Dilepton Rapidity Distribution in the Drell-Yan Process at Next-to-Next-to-Leading Order in QCD

We compute the rapidity distribution of the virtual photon produced in the Drell-Yan process through next-to-next-to-leading order in perturbative QCD. We introduce a powerful new method for calculating differential distributions in hard scattering processes. This method is based upon a generalization of the optical theorem; it allows the integration-by-parts technology developed for multiloop diagrams to be applied to noninclusive phase-space integrals, and permits a high degree of automation. We apply our results to the analysis of fixed-target experiments.

Figure 1

The CMS rapidity distribution of the lepton pair produced in $pp$ collisions at LO (lower band), NLO (middle band), and NNLO (upper band), compared with E866 data. The upper (lower) edge of each band denotes the renormalization/factorization scale choice $\mu =M/2$ $\mu =2M$).

Figure 2

The NNLO corrections for the partonic channels $q\overline{q}$ and $qg$, normalized to the complete NNLO differential cross section, for $\sqrt{s}=38.76\mathrm{G}\mathrm{e}\mathrm{V}$, $M=8\mathrm{G}\mathrm{e}\mathrm{V}$, and $\mu =M$.

Figure 3

The $K$ factors $K^{\mathrm{N}\mathrm{L}\mathrm{O}}(Y)={\sigma }^{\mathrm{N}\mathrm{L}\mathrm{O}}/{\sigma }^{\mathrm{L}\mathrm{O}}$, $K^{\mathrm{N}\mathrm{N}\mathrm{L}\mathrm{O}}(Y)={\sigma }^{\mathrm{N}\mathrm{N}\mathrm{L}\mathrm{O}}/{\sigma }^{\mathrm{L}\mathrm{O}}$, and $K^{(2)}(Y)={\sigma }^{\mathrm{N}\mathrm{N}\mathrm{L}\mathrm{O}}/{\sigma }^{\mathrm{N}\mathrm{L}\mathrm{O}}$, for $\mu =M$.