Abstract
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.
Highlights
The search for non-standard effects can be conducted in various ways, from which the study of Z-boson decay in e+ e− collisions is discussed in this paper
In the context of the well known integration-by-parts (IBP) reductions [25] and differential equations method [26,27,28,29] for Feynman integrals, we present an improved strategy that is capable of computing an arbitrary three-loop self-energy diagram, which is needed for this project
We discussed the present capabilities of these methods with suitable three-loop examples
Summary
The search for non-standard effects can be conducted in various ways, from which the study of Z-boson decay in e+ e− collisions is discussed in this paper This process was essential in the LEP era, leading to the precise knowledge of essential parts of the Standard. Up to 5 × 1012 Z-boson decays are planned to be observed at the Z-boson resonance with the FCC-ee collider, which is about six orders of magnitude more than at LEP This will lead to very accurate experimental measurements of the socalled Electro-Weak Pseudo-Observables (EWPOs), if the systematic experimental errors can be kept appropriately small. This level of accuracy is sensitive to virtual beyond-the-standard-model (BSM) effects from particles with multi-TeV masses and/or very feeble interactions.
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