Automating QCD amplitudes with on-shell methods
Simon Badger
TL;DR
The paper surveys modern on-shell approaches to QCD scattering amplitudes and their use in precision LHC phenomenology. It details one-loop unitarity and integrand-reduction frameworks, including the canonical decomposition $A^{(1)}_n = \sum_i c_i I^{4-2\epsilon}_i + \text{rational}$ and the parametrisation $\int d^{4-2\epsilon} \sum_i \frac{\Delta_i(k)}{\prod D_\alpha(k)}$. It discusses extensions to $D$-dimensional unitarity for multi-loop integrands, the maximal unitarity program with IBP, and the role of non-minimal integral bases in non-supersymmetric theories, with concrete results such as multi-gluon amplitudes. The article also highlights momentum twistors as a practical, rational framework for kinematics that linearises constraints and can be applied to general gauge theories to facilitate analytic and numerical computations.
Abstract
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.