Decomposition of one-loop QCD amplitudes into primitive amplitudes based on shuffle relations

We present the decomposition of QCD partial amplitudes into primitive amplitudes at one-loop level and tree level for arbitrary numbers of quarks and gluons. Our method is based on shuffle relations. This method is purely combinatorial and does not require the inversion of a system of linear equations.Comment: 46 pages, version to be published, v3: eq. 39 correcte

NLO corrections to Z production in association with several jets

In this talk we report on first results from the NLO computation of Z production in association with five jets in hadron-hadron collisions. The results are obtained with the help of the numerical method, where apart from the phase space integration also the integration over the loop momentum is performed numerically. In addition we discuss several methods and techniques for the improvement of the Monte Carlo integration.Comment: 7 pages, talk given at Loops and Legs 201

Numerical NLO QCD calculations

We present an algorithm for the numerical calculation of one-loop QCD amplitudes. The algorithm consists of subtraction terms, approximating the soft, collinear and ultraviolet divergences of one-loop amplitudes and a method to deform the integration contour for the loop integration into the complex space. The algorithm is formulated at the amplitude level and does not rely on Feynman graphs. Therefore all required ingredients can be calculated efficiently using recurrence relations. The algorithm applies to massless partons as well as to massive partons.Comment: 62 pages, version to be publishe

Numerical precision calculations for LHC physics

In dieser Arbeit stelle ich Aspekte zu QCD Berechnungen vor, welche eng verknüpft sind mit der numerischen Auswertung von NLO QCD Amplituden, speziell der entsprechenden Einschleifenbeiträge, und der effizienten Berechnung von damit verbundenen Beschleunigerobservablen. Zwei Themen haben sich in der vorliegenden Arbeit dabei herauskristallisiert, welche den Hauptteil der Arbeit konstituieren. Ein großer Teil konzentriert sich dabei auf das gruppentheoretische Verhalten von Einschleifenamplituden in QCD, um einen Weg zu finden die assoziierten Farbfreiheitsgrade korrekt und effizient zu behandeln. Zu diesem Zweck wird eine neue Herangehensweise eingeführt welche benutzt werden kann, um farbgeordnete Einschleifenpartialamplituden mit mehreren Quark-Antiquark Paaren durch Shufflesummation über zyklisch geordnete primitive Einschleifenamplituden auszudrücken. Ein zweiter großer Teil konzentriert sich auf die lokale Subtraktion von zu Divergenzen führenden Poltermen in primitiven Einschleifenamplituden. Hierbei wurde im Speziellen eine Methode entwickelt, um die primitiven Einchleifenamplituden lokal zu renormieren, welche lokale UV Counterterme und effiziente rekursive Routinen benutzt. Zusammen mit geeigneten lokalen soften und kollinearen Subtraktionstermen wird die Subtraktionsmethode dadurch auf den virtuellen Teil in der Berechnung von NLO Observablen erweitert, was die voll numerische Auswertung der Einschleifenintegrale in den virtuellen Beiträgen der NLO Observablen ermöglicht. Die Methode wurde schließlich erfolgreich auf die Berechnung von NLO Jetraten in Elektron-Positron Annihilation im farbführenden Limes angewandt.In this thesis I present aspects of QCD calculations, which are related to the fully numerical evaluation of next-to-leading order (NLO) QCD amplitudes, especially of the one-loop contributions, and the efficient computation of associated collider observables. Two interrelated topics have thereby been of concern to the thesis at hand, which give rise to two major parts. One large part is focused on the general group-theoretical behavior of one-loop QCD amplitudes, with respect to the underlying SU(N) theory, in order to correctly and efficiently handle the color degrees of freedom in QCD one-loop amplitudes. To this end a new method is introduced that can be used in order to express color-ordered partial one-loop amplitudes with multiple quark-antiquark pairs as shuffle sums over cyclically ordered primitive one-loop amplitudes. The other large part is focused on the local subtraction of divergences off the one-loop integrands of primitive one-loop amplitudes. A method for local UV renormalization has thereby been developed, which uses local UV counterterms and efficient recursive routines. Together with suitable virtual soft and collinear subtraction terms, the subtraction method is extended to the virtual contributions in the calculations of NLO observables, which enables the fully numerical evaluation of the one-loop integrals in the virtual contributions. The method has been successfully applied to the calculation of jet rates in electron-positron annihilation to NLO accuracy in the large-N limit.230 S

The chirality-flow formalism

We take a fresh look at Feynman diagrams in the spinor-helicity formalism. Focusing on tree-level massless QED and QCD, we develop a new and conceptually simple graphical method for their calculation. In this pictorial method, which we dub the chirality-flow formalism, Feynman diagrams are directly represented in terms of chirality-flow lines corresponding to spinor inner products, without the need to resort to intermediate algebraic manipulations.Comment: 44 pages, 3 figure

Herwig 7.1 Release Note

A new release of the Monte Carlo event generator Herwig (version 7.1) is now available. This version introduces a number of improvements, notably: multi-jet merging with the dipole shower at LO and NLO QCD; a new model for soft interactions and diffraction; improvements to mass effects and top decays in the dipole shower, as well as a new tune of the hadronisation parameters.Comment: 7 pages, 7 figures. Herwig is available from https://herwig.hepforge.org

Updates to the One-loop Provider NLOX

We describe the 1.2 update to NLOX, a computer program for calculations in high-energy particle physics. New features since the 1.0 release and other changes are described, along with usage documentation.Comment: 8 page