Abstract We present a quantum-field-theoretical study of bremsstrahlung, wherein an electron radiates a final-state photon as it propagates through the external electromagnetic field of a heavy ion. Crucially, this external field is linearly polarized and can be accurately described using the equivalent photon approximation via transverse-momentum-dependent photon distributions. Starting from the photon two-point correlator, the background-modified photon propagator is parameterized accordingly. Furthermore, the Coulomb correction is incorporated through a gauge-link formalism, and soft-photon radiation is resummed with a Sudakov factor, yielding an analytic form of the polarized Bethe–Heitler spectrum. As highlighted in our numerical figures for the EIC and EicC kinematics, this polarization manifests as a characteristic 2 cos 2 ϕ azimuthal modulation, yielding a few percent at EicC and reaching up to approximately 50% at EIC in the differential cross-section. Our graphical results distinctly illustrate the interplay of these effects, demonstrating strong Sudakov suppression at low transverse momentum and a mild Coulomb-induced enhancement at larger q_ q ⊥.
Zhang et al. (Tue,) studied this question.