A numerical algorithm for efficiently obtaining a Feynman parameter representation of one-gluon loop QCD Feynman diagrams for a large number of external gluons

A numerical program is presented which facilitates a computation pertaining to the full set of one-gluon loop diagrams (including ghost loop contributions), with M attached external gluon lines in all possible ways. The feasibility of such a task rests on a suitably defined master formula, which is expressed in terms of a set of Grassmann and a set of Feynman parameters. The program carries out the Grassmann integration and performs the Lorentz trace on the involved functions, expressing the result as a compact sum of parametric integrals. The computation is based on tracing the structure of the final result, thus avoiding all intermediate unnecessary calculations and directly writing the output. Similar terms entering the final result are grouped together. The running time of the program demonstrates its effectiveness, especially for large M.Comment: 32 pages, 5 figures. in press Computer Physics Communication

Applications of Modern Methods for Scattering Amplitudes

The large amount of new high energy data being collected by the LHC experiments has the potential to provide new information about the nature of the fundamental forces through precision comparisons with the Standard Model. These precision measurements require intensive perturbative scattering amplitude computations with large multiplicity final states. In this thesis we develop new on-shell methods for the analytic computation of scattering amplitudes in QCD which offer improved evaluation speed and numerical stability over currently available techniques and also allow us to explore the structure of amplitudes in gauge theories. We apply these techniques to extract compact analytic expression for the triple collinear splitting functions at one-loop in QCD and supersymmetric gauge theories which contribute to the universal factorisation at N${}^3$LO. We also investigate improvements to dimensionally regulated one-loop amplitude computations by combining the six-dimensional spinor helicity formalism and a momentum twistor parameterisation with the integrand reduction and generalised unitarity methods. This allowed the development of a completely algebraic approach to the computation of dimensionally regulated amplitudes in QCD including massive fermions. We present applications to Higgs plus five-gluon scattering in the large top mass limit and top pair production with up to three partons. In the case of massive one-loop amplitudes we present a new approach to the problem of wave-function renormalisation which only requires gauge invariant, on-shell building blocks. Massive one-loop amplitudes contain information that cannot be extracted from unregulated cuts, the new approach instead constrains the amplitudes using the universal poles in 6-2\eps dimensions which can be computed from an effective Lagrangian on dimension six operators

The rational parts of one-loop QCD amplitudes I: The general formalism

A general formalism for computing only the rational parts of oneloop QCD amplitudes is developed. Starting from the Feynman integral representation of the one-loop amplitude, we use tensor reduction and recursive relations to compute the rational parts directly. Explicit formulas for the rational parts are given for all bubble and triangle integrals. Formulas are also given for box integrals up to two-masshard boxes which are the needed ingredients to compute up to 6-gluon QCD amplitudes. We use this method to compute explicitly the rational parts of the 5- and 6-gluon QCD amplitudes in two accompanying papers.Comment: 49 pages, 8 figure and LaTeX file; minor corrections, references added, to be published in Nucl. Phys.

The two-loop helicity amplitudes for gg → V 1 V 2 → 4 leptons

We compute the two-loop massless QCD corrections to the helicity amplitudes for the production of two electroweak gauge bosons in the gluon fusion channel, gg → V 1 V 2, keeping the virtuality of the vector bosons V 1 and V 2 arbitrary and taking their decays into leptons into account. The amplitudes are expressed in terms of master integrals, whose representation has been optimised for fast and reliable numerical evaluation. We provide analytical results and a public C++ code for their numerical evaluation on HepForge at http://vvamp.hepforge.org. © 2015, The Author(s)

One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts

The success of the experimental program at the Tevatron re-inforced the idea that precision physics at hadron colliders is desirable and, indeed, possible. The Tevatron data strongly suggests that one-loop computations in QCD describe hard scattering well. Extrapolating this observation to the LHC, we conclude that knowledge of many short-distance processes at next-to-leading order may be required to describe the physics of hard scattering. While the field of one-loop computations is quite mature, parton multiplicities in hard LHC events are so high that traditional computational techniques become inefficient. Recently new approaches based on unitarity have been developed for calculating one-loop scattering amplitudes in quantum field theory. These methods are especially suitable for the description of multi-particle processes in QCD and are amenable to numerical implementations. We present a systematic pedagogical description of both conceptual and technical aspects of the new methods.Comment: 183 pages, 21 figures, 699 equations; published versio

Finite scattering amplitudes in field theory

In this thesis we explore the infrared problem perturbatively in massless field theory. We review the current conventional methods and theorems that are applied in the calculation of QCD jet observables and then discuss the formulation of an alternative approach called the Asymptotic Interaction Picture (AIP). The AIP is based on a unitary transformation such that long-ranged interactions are present in the asymptotic Lagrangian and thus the states associated with this picture are no longer free Fock states but are asymptotic states containing soft and collinear interactions. Under the guidance of the AIP we are led to modifying conventional perturbation theory, cutting up amplitudes in a manner that allows for the construction of infrared finite amplitudes that are in correspondence with the asymptotic states of the AIP. We apply this formalism to several NLO corrections to QCD observables and construct dressed states who's amplitudes are finite in all regions of phase space. Using these amplitudes we compute several observables and show agreement with the conventional calculations in infrared safe regions. Higher-order calculations are then investigated in ϕ (^3)theory and the infrared pole structure is shown to behave as expected such that NNLO corrections to dressed states are obtained. Finally we present part of the NNLO correction to the dressed two-parton amplitude in QCD and show that, with several provisos, this approach may potentially be applied to the precision calculations of observables at the International Linear Collider (ILC). We therefore give a possible alternative to current subtraction methods at NNLO when no initial state radiation is present

Automating QCD amplitudes with on-shell methods

We review some of the modern approaches to scattering amplitude computations in QCD and their application to precision LHC phenomenology. We emphasise the usefulness of momentum twistor variables in parameterising general amplitudes.Comment: 8 pages, proceedings contribution to ACAT 2016, Valparaiso, Chile, 18-22 Jan 201