Drell-Yan Cross Section to Third Order in the Strong Coupling Constant

We present phenomenological results for the inclusive cross section for the production of a lepton pair via virtual photon exchange at next-to-next-to-next-to-leading order in perturbative QCD. In line with the case of Higgs production, we find that the hadronic cross section receives corrections at the percent level, and the residual dependence on the perturbative scales is reduced. However, unlike in the Higgs case, we observe that the uncertainty band derived from scale variation is no longer contained in the band of the previous order.

Figure 1

The light red area in the left plot represents the PDF uncertainty, the dark red area corresponds to the combination in quadrature of $\mathrm{PDF}+{\alpha }_s$ uncertainty. The right plot shows the uncertainty on the cross section due to missing ${\mathrm{N}}^3\mathrm{LO}$ PDFs.

Figure 2

The cross section as a function of the invariant mass $Q^2$ of the lepton pair for small (left) and large (right) values of $Q$.

Figure 3

Dependence of the cross section on either ${\mu }_F$ or ${\mu }_R$ with the other scale held fixed.

Figure 4

Contributions of the different partonic channels at ${\mathrm{N}}^3\mathrm{LO}$, as a function of the invariant mass $Q$ and normalized to the ${\mathrm{N}}^3\mathrm{LO}$ cross section. The red band correspond to the variation of the ${\mathrm{N}}^3\mathrm{LO}$ correction under variation of the factorization and renormalization scale as described in the text.