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

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.PACS numbers: 12.38. Bx,13.85.Qk The production of lepton pairs in hadronic collisions, known as the Drell-Yan (DY) process [1], was the first application of parton model ideas beyond deep inelastic scattering. Due to its clean theoretical interpretation in terms of quark-antiquark annihilation into a vector boson, and large event rates, the DY process has been studied extensively, and will continue to be investigated at both the Tevatron and the LHC. The DY process provides valuable information about parton distribution functions (pdfs), enables measurements of the production rates and masses of W and Z bosons, and furnishes a sensitive test for many varieties of new physics, such as the additional gauge bosons that appear in many extensions of the Standard Model. It will also be used for the more prosaic purpose of monitoring partonic luminosities at the LHC.Despite the importance of the DY process and the significant amount of work devoted to its description, the calculation of higher order QCD corrections has proceeded slowly. The next-to-leading order (NLO) QCD corrections to the total cross section, and the x F and rapidity distributions, were calculated nearly 25 years ago [2]; the NNLO corrections to the total cross section were obtained eleven years later [3]. No complete calculation of the NNLO QCD corrections to any differential distribution has been performed, although partial results exist [4].Recently, the NNLO virtual corrections to several interesting hard scattering processes in QCD have been computed [5]; however, the calculation of real emission contributions, required for complete NNLO predictions, is still in progress. These contributions entail a careful analysis of perturbative multiparticle final states in generic hard scattering events. While it is certainly useful to solve this problem in complete generality, it is also useful to study specific examples, especially those most urgently needed in experimental analyses. It is possible to develop alternative methods of calculation which can be used to compute basic differential distributions.In Refs. [6,7] it was shown how to combine the optical theorem with multi-loop computational methods to compute phase space integrals. In this Letter we present a non-trivial application of these ideas; we compute the rapidity distribution of the virtual photon produced in the DY process through NNLO in perturbative QCD.We shall apply our results to the production of lepton pairs in proton-prot...

On the calculation of soft phase space integral

“…It was then realized that the same method can also be applied to phase space integral with small modification [7,9]. The reason is that on-shell condition for phase space integral can be regarded as Feynman propagator for the purpose of IBP reduction or calculating derivative,…”

“…In that case analytic inclusive phase space integrals can be used in the construction of infrared subtraction terms for Next-to-Next-to-Leading Order (NNLO) calculation [4]. Moreover, when appropriate subtraction method was not yet available, analytic integral was the only method for obtaining cross section or distribution at NNLO at hadron collider [5][6][7][8][9].…”

Structure Functions and Parton Distributions

“…Until very recently, only inclusive Drell-Yan and DIS partonic cross sections were known at NNLO [12]. In the last couple of years, thanks to the development of new computational techniques, NNLO results have been obtained for inclusive Higgs production [13] and, more importantly, for a number of less inclusive observables, specifically Drell-Yan and W rapidity distributions in hadronic collisions [14]. On the other hand, the full set of NNLO anomalous dimensions or splitting functions has also been determined [15] after an effort of more than a decade.…”

Drell-Yan production atNNLL′+NNLOmatched to parton showers

“…The few fluctuations observed in the plot are of a statistical nature, as evidenced by the fact that they grow larger toward larger rapidities, where the statistics is poorer. The rapidity distribution of the vector boson has also been validated against the independent NNLO calculation provided by VRAP [83].…”