N3LO Corrections to Jet Production in Deep Inelastic Scattering using the Projection-to-Born Method

TL;DR

This work introduces a generalisation of the Projection-to-Born method to N3LO QCD and applies it to exclusive jet production in deep inelastic scattering. By combining inclusive N3LO results for the Born state with NNLO corrections for X+jet, the authors achieve fully differential predictions with robust infrared subtraction. The N3LO results in DIS show substantially reduced theoretical uncertainties and improved agreement with ZEUS data, especially in forward regions where logarithmic effects are important. The approach holds promise for extending high-precision exclusive predictions to other processes at hadron colliders, enhancing precision tests of QCD and PDF determinations.

Abstract

Computations of higher-order QCD corrections for processes with exclusive final states require a subtraction method for real-radiation contributions. We present the first-ever generalisation of a subtraction method for third-order (N3LO) QCD corrections. The Projection-to-Born method is used to combine inclusive N3LO coefficient functions with an exclusive second-order (NNLO) calculation for a final state with an extra jet. The input requirements, advantages, and potential applications of the method are discussed, and validations at lower orders are performed. As a test case, we compute the N3LO corrections to kinematical distributions and production rates for single-jet production in deep inelastic scattering in the laboratory frame, and compare them with data from the ZEUS experiment at HERA. The corrections are small in the central rapidity region, where they stabilize the predictions to sub per-cent level. The corrections increase substantially towards forward rapidity where large logarithmic effects are expected, thereby yielding an improved description of the data in this region.

Figures (4)

• Figure 1: Comparison of results up to NNLO obtained with the P2B and the antenna subtraction methods. The upper frames in each plot show the absolute predictions obtained using the P2B method. The lower frames display the ratio of the predictions obtained in the P2B and antenna subtraction computations for the NLO-only and NNLO-only contributions to the differential cross sections, with error bars and filled areas representing numerical integration errors of the P2B and antenna-subtraction results, respectively. The cuts and jet definition are as in Eqs. \ref{['eq:diff:cuts']} and \ref{['eq:diff:jets']}.
• Figure 2: Kinematical distributions in single inclusive jet production in deep inelastic scattering up to N${}^{3}$LO in QCD, compared to ZEUS measurements zeus_lab_diff. The error bars on the data represent the statistical and systematic uncertainties added in quadrature; the uncertainty in the absolute energy scale of the jets is shown separately as a shaded yellow band.
• Figure 3: Comparison of ZEUS data to theoretical predictions up to N${}^{3}$LO in QCD for the two-jet rate, normalised according to Eq. \ref{['eq:JRNORM']}. Data are corrected to give parton level results and were extracted from Fig. 9 of Ref. zeus_lab_rate; the error bars show the statistical uncertainties.
• Figure 4: Predictions up to N${}^{3}$LO in QCD for zero-, one-, two-, three-, and four-jet rates in the JADE algorithm for the kinematical cuts of Eq. \ref{['eq:rates:cuts']}.