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Singlular structure of two-loop amplitudes and their numerical evaluation

Applicant Anastasiou Charalampos
Number 179016
Funding scheme Project funding (Div. I-III)
Research institution Institut für Theoretische Physik ETH Zürich
Institution of higher education ETH Zurich - ETHZ
Main discipline Theoretical Physics
Start/End 01.04.2018 - 31.03.2022
Approved amount 684'763.00
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Keywords (3)

numerical methods; perturbative QCD; Feynman integrals

Lay Summary (Italian)

In this project, we aim to develop a new mathematical methods for the evaluation of Feynman diagrams and scattering amplitudes in Quantum Field Theory.
Lay summary
La probabilità che un evento si verifichi in un processo di 
scattering viene calcolata dai diagrammi di Feynman.
Un numero infinito di diagrammi contribuisce a questa probabilità,
ma la maggior parte della ha origine dal più semplice di essi.
Per raggiungere una precisione più alta di oggi, diagrammi di Feynman
più complicati devono essere presi in considerazione.
Tradizionalmente, questi sono calcolati con metodi analitici o
seminumerici, che hanno una portata limitata. In nostro progetto, introduciamo un
metodo puramente numerico per la valutazione dei diagrammi di Feynman.
In nostro approccio, identifichiamo le singolarità dei integrali di Feynman al niveo
del integrando ed introduciamo sottrazioni o le deformità delle integrazioni
per eliminarli o evitarli. Dopo il trattamento delle singolarità, gli integrali
saranno valutati con tecniche Monte-Carlo adattative.

Direct link to Lay Summary Last update: 17.07.2018

Responsible applicant and co-applicants



The Large Hadron Collider is performing very precise measurements ofproton scattering processes. Two-loop amplitudes are a main ingredient for calculating most cross-sections at next-to-next-leading-order (NNLO) in the QCD coupling expansion,a perturbative order which yields a comparable level of precision as typical measurements.For loop induced processes, two-loop amplitudes are required alreadyat next-to-leading-order (NLO). In recent years we have witnessed the computation of many processes atNNLO and even NNNLO, in a large part due to progress in analyticcomputational methods for the evaluation of two-loop scattering amplitudes. However, we observe that analytical methods are quickly reachingtheir full potential and that new breakthroughs are required for theirapplication to new problems of high relevance for the LHC precisionphysics program. In this project we will develop methods for the evaluationof two-loop amplitudes numerically. We will first study theuniversality of the singularities (soft, collinear, ultraviolet) of two-loop amplitudes bothin momentum and in Feynman parameter space. We will use gaugesymmetry properties in order to simplify the singular limits of theloop integrands (in both Feynman-parameter and momentum-spacerepresentations). We wil then work out local approximations for theintegrands of two-loop amplitudes, using subtraction, physicalsector-decomposition (ordering of integrations) andcontour-deformation techniques. These approximations are expected tobe of a universal nature and we will formulate how to use them inorder to render their difference with any two-loop QCD amplitudenumerically integrable. We will complete ouralgorithm for the numerical evaluation of two-loop amplitudes byintegrating analytically in dimensional regularisation the universalsingular approximations of two-loop amplitudes. As a proof of principle, we will test our methods in the calculationof two-loop amplitudes for 3 partons and 2 photons. these are relevantfor the estimation of the background in the diphoton-signal of a Higgswhich is produced in association with a jet. Our algorithms will beconstructed with universality in mind and we hope that at the end ofthe project we will be able to learn how to use them for morecomplicated processes with massive particles (like the production of a Higgs boson in association with a top-quark pair).