Abstract
The angular distributions of lepton pairs in the Drell-Yan process can provide rich information on the underlying QCD production mechanisms. These dynamics can be parameterised in terms of a set of frame dependent angular coefficients, Ai=0,…,7, which depend on the invariant mass, transverse momentum, and rapidity of the lepton pair. Motivated by recent measurements of these coefficients by ATLAS and CMS, and in particular by the apparent violation of the Lam-Tung relation A0 − A2 = 0, we perform a precision study of the angular coefficients at mathcal{O}left({alpha}_{mathrm{s}}^3right) in perturbative QCD. We make predic-tions relevant for pp collisions at sqrt{s}=8 TeV, and perform comparisons with the available ATLAS and CMS data as well as providing predictions for a prospective measurement at LHCb. To expose the violation of the Lam-Tung relationship we propose a new observable ΔLT = 1 − A2/A0 that is more sensitive to the dynamics in the region where A0 and A2 are both small. We find that the mathcal{O}left({alpha}_{mathrm{s}}^3right) corrections have an important impact on the pT,Z distributions for several of the angular coefficients, and are essential to provide an adequate description of the data. The compatibility of the available ATLAS and CMS data is reassessed by performing a partial χ2 test with respect to the central theoretical prediction which shows that χ2/Ndata is significantly reduced by going from mathcal{O}left({alpha}_{mathrm{s}}^2right) to mathcal{O}left({alpha}_{mathrm{s}}^3right) .
Highlights
Distributions for the angular coefficients can be extracted experimentally through fits to the measured final-state lepton kinematics, which can be compared to the corresponding predictions obtained in pQCD
The angular distributions of lepton pairs in the Drell-Yan process can provide rich information on the underlying QCD production mechanisms. These dynamics can be parameterised in terms of a set of frame dependent angular coefficients, Ai=0,...,7, which depend on the invariant mass, transverse momentum, and rapidity of the lepton pair
The compatibility of the available ATLAS and CMS data is reassessed by performing a partial χ2 test with respect to the central theoretical prediction which shows that χ2/Ndata is significantly reduced by going from O(αs2) to O(αs3)
Summary
We consider the inclusive production of lepton pairs through the decay of an intermediate gauge boson, p(p1) + p(p2) → V (q) + X → (k1) + ̄(k2) + X as depicted in figure 1. Hij of the hadronic tensor, are directly related to the eight angular coefficients A0,...,7 and the unpolarised cross section. The unpolarised cross section (2.6) completes eq (2.8) as the ninth linearly independent combination of the Hij. Let us choose a specific reference frame by defining the direction of the axes in the lepton-pair rest frame. The tensor structures multiplying H2,3,4 only involve momenta lying inside the hadronic plane and it is solely the tensor gμν multiplying the form factor H1 which has a non-vanishing component orthogonal to it. One of the goals of this work is to assess the compatibility of the observed extent of the Lam-Tung violation with that expected in predictions based on pQCD This can be done by directly studying the pT,Z distribution for the difference of the angular coefficients A0 and A2. The data will be re-expressed in terms of ∆LT
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