Two loops in context

The article “The two-loop explosion” (CERN Courier April 2017 p18) summarises the current status of precision theory predictions for scattering processes at the LHC, driven by the impressive performance of the LHC experiments. While this is a new situation at CERN, it is not without precedent at a hadron collider. In fact, it had already been apparent in the late 1990s at the electron–proton collider HERA, then operated at DESY, that two- and even three-loop computations in QCD were needed to match the high accuracy of the data. Since then the theory community has made steady advances by achieving two-loop predictions also for electron–positron collisions and, in some cases, pushing as far as the five-loop level.

This progress is based on a number of developments. Factorisation of physics from different length scales has been used systematically to establish effective theories in the soft and collinear limits, helping to organise the sometimes tedious process of cancelling infrared divergences in physical cross-sections. Deeper insight into the analytical structure of scattering amplitudes and new research in mathematics on iterated integrals, hyper-logarithms and periods have also revealed the algebraic structure encoded in Feynman diagrams. Finally, there has been constant progress in computer algebra as the key technology in multi-loop calculations. The computational challenge to set up and solve large systems of equations, even of terabyte size, can be overcome with symbolic manipulation systems such as FORM. It is only during recent years that suitable open-source software and relatively inexpensive hardware have become widely available.

Thus, continuous efforts and investments in theory research during the past decades are bearing fruit, allowing theory predictions in 2017 to indeed match the precision required by many LHC measurements.

• Sven-Olaf Moch, University of Hamburg.