ar X iv : h ep - p h / 02 11 21 9 v 1 1 4 N ov 2 00 2 Higher order QED corrections to deep inelastic scattering

Deep inelastic electron–nucleon scattering allows for fundamental QCD tests investigating the scaling violations of structure functions in the perturbative regime of large values of Q. The detailed knowledge of the structure functions enables to study various aspects of the dynamics of nonAbelian gauge theory, and is necessary for the future experimental search for the Higgs–boson and new particles at TEVATRON and LHC. One of the major goals of the experiments H1 and ZEUS at the ep–collider HERA at DESY is to perform a QCD test at large space–like virtualities Q at high precision. This presumes to know the QED radiative corrections to the double– differential scattering cross sections of deeply inelastic ep corrections as precisely as possible. Previous calculations of the radiative corrections for the unpolarized cross sections at leading order [1– 5], the leading–log level [7–12] to leading and higher orders, and QED–resummations of small– x terms [11,13] revealed that these corrections are very large, in a wide kinematic range of x and Q. The corrections are, moreover, complicated by a new type of sizeable contributions as the Compton–peak [ 14]. This makes it necessary to extend the calculations to higher orders. The higher order leading–logarithmic contributions O [ (αL) ] to QED corrections are obtained as the leading order solution of the associated renormalization group equations [ 15] for mass factorization. These corrections are universal,