Calculation of QCD jet cross sections at next-to-leading order

TL;DR

The paper introduces a general subtraction-based framework for calculating infrared-safe QCD jet cross sections at next-to-leading order, applicable to N-jet production in hadron collisions and extendable to e+e− and DIS. It achieves this by partitioning the real-emission phase space into regions so that only a single Lorentz invariant can become singular, and by constructing explicit soft and collinear subtraction terms that cancel against virtual and collinear pieces in dimensional regularization and the MSbar scheme. The finite remainder is computed in four dimensions, with analytic soft and collinear integrals provided to enable straightforward Monte Carlo implementation. The authors demonstrate the method on three-jet observables in e+e− annihilation, showing numerical results in agreement with established benchmarks and asserting the approach’s adaptability to hadron-hadron processes in a companion study.

Abstract

A general method for calculating \NLO cross sections in perturbative QCD is presented. The algorithm is worked out for calculating $N$-jet cross sections in hadron-hadron collisions. The generalization of the scheme to performing caclulations for other QCD process, such as electron-positron annihilation or in deep inelastic scattering is also straightforward. As an illustration several three-jet cross section distributions in electron-positron annihilation, calculated using the algorithm, are presented.

Figures (1)

• Figure 1: Coefficient of $(\alpha_s/(2\pi))^2$ for the thrust, C-parameter distributions and the $y_{\rm cut}$ distributions of the Jade E and $k_\perp$-clustering algorithms. The thrust distribution is multiplied by ($1-t$), the C-parameter distribution is multiplied by $C$, while the distributions of the clustering algorithms are multiplied by $y_{\rm cut}$. The dotted histograms show the statistical errors.