Studying Bremsstrahlung in Polarized Background Field at EIC and EicC

We present a quantum-field-theoretical study of bremsstrahlung from an electron propagating in a linearly polarized background photon field. Starting from the photon two-point correlator, the background-modified photon propagator is parameterized via transverse-momentum-dependent photon distributions. 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. Numerical illustrations show a characteristic $\cos 2\phi$ azimuthal modulation of a few percent in the differential distribution, with Sudakov suppression at low transverse momentum and mild Coulomb-induced enhancement at larger $q_\perp$.