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The bremsstrahlung cross section is calculated at leading order for polarizedbeams of electrons and ions, which is needed for luminosity measurements at theupcoming Electron Ion Collider (EIC). Analytic expressions, differential in theemitted photon energy and polar angle, are derived. The component of the crosssection which depends on the beam polarizations is found to be highlysuppressed with respect to the unpolarized Bethe-Heitler component, owing tothe low $q^2$ that characterizes the bremsstrahlung process.

Bremsstrahlung Cross Section with Polarized Beams for Luminosity Determination at the EIC