Radiative Analysis of Lepton-Proton Scattering via Low-energy Efective Field Theory

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In this thesis we have presented a complete analysis of radiative correction to elastic lepton-protonscattering using efective feld theory (EFT) keeping in mind the ongoing Muon Scattering Experiment(MUSE) at PSI. The MUSE seeks to fnd a resolution to the famous Proton Radius Puzzle, a seriousdiscrepancies associated with the measured values of the proton's charge radius from diferentexperiments, through a simultaneous study of very low-energy electron-proton and muon-proton scatteringswith precedented accuracies. The work in the thesis encompasses three vital aspects associated with thesystematic analysis of radiative corrections to the lepton-proton scattering process: 1) accounting for theinelastic radiative tail efects constituting the dominant background for the basic elastic process, 2)systematics associated with hadronic efects in the two-photon exchange (TPE) contributions to the elasticcross section, and 3) accurate estimate of the infrared divergence free radiative contributions incorporatingdominant hadronic recoil efects. The EFT that we have used is the so-called Heavy Baryon ChiralPerturbation Theory (HBChPT), the non-relativistic analog of Baryon Chiral Perturbation Theory, which istailor-made to ideally describe the dynamics of nucleon at low-energies. The frst work of this thesis is asystematic calculation of the cross-section for the lepton-proton bremsstrahlung process in HBChPT atnext-to-leading order (NLO). This process corresponds to an undetected background signal for theproposed MUSE experiment. In the second work, we evaluate the TPE corrections to the low-energy elasticlepton-proton scattering at NLO accuracy, including a non-zero lepton mass. We consider the elastic protonintermediate state in the two-photon exchange invoking soft photon approximation. The infrared singularcontributions are projected out using dimensional regularization. In the fnal work, the full radiativecorrection to the elastic lepton proton scattering, including all the virtual and corresponding soft photonemission diagrams up to NLO in HBChPT, is taken into account. We demonstrate the systematiccancellation of the infrared singularities amongst the various diagrams contributing to the elastic cross-section.
Supervisor: Udit Raha