Applications of Modern Methods for Scattering Amplitudes

Abstract

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 NLO. 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
dimensions which can be computed from an effective Lagrangian on
dimension six operators.