Radiative spin-flip and polarization in a helical undulator

A recent claim that spin-flip photon emission in a helical undulator can lead to significant depolarization of a high-energy polarized electron beam is shown to be erroneous. Such a claim would, if true, have serious consequences for the International Linear Collider. The critical error in the calculation is identified (omission of a key term in the interaction Hamiltonian). The resulting cancellations in the spin-flip matrix element are explained. A simple argument is also given why the equilibrium degree of radiative polarization is almost zero for ultrarelativistic electrons radiating via spin-flip transitions in a helical undulator. Fundamentally, it is because the direction of the quantization axis of the spin eigenstates is almost orthogonal to the normal to the plane of formation of the radiation.