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Automatization of perturbative QCD at very high orders.

Periodic Reporting for period 3 - PertQCD (Automatization of perturbative QCD at very high orders.)

Reporting period: 2019-10-01 to 2021-03-31

An important goal of modern physics is to understand in a quantitative manner the fundamental laws which govern interactions at the level of elementary particles (electrons, muons, quarks, gluons, Higgs, electroweak bosons, etc).
Currently, the Large Hadron Collider probes their validity at the tiniest distances ever accessed by humans. The LHC experiments perform very precise measurements of excellent statistical samples of particle collisions. To figure out whether
our standard model (SM) of high energy physics is correct, we need to confront the date with theoretical predictions. The aim of our project is to provide very precise theoretical predictions for the processes which take place at collider experiments.
This is a formidable task. The Standard Model of particle interactions is a quantum field theory. The mathematical objects (probability amplitudes) which give the probability of a certain event to take place at the LHC cannot be evaluated exactly by
means of known mathematical methods. They can only be evaluated approximately, as a perturbative expansion around the limit of vanishing strengths of particle interactions. Currently, the first two terms (leading order and next-toleading-order) in this perturbative
series are computable with automated methods for LHC processes. This yields a typical theoretical precision of approximately 15%-30%, to be contrasted with a typical (achieved or anticipated) precision of 5% or better.
In this project, we develop mathematical and computational methods for the next-to-next-to-leading (NNLO) and next-to-next-to-next-to-next-to-leading (N3LO) terms in the perturbative series. Our work, has the potential to reduce the theoretical uncertainty for most interesting LHC observables
to the same level as the experimental uncertainty or better.
We have been developing methods for the analytic computation of amplitudes at NNLO and N3LO, which exploit their anticipated physical properties.
As practical application, we achieved for the first time the evaluation of the rapidity distribution of the Higgs particle. We also computed several previously
intractable effects which now yield a very precise estimate of the number of Higgs bosons being produced at the LHC.
In separate works, we automated the evaluation of NLO corrections due to the electorweak force for generic LHC processes.
Finally, we could apply our amplitude calculation methods for a more precise simulation of newly discovered gravitational waves signal.
Our computations constitute major part of the wtate-of-the-art in pertuutbative Quantum Field Theory. /
We anticipate that by the end of the project we will have developed techniques for the automation of NNLO corrections at the LHC.