Leptonic radiative corrections to lepton-proton scattering
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Abstract
Low energy precision experiments have become an important tool in the search for new
physics beyond the Standard Model (SM). These experiments can exclude new physics at mass scales extending well into the TeV range and are complementary to searches at the Large Hadron Collider (LHC).
With polarized elastic electron proton scattering, one can determine the weak charge of the proton, which is related to the weak mixing angle in the SM. This can be achieved by measuring the asymmetry between leptons with positive and negative helicities. Deviations from the SM prediction for the weak mixing angle can provide important tests of models beyond the SM.
A future experiment that plans to measure the weak charge of the proton at low energies and with high precision is the P2 experiment that will take place at the new MESA facility in Mainz. The present work is mostly motivated by this experiment and shows results that are relevant for this particular measurement. In addition, a μp scattering experiment, called MUSE, has been also proposed at the PSI with the aim to study the proton radius puzzle.
In order to match the experimental precision of such experiments it is necessary not only
to have an exhaustive treatment of first order radiative corrections, but also to go beyond
first order and include a treatment of second order radiative corrections. In this work we aim to provide such a calculation for polarized and unpolarized lepton nucleon scattering, that includes both virtual and real corrections to the lepton lines.
We re-derive first order corrections, including also hadronic corrections, relying as little
as possible on approximations. The main focus is however on second order corrections, including a new calculation of two photon bremsstrahlung. Photon radiation leads to a shift in the measured Q2 , that translates in a 5% correction to the parity violating asymmetry. For this reason we present the effects of first and second order photon radiation on the asymmetry. Finally we present a first order calculation of lepton carbon scattering which is also relevant for the MESA experiments.
All the calculations that were done in this work were included in a Monte Carlo event
generator called POLARES, that can be used to simulate both unpolarized and polarized lepton nucleon scattering events for the aforementioned experiments and possibly other future low energy precision experiments.