Order $\alpha_s^{2}$ contributions to the Drell-Yan cross section at fixed target energies

Abstract

{}From the literature one infers that the bulk of the order $\alpha_{s}$ corrections to the Drell-Yan cross sections $d\sigma/dm$ and $m^{3}d^{2}\sigma/dmdx_{F}$ is constituted by the soft plus virtual gluon part of the coefficient function. In the case of $d\sigma/dm$ it can be shown that at fixed target energies the effect of the exact order $\alpha_{s}^{2}$ corrected coefficient function is very well approximated by its soft plus virtual gluon part. Since the complete order $\alpha_{s}^{2}$ contribution to the coefficient function is missing we have to assume that the same approximation also holds for $m^{3}d^{2}\sigma/dmdx_{F}$. It appears that the discrepancy between the exact order $\alpha_{s}$ corrected cross section and the massive lepton pair data taken at fixed target experiments can be partially explained by including the order $\alpha_{s}^{2}$ soft plus virtual gluon part of the coefficient function.