# Lepton mass effects for beam-normal single-spin asymmetry in elastic muon-proton scattering

## TL;DR

This paper calculates the beam-normal single-spin asymmetry in elastic muon-proton scattering without ultrarelativistic assumptions, highlighting muon mass effects at energies of a few hundred MeV and their impact on experimental uncertainties.

## Contribution

It provides the first estimation of muon mass effects on asymmetry at low energies, relevant for precision muon-proton scattering experiments like MUSE.

## Key findings

- Muon asymmetry estimated at about 0.1% for MUSE kinematics.
- Mass effects are significant at energies below a few hundred MeV.
- Backward scattering shows the largest asymmetry contribution.

## Abstract

We estimate the beam-normal single-spin asymmetry in elastic lepton-proton scattering without employing the ultrarelativistic approximation. Our calculation is relevant for analyses of muon scattering at energies of few hundred MeV and below -- when effects of the muon mass become essential. At such energies, the transverse polarization of the muon beam is expected to contribute significantly to the systematic uncertainty of precision measurements of elastic muon-proton scattering. We evaluate such systematics using an example of the MUSE experiment at PSI. The muon asymmetry is estimated at about 0.1\% in kinematics of MUSE and it is the largest for scattering into a backward hemisphere.