Radiative corrections to polarization observables in electron-proton scattering

We consider radiative corrections to polarization observables in elastic electron-proton scattering, in particular, for the polarization transfer measurements of the proton form factor ratio $\mu G_E/G_M$. The corrections are of two types: two-photon exchange (TPE) and bremsstrahlung (BS); in the present work we pay special attention to the latter. Assuming small missing energy or missing mass cutoff, the correction can be represented in a model-independent form, with both electron and proton radiation taken into account. Numerical calculations show that the contribution of the proton radiation is not negligible. Overall, at high $Q^2$ and energies, the total correction to $\mu G_E/G_M$ grows, but is dominated by TPE. At low energies both TPE and BS may be significant; the latter amounts to $\sim 0.01$ for some reasonable cut-off choices.

Figure 1

Bremsstrahlung diagrams.

Figure 2

Bremsstrahlung correction to $\mu G_E/G_M$ ratio vs. $Q^2$ at different beam energies, as labeled on the plot. Solid line—missing energy cutoff, dashed line–missing mass cutoff; thick line—full radiation, thin line—electron only.

Figure 3

Bremsstrahlung correction to $\mu G_E/G_M$ ratio vs. beam energy at fixed scattering angle ${90}^{\circ }$. Curve types are the same as in Fig. 2.

Figure 4

Radiative corrections to $\mu G_E/G_M$ ratio vs. $Q^2$, bremsstrahlung (dashed), TPE (dash-dotted), and total (solid). Missing energy cutoff $r_m=0.1\epsilon$.