Longitudinal virtual photons and the interference terms in ep collisions

The importance of the contributions of the longitudinally polarized virtual photon in ep collisions is investigated. We derive the factorization formulae for the unpolarized inclusive and semi-inclusive ep collisions in an arbitrary reference frame. The numerical calculations for the prompt photons production in the unpolarized Compton process (e p --> e gamma X) at the ep HERA collider are performed in the Born approximation. We studied various distributions in the ep centre-of-mass frame and found that the differential cross section for the longitudinally polarized intermediate photon and the term due to the interference between the longitudinal- and transverse- polarization states of the photon are small, i.e. below 10% of the cross section. Moreover, these two contributions almost cancel one another, leading to a stronger domination of the transversely polarized virtual photon, even for its large virtuality. Relevance of the resolved longitudinal photon in a jet production in DIS events at HERA is commented. A relatively large (about 30%) effect due to the longitudinal-transverse interference term was found in the azimuthal-angle distribution in the Breit frame.