Photoproduction of Drell-Yan lepton pairs

We investigate the Drell-Yan reaction $\gamma p\to \left({\mu }^{+}{\mu }^{-}\right)X$ with an eye to experimental determination of the photon structure functions. Contributions to the process from both the nonhadronic anomaly and the vector-dominance piece are estimated: we find that the cross section from the anomaly dominates the vector-dominance contribution at large $Q^2$. The background from Bethe-Heitler pairs is also calculated; it is somewhat suppressed by going to $y=0\mathrm{}$, and further suppressed relative to the Drell-Yan contribution for fixed $Q^2$ by looking at high center-of-mass energies and at small $Q_{\perp }$ for the pair. Overall we find that the absolute Drell-Yan cross sections in the regions of interest are very small; experimental study of the process will be difficult.