References and useful material
This page collects publications detailing our effort towards the ultimate goal of efficiently computing perturbative cross-sections at arbitrary orders. Needless to say that our work builds upon that of many others whose references can be found in our citations.
Loop-Tree Duality
Our journey started with a first publication summarizes the muli-loop generalisation of Loop-Tree Duality (LTD)
Loop-Tree Duality for Multiloop Numerical Integration
It can be used for the numerical evaluation of finite loop integrals, also for physical kinematics when using a contour deformation discussed in this following publication
Numerical Loop-Tree Duality: contour deformation and subtraction
The original expression of Loop-Tree Duality suffers from spurious singularities that can be algorithmically removed so as to make it manifestly causal (cLTD)
Manifestly Causal Loop-Tree Duality
An alternative approach to regularising theshold singularities at one-loop was also worked out by Dario Kermanschah
Numerical integration of loop integrals through local cancellation of threshold singularities
Finally, Zeno Capatti discovered an even more elegant cross-Free Family (cFF) formulation of LTD that is more compact and only retains physical thresholds
Exposing the threshold structure of loop integrals
All these equivalent formulations LTD, cLTD and cFF can be readily generated from a Mathematica package available at
Local Unitarity
Equipped with the LTD expressions discussed above, we worked out the original construction of Local Unitarity (LU) is described in detailed at
It is then further refined to detail the handling of self-energy corrections and renormalisation at arbitrary perturbative orders in
Local unitarity: cutting raised propagators and localising renormalisation
Miscellaneous
A brilliant semester student, Max Hofer, computed the forward-backward asymmetry at NLO for the process \(e^+ e^- \rightarrow Q \overline{Q}\) using Local Unitarity. His report offers a good first introduction to our framework:
Computing electroweak quantum corrections using Local Unitarity
A standalone Mathematica notebook playground allows you to explore an explicit implementation of Local Unitarity for the computation of the inclusive NLO correction to the process \(e^+ e^- \rightarrow \gamma \rightarrow d\bar{d}\) yielding the infamous \(\alpha_s / \pi\) K-factor
A Mathematica playground for computing a simple inclusive NLO correction