  The polarization dynamics of electrons including multiple nonlinear Compton
scattering during the interaction of a circularly-polarized ultraintense laser
pulse with a counterpropagating ultrarelativistic electron beam is
investigated. While electron polarization emerges mostly due to spin-flips at
photon emissions, there is a non-radiative contribution to the polarization
which stems from the one-loop QED radiative corrections to the self-energy,
which admits of a simple physical model. We put forward a method to single out
the non-radiative contribution to the polarization, employing the reflection
regime of the interaction when the radiation reaction is significant. The
polarization of electrons that penetrate in the forward direction through a
colliding laser is shown to be dominated by the loop effect, while the
reflected electrons are mostly polarized by spin-flips at photon emissions. We
confirm this effect by quantum Monte Carlo simulations considering the helicity
transfer from the laser field to the electrons, taking into account the
opposite sign of the polarizations induced by the non-radiative loop effect and
radiative spin-flip. Our Monte Carlo simulations show a polarization signal as
high as $\gtrsim 10\%$ from the non-radiative effect, amenable for experimental
detection with current technology.
