Abstract
We consider the transverse-momentum ($q_T$) distribution of Drell-Yan lepton pairs produced, via $W$ and $Z/\gamma^*$ decay, in hadronic collisions. At small values of $q_T$, we resum the logarithmically-enhanced perturbative QCD contributions up to next-to-next-to-leading logarithmic accuracy. Resummed results are consistently combined with the known ${\mathcal O}(\alpha_S^2)$ fixed-order results at intermediate and large values of $q_T$. Our calculation includes the leptonic decay of the vector boson with the corresponding spin correlations, the finite-width effects and the full dependence on the final-state lepton(s) kinematics. The computation is encoded in the numerical program DYRes, which allows the user to apply arbitrary kinematical cuts on the final-state leptons and to compute the corresponding distributions in the form of bin histograms. We present a comparison of our results with some of the available LHC data. The inclusion of the leptonic decay in the resummed calculation requires a theoretical discussion on the $q_T$ recoil due to the transverse momentum of the produced vector boson. We present a $q_T$ recoil procedure that is directly applicable to $q_T$ resummed calculations for generic production processes of high-mass systems in hadron collisions.
Highlights
The resummed and fixed-order calculations, which are valid at small and large values of qT, respectively,can be consistently matched at intermediate values of qT to achieve a uniform theoretical accuracy for the entire range of transverse momenta
In this paper we extend the next-to-next-to-leading logarithmic (NNLL)+NNLO calculation of ref. [59] to W boson production, and we include the leptonic decay of the vector boson with the corresponding spin correlations
We see that the next-to-leading logarithmic (NLL)+NLO (NNLL+NNLO) total cross section agrees with the NLO (NNLO) result to better than 1% accuracy
Summary
We briefly recall the main features of the transverse-momentum resummation formalism that we use in this paper. Using the resummation expansion parameter L in eq (2.7) and the matching procedure (which implements the perturbative unitarity constraint on the total cross section) with the complete fixed-order calculation, our resummation formalism [41] formally achieves a uniform theoretical accuracy in the region of small and intermediate values of qT , and it avoids the introduction of large unjustified higher-order contributions in the large-qT re-. In the large-qT region, the results of the resummed calculation are consistent with the customary fixed-order results and, typically [41, 59], show larger theoretical uncertainties (e.g., larger dependence with respect to auxiliary-scale variations) with respect to the corresponding fixed-order results This feature is not unexpected, since the theoretical knowledge (and the ensuing resummation) of large logarithmic contributions at small qT cannot improve the theoretical predictions at large values of qT.
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