Vitti, Marco (2018) Hadronic Contributions to Muon-Electron Scattering at NNLO. [Magistrali biennali]
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In this thesis we evaluated the hadronic contributions to the cross section of muon-electron scattering at next-to-next-to-leading order (NNLO). These O(alpha^4) terms are related to hadronic vacuum polarization (HVP) insertions in diagrams contributing to the amplitude at NLO and NNLO. We identified four classes of contributions. Those from Class I arise from products of diagrams involving two vacuum polarization (VP) insertions, while Class II contributions involve one-loop QED diagrams with one HVP insertion in the t-channel photon. The contributions from these two classes were calculated using the factorization property of the VP function, and were expressed in terms of the QED corrections to the cross section at NLO. The bremsstrahlung contributions of Class III were analyzed in the soft-photon limit and were employed in the proof of the cancellation of IR divergences for the entire set of these hadronic contributions. Finally, the most challenging terms were the irreducible two-loop diagrams of Class IV, arising from one-loop QED vertex and box diagrams with a HVP insertion appearing inside the loop. These contributions were evaluated using a dispersive approach. The hadronic contributions obtained in this thesis are essential for the interpretation of data coming from the recently proposed MUonE experiment at CERN, which aims to provide a novel determination of the hadronic leading-order (HLO) contribution to the anomalous magnetic moment of the muon.
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