Dilepton rapidity distribution in the Drell-Yan process at NNLO in QCD

TL;DR

A powerful new method for calculating differential distributions in hard scattering processes is introduced, based upon a generalization of the optical theorem, that 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.

Abstract

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 multi-loop diagrams to be applied to non-inclusive phase-space integrals, and permits a high degree of automation. We apply our results to the analysis of fixed target experiments.

Figures (3)

• 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), for parameter choices relevant for fixed target experiments, along 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 $q\bar{q}$ and $qg$, normalized to the complete NNLO differential cross section, for $\sqrt{s} = 38.76$ GeV, $M=8$ GeV, and $\mu=M$.
• Figure 3: The K-factors $K^{\rm NLO}(Y)=\sigma^{\rm NLO}/ \sigma^{\rm LO}$, $K^{\rm NNLO}(Y)=\sigma^{\rm NNLO}/ \sigma^{\rm LO}$, and $K^{(2)}(Y) = \sigma^{\rm NNLO}/ \sigma^{\rm NLO}$, for $\mu=M$.