Order alpha s2 contributions to the Drell-Yan cross section at fixed target energies.

Abstract

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