Drell-Yan lepton-pair production: $q_T$ resummation at N$^3$LL accuracy and fiducial cross sections at N$^3$LO

We present high-accuracy QCD predictions for the transverse-momentum (qT ) distribution and fiducial cross sections of Drell–Yan lepton pairs produced in hadronic collisions. At small value of qT we resum to all perturbative orders the logarithmically enhanced contributions up to next-to-next-to-next-to-leading logarithmic (NLL) accuracy, including all the next-to-next-to-next-to-leading order (NLO) (i.e. O(α S)) terms. Our resummed calculation has been implemented in the public numerical program DYTurbo, which produces fast and precise predictions with the full dependence on the final-state leptons kinematics. We consistently combine our resummed results with the known O(α S) fixed-order predictions at large values of qT thus obtaining full NLO accuracy also for fiducial cross sections. We show numerical results at LHC energies discussing the reduction of the perturbative uncertainty with respect to lower-order March 2021 ar X iv :2 10 3. 04 97 4v 2 [ he pph ] 2 5 M ar 2 02 1 After the successful operation of the first two runs of the Large Hadron Collider (LHC) at CERN and the discovery of the long sought Higgs boson, a major task of the high-energy physics community has become a direct investigation of the electroweak symmetry breaking mechanism. In the absence of clear direct signals of new physics phenomena, precision studies give us a unique opportunity to search for possible deviations from Standard Model (SM) predictions. In this scenario it is clear that theoretical predictions for SM cross sections and associated distributions at an unprecedented level of accuracy are indispensable to fully exploit the discovery potential provided by the collected and forthcoming collider data. The electroweak (EW) vector boson production, through the Drell–Yan (DY) mechanism [1, 2], is one of the most important hard-scattering process at hadron colliders both in the contest of SM precision studies [3, 4, 5, 6, 7] and for searches of physics signals beyond the SM [8, 9, 10, 11]. It is thus extremely important to provide accurate theoretical predictions, through detailed computations of the higher-order radiative corrections in QCD and in the EW theory, for vector boson production cross sections and related kinematical distributions. Among the various kinematical distributions the vector boson transverse-momentum (qT ) spectrum plays a special role since its uncertainty directly affects the W -boson mass measurement [12, 13, 14]. The next-to-next-to-leading order (NNLO) QCD corrections have been computed for the total cross section [15, 16], the rapidity distribution [17] and at fully differential level including the leptonic decay of the vector boson [18, 19, 20, 21]. More recently next-to-next-to-next-to-leading order (NLO) QCD calculations of the total cross section have been performed in Refs. [22, 23]. The next-to-leading order (NLO) EW corrections, the mixed QCD-EW and QCD-QED corrections have also been computed [24]–[47]. In the large-qT region, where qT is of the order of the invariant mass of the lepton pair M , the fixed-order QCD corrections for the qT distribution are known up to O(α S) in analytic form [48, 49, 50, 51, 52] and up to O(α S) numerically through the fully exclusive NNLO calculation of vector boson production in association with jets [53, 54, 55, 56, 57]. However the bulk of the vector boson cross section lies in the small-qT region (qT M) where the reliability of the fixed-order expansion is spoiled by the presence of large logarithmic corrections of the type ln(M/q T ) due to the initial-state radiation of soft and/or collinear partons. In order to obtain reliable perturbative QCD predictions, the enhanced-logarithmic terms have to be evaluated and systematically resummed to all orders in perturbation theory [58, 59, 60, 61, 62, 63]. Resummed calculations at different levels of theoretical accuracy have been performed in Refs. [64]– [72] also applying methods from Soft Collinear Effective Theory [73]–[79] and transverse-momentum dependent factorisation [80]–[85]. In this Letter we apply the QCD transverse-momentum resummation formalism of Refs. [61, 65, 68] for the case of Z/γ∗ boson production up to NLL accuracy. We analytically include all the NLO terms at small-qT reaching full N LL+NLO accuracy in the small-qT region †. We implement our resummed calculation in the public numerical program DYTurbo [86] which provides fast and numerically precise predictions both for resummed and fixed-order QCD calculations including the full kinematical dependence of the decaying lepton pair with the corresponding spin correlations and the finite-width effects. We consistently match our resummed predictions with the NNLO numerical results at large-qT calculated in Refs. [54, 57] and reported in Ref. [71] thus including theO(α S) corrections for the entire spectrum of qT . By using the connection between the qT resummation and the qT subtraction formalism [87] for fixed-order calculations we analytically †Sometime in the literature this is referred as N3LL′ accuracy.