Executive Summary : | The proton radius puzzle remains a significant issue, despite a decade of efforts since its inception in 2012. Several high-precision lepton-proton scattering experiments are currently underway to resolve this conundrum. One such experiment, MUSE, is designed to scatter muons and re-do electron scattering measurements at very low momentum transfers. A simultaneous data analysis of the two leptonic flavors is likely to identify discrepancies or gaps in our understanding of the underlying lepton-proton interaction mechanism. The precise extraction of the proton's electromagnetic radii requires high-quality cross section data and a radiative "unfolding" analysis before extracting meaningful information. An accurate theoretical assessment of radiative corrections to the elastic lepton-proton cross section is required to reduce systematic errors in extracting observables. The research proposal aims to perform a rigorous model-independent analysis based on low-energy effective field theory (EFT) to provide analytical estimates of higher order corrections pertinent to the low-energy elastic scattering process and the corresponding lepton-proton "hard" photon bremsstrahlung process. The later precision results integrated into detector simulation codes could provide robust estimation of the background contributions. A four-fold analytical improvement is proposed, based on recent theoretical findings by the PI and his collaborators, targeting an improved precision goal of about 1% in the elastic cross section. The full systematic model-independent EFT evaluation takes into account all major sources of uncertainties, both in the pure hadronic sector and those due to QED radiative effects, as well as the potentially large proton's recoil corrections (chiral-radiative corrections). |