The Dipole Formalism for the Calculation of QCD Jet Cross Sections at Next-to-Leading Order

TL;DR

This paper introduces the dipole formalism, a universal subtraction framework for NLO QCD jet cross sections that cleanly isolates soft and collinear divergences via process-independent dipole counterterms. By constructing dipole factorization formulae and an analytic integration of the subtraction term, the authors enable straightforward four-dimensional Monte Carlo implementations for arbitrary jet observables and processes. They derive the final master equations and demonstrate the method with a detailed e^+e^− → 3 jets calculation, achieving pole cancellation and matching known results. The approach promises broad applicability to general NLO QCD predictions, with companion work extending to initial-state hadrons and fragmentation processes.

Abstract

In order to make quantitative predictions for jet cross sections in perturbative QCD, it is essential to calculate them to next-to-leading accuracy. This has traditionally been an extremely laborious process. Using a new formalism, imaginatively called the dipole formalism, we are able to construct a completely general algorithm for next-to-leading order calculations of arbitrary jet quantities in arbitrary processes. In this paper we present the basic ideas behind the algorithm and illustrate them with a simple example.

Figures (1)

• Figure 1: Coefficient of $(\alpha_{\mathrm{S}}/2\pi)^2$ for the thrust and $C$-parameter distributions. The dotted histograms show the size of the statistical errors.