Study of leptonic systems and loop calculation techniques

Abstract

Proper handling of divergent integrals is presented, first with the example of the photon-photon scattering. The classic result of this process was questioned, because the necessity of regularization in the classic calculation was not clear. This challenge has its counterpart. The standard result for the decay of the Higgs boson into two photons was also questioned for a similar reason. We have verified the classic result of the photon-photon scattering, and have confirmed the necessity of regularization. The need to implement the regularization procedure in the calculation of the Higgs decay process is tested with multiple calculational approaches. We find once again the standard result to be correct. We numerically study properties of leptonic systems. The first system is the positronium ion, a three-body system consisting of two electrons and a positron. The gyromagnetic factor of the positronium ion is determined with first relativistic corrections. We calculate the modified g -factor of this system for the first time. Our final topic is the computation of the spin asymmetry of the muon decay in perturbative QED. We point out that at the alpha squared level the asymmetry requires a careful definition due to multi-lepton final states and suggest to use familiar QCD techniques to define it in an infra-red safe way. We find that the TWIST measurement of the asymmetry is in excellent agreement with the Standard Model.