$, and power corrections in event shapes. Overall, it provides essential tools and methodologies for precision QCD tests against HERA data and for extracting fundamental parton densities and coupling constants.
Abstract
The large center of mass energy and increasing statistical precision for a wide range of hadronic final state observables at the HERA lepton-proton collider has provided a detailed testing ground for QCD dynamics. Fully flexible next-to-leading order calculations are mandatory on the theoretical side for such tests and will be discussed in detail. Next-to-leading order QCD predictions for one- and two-jet cross sections in deep inelastic scattering with complete neutral current ($γ^\ast$ and/or $Z$) and charged current ($W^\pm$) exchange together with leading order results for three- and four-jet final states are presented. The theoretical framework, based on the phase space slicing method and the use of universal crossing functions, is described in detail. All analytical formulae necessary for the next-to-leading order calculations are provided. The numerical results are based on the fully differential $ep \to n$ jets event generator \docuname which allows to analyze any infrared and collinear safe observable and general cuts in terms of parton 4-momenta. The importance of higher order corrections is studied for various jet algorithms. Implications and comparisons with (ongoing) experimental analyses for jet cross sections at high $Q^2$, the determination of $α_s(μ_R)$, the gluon density, power corrections in event shapes and the associated forward jet production in the low $x$ regime at HERA are discussed. A study of jet cross sections in polarized electron and polarized proton collisions shows that dijet events provide a good measurement of the polarized gluon distribution $Δg(x_g)$, in a region, where $x_g Δg(x_g)$ is expected to show a maximum.