Unitarity and On-Shell Recursion Methods for Scattering Amplitudes

TL;DR

This thesis reviews advanced calculational techniques for scattering amplitudes in quantum field theory, focusing on on-shell recursion and unitarity methods, and demonstrates their application to complex loop and tree-level processes.

Contribution

It connects on-shell recursion relations with MHV rules and extends these methods to graviton scattering and loop calculations in supergravity and Higgs-gluon processes.

Findings

Relation of recursion to MHV rules for gauge amplitudes

Extension of MHV rules to graviton scattering

Calculation of one-loop Higgs-gluon amplitude

Abstract

This thesis describes some of the recent (and some less recent) developments in calculational techniques for scattering amplitudes in quantum field theory. The focus is on on-shell recursion relations in complex momenta and on the use of unitarity methods for loop calculations. In particular, on-shell recursion is related to the MHV rules for computing tree-level gauge amplitudes and used to extend the MHV rules to graviton scattering. Combinations of unitarity cut techniques and recursion are used to argue for the "No-Triangle Hypothesis" in N=8 supergravity which is related to its UV behaviour. Finally, combinations of unitarity and recursion are used to demonstrate the full calculation of a one-loop amplitude involving a Higgs particle and four gluons in the limit of large top mass. The present version is edited to incorporate some of the comments and suggestions of the evaluation committee, but has not been updated for developments in the meantime.