Multiparton NLO corrections by numerical methods

TL;DR

This paper presents a numerical algorithm for calculating next-to-leading order QCD corrections to jet observables in electron-positron annihilation, efficiently handling divergences and contour deformation without Feynman graphs.

Contribution

It introduces a novel amplitude-level numerical method for NLO QCD calculations that avoids Feynman diagrams and uses recurrence relations for efficiency.

Findings

Successfully computed NLO corrections for up to 7 jets

Demonstrated the efficiency of the contour deformation technique

Validated the method with jet observable results in e+ e- annihilation

Abstract

In this talk we discuss an algorithm for the numerical calculation of one-loop QCD amplitudes and present results at next-to-leading order for jet observables in electron-positron annihilation calculated with the above-mentioned method. The algorithm consists of subtraction terms, approximating the soft, collinear and ultraviolet divergences of QCD one-loop amplitudes, as well as a method to deform the integration contour for the loop integration into the complex plane to match Feynman's i delta rule. The algorithm is formulated at the amplitude level and does not rely on Feynman graphs. Therefore all ingredients of the algorithm can be calculated efficiently using recurrence relations. The application of this method to the leading-colour contribution of e+ e- --> n jets, with n up to seven, demonstrates the efficiency of the approach.