Precision calculation of processes used for luminosity measurement at the ZEUS experiment

The process pe -> pe+gamma with the photon emitted along the electron beam axis is used for luminosity measurement at HERA. In this paper the process is calculated including one-loop QED radiative corrections. In the ZEUS experiment, both the electron and the photon can be detected. Therefore both photon and electron spectra with and without the gamma-e coincidence are analyzed. We also calculate the process pe -> pel+l- which contributes to the background in the electron tagger.