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 . 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 cut-off, 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 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 ~ 0.01 for some reasonable cut-off choices.

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