Deep Inelastic Scattering with a Tagged Photon: QED Corrections for the $\Sigma$ Method

After a brief review of the kinematics of deep inelastic scattering (DIS) within the so-called $\Sigma$ method, we derive the necessary formulae for the treatment of QED radiative corrections to DIS originating from hard photon radiation. The results are applied to a calculation of the corrections to DIS with a tagged photon with next-to-leading logarithmic accuracy under HERA conditions. It turns out that the next-to-leading order corrections are quite important for the $\Sigma$ method. We also discuss the dependence of the corrections on the longitudinal structure function of the proton, $F_L$, in the region of low $Q^2$ and moderate $x$.