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.
Highlights
The real part of the twophoton exchange (TPE) amplitude generates a correction to the Born cross section of unpolarized electron-proton (e−p) scattering that may be substantial enough to be possibly responsible for the proton form factor puzzle [10,11,20,26,27]
We study the relevance of the lepton mass on the respective single-spin asymmetry (SSA), and our results are presented in the kinematics of the future MUon Scattering Experiment (MUSE) [65,66] at PSI
We calculated the elastic contribution to the beamnormal single-spin asymmetry in elastic lepton-proton scattering
Summary
The proton form factor [1,2,3] and proton radius [4,5,6] puzzles have brought significant experimental [7,8,9] and theoretical interest [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25] to studies of the twophoton exchange (TPE) amplitude in elastic lepton-proton (lp) scattering. Unlike the beam-normal asymmetry, the target-normal SSA for the elastic scattering process lN↑ → lN, which we denote as ANy , is not suppressed by the lepton helicity factor m For this reason, one expects ANy to be of order 10−3–10−2 for an unpolarized electron beam of GeV energy scattered by a polarized nucleon. This means that effects due to transverse polarization of the muon (or antimuon) beam are substantial enough to be taken into consideration in respective precision measurements of elastic μÆp scattering Our calculation of both Bey and Bμy accounts for the elastic intermediate contribution in the TPE loop and can be used in analyses of elastic ep and μp scattering measurements that are performed below the pion production threshold. We provide analytical expressions that may be employed for a model-dependent calculation of the inelastic contribution to Bly for leptonproton scattering above the pion production threshold
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