Photon bremsstrahlung from quark jet via transverse and longitudinal scattering: Single versus multiple scattering

We study the production of jet-bremsstrahlung photons through scattering with the constituents of dense nuclear matter within the framework of deep-inelastic scattering off a large nucleus. Applying a gradient expansion up to the second order for the exchanged three-dimensional momentum between jet and medium, we derive the single-photon bremsstrahlung spectrum with the inclusion of contributions from the transverse broadening as well as the longitudinal drag and diffusion of the hard parton's momentum. We also compare the medium-induced photon radiation spectra for single scattering and from the resummation of multiple scatterings. It is found that the coupling between different scatterings can give an additional contribution to medium-induced photon radiation, while for small momentum exchange the leading contribution from the drag and diffusions to the photon emission spectra remain the same for single and multiple scatterings.