Automated calculations for multi-leg processes

TL;DR

The paper surveys the challenges and methodologies for automated calculations of multi-leg processes at the LHC, focusing on high-multiplicity final states that require beyond-leading-order predictions. It integrates approaches across the amplitude pipeline, from computer algebra and quantum-number management (helicity, color, SUSY relations) to twistor-inspired on-shell methods, unitarity-based one-loop techniques, and multi-loop tools such as Mellin–Barnes, polylogarithms, and sector decomposition. A central theme is the systematic handling of infrared divergences and the development of subtraction and slicing schemes to enable finite, computable predictions at NLO and NNLO. The practical impact is a coherent framework and roadmap for automating precise, scalable calculations of complex hadronic processes at current and future colliders.

Abstract

The search for signals of new physics at the forthcoming LHC experiments involves the analysis of final states characterised by a high number of hadronic jets or identified particles. Precise theoretical predictions for these processes require the computation of scattering amplitudes with a large number of external particles and beyond leading order in perturbation theory. The complexity of a calculation grows with the number of internal loops as well as with the number of external legs. Automatisation of at least next-to-leading order calculations for LHC processes is therefore a timely task. I will discuss various approaches.

Figures (11)

• Figure 1: A schematic and simplified description of an event in hadron-hadron collisions.
• Figure 2: Modelling of jets in perturbation theory. At leading-order a jet is modelled by a single parton, at next-to-leading order either by one or two partons. At next-to-next-to-leading order a jet is modelled by one, two or three partons.
• Figure 3: Scale-dependence of the cross-section for the process $pp\rightarrow t\bar{t}+\hbox{jet}$. The leading-order prediction shows a strong scale-dependence. The next-to-leading order prediction reduces significantly the scale-dependence. The plot is taken from Dittmaier:2007wz.
• Figure 4: Off-shell recurrence relation: In an off-shell current particle $n+1$ is kept off-shell. This allows to express an off-shell current with $n$ on-shell legs in terms of currents with fewer legs.
• Figure 5: MHV diagrams contributing to the tree-level six-gluon amplitude $A_6(1^-,2^-,3^-,4^+,5^+,6^+)$.