Toward Three-Loop Feynman Massive Diagram Calculations

There are many methods of searching for traces of the so-called new physics in particle physics. One of them, and the main focus of this paper, is athe study of the Z-boson decay in e+e− collisions. An improvement in the precision of calculations of the Standard Model (SM) electroweak pseudo-observa...

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Bibliographic Details
Published in:Symmetry (Basel) 2021-06, Vol.13 (6), p.975
Main Authors: Dubovyk, Ievgen, Usovitsch, Johann, Grzanka, Krzysztof
Format: Article
Language:English
Subjects:
Accuracy
Decay
Differential equations
Electroweak model
Energy
Feynman multi-loop integrals
Integrals
integration-by-parts
Kinematics
Mellin–Barnes method
Methods
Particle physics
sector decomposition method
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Summary:There are many methods of searching for traces of the so-called new physics in particle physics. One of them, and the main focus of this paper, is athe study of the Z-boson decay in e+e− collisions. An improvement in the precision of calculations of the Standard Model (SM) electroweak pseudo-observables, such as scattering asymmetries, effective weak mixing angles, and decay widths, related to the Z-boson will meet severe experimental requirements at the planned e+e− colliders and will increase the chance to detect non-standard effects in experimental analysis. To reach this goal, one has to calculate the next order of perturbative SM theory, namely three-loop Feynman integrals. We discuss the complexity of the problem, as well as the methods crucial for completing three-loop calculations. We show several numerical solutions for some three-loop Feynman integrals using sector decomposition, Mellin–Barnes (MB), and differential equation methods.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym13060975