In this thesis we elaborate on the modern techniques for the evaluation of Scattering Amplitudes in Quantum Field Theory, and apply them to the calculation of at one loop in Quantum Electrodynamics, within the Dimensional Regularization scheme. The corresponding Feynman diagrams contribute to the so called real-virtual term of the Next-to-Next-to-Leading-Order corrections to scattering. Their calculation is crucial for a novel estimation of the leading Hadronic corrections to the muon’s anomalous magnetic moment, which is the goal of the MUonE experiment, recently proposed at CERN. First, we review the theoretical background behind the contributions to the muon’s magnetic moment and the connection with scattering. Then, we elaborate on the algorithimic steps required by the evaluation of multi-loop Feynman amplitudes, from the form-factor decomposition, to the reduction onto a basis of Master Integrals, and, finally, to the calculation of the latter by means of the Differential Equations method. We outline the modern frameworks based on Unitarity of the S-matrix, which employ amplitude cuts to construct a decomposition onto Master Integrals in the Generalised Unitarity framework. This includes Integrand-level Decomposition methods which take advantage of the polynomial properties of Feynman amplitude integrands and offer a higher level of automation for the calculation of complex amplitudes. Specifically we detail the more recent Adaptive Integrand Decomposition and its automated code implementation AIDA used to carry out the calculations presented. We illustrate the Momentum Twistor parametrisation for particle kinematics used by AIDA, and introduce four and five-point twistor parametrisations suitable for our goals. We present our results on the Master Integral decompositions of and at one-loop, both considering massive and massless electrons, and finally we review the evaluation of the Master Integrals for in the limit with Differential Equations.

Unitarity-based Methods for Muon-Electron Scattering in Quantum Electrodynamics

Dondi, Giulio
2019/2020

Abstract

In this thesis we elaborate on the modern techniques for the evaluation of Scattering Amplitudes in Quantum Field Theory, and apply them to the calculation of at one loop in Quantum Electrodynamics, within the Dimensional Regularization scheme. The corresponding Feynman diagrams contribute to the so called real-virtual term of the Next-to-Next-to-Leading-Order corrections to scattering. Their calculation is crucial for a novel estimation of the leading Hadronic corrections to the muon’s anomalous magnetic moment, which is the goal of the MUonE experiment, recently proposed at CERN. First, we review the theoretical background behind the contributions to the muon’s magnetic moment and the connection with scattering. Then, we elaborate on the algorithimic steps required by the evaluation of multi-loop Feynman amplitudes, from the form-factor decomposition, to the reduction onto a basis of Master Integrals, and, finally, to the calculation of the latter by means of the Differential Equations method. We outline the modern frameworks based on Unitarity of the S-matrix, which employ amplitude cuts to construct a decomposition onto Master Integrals in the Generalised Unitarity framework. This includes Integrand-level Decomposition methods which take advantage of the polynomial properties of Feynman amplitude integrands and offer a higher level of automation for the calculation of complex amplitudes. Specifically we detail the more recent Adaptive Integrand Decomposition and its automated code implementation AIDA used to carry out the calculations presented. We illustrate the Momentum Twistor parametrisation for particle kinematics used by AIDA, and introduce four and five-point twistor parametrisations suitable for our goals. We present our results on the Master Integral decompositions of and at one-loop, both considering massive and massless electrons, and finally we review the evaluation of the Master Integrals for in the limit with Differential Equations.
2019-11-25
165
Perturbation theory, Feynman integrals, Scattering amplitude
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12608/22606