Abstract
Drell-Yan lepton pairs with finite transverse momentum are produced when the vector boson recoils against (multiple) parton emission(s), and is determined by QCD dynamics. At small transverse momentum, the fixed order predictions break down due to the emergence of large logarithmic contributions. This region can be studied via the p ZT distribution constructed from the energies of the leptons, or through the \( {\phi}_{{}^{\eta}}^{\ast } \) distribution that relies on the directions of the leptons. For sufficiently small transverse momentum, the \( {\phi}_{{}^{\eta}}^{\ast } \) observable can be measured experimentally with better resolution. We study the small p ZT and \( {\phi}_{{}^{\eta}}^{\ast } \) distributions up to next-to-next-to-leading order (NNLO) in perturbative QCD. We compute the \( {\phi}_{{}^{\eta}}^{\ast } \) distributions for the fully inclusive production of lepton pairs via Z/γ∗ to NNLO and normalise them to the NNLO cross sections for inclusive Z/γ∗ production. We compare our predictions with the \( {\phi}_{{}^{\eta}}^{\ast } \) distribution measured by the ATLAS collaboration during LHC operation at 8 TeV. We find that at moderate to large values of \( {\phi}_{{}^{\eta}}^{\ast } \), the NNLO effects are positive and lead to a substantial improvement in the theory-data comparison compared to next-to-leading order (NLO). At small values of p ZT and \( {\phi}_{{}^{\eta}}^{\ast } \) , the known large logarithmic enhancements emerge through and we identify the region where resummation is needed. We find an approximate relationship between the values of p ZT and \( {\phi}_{{}^{\eta}}^{\ast } \) where the large logarithms emerge and find perturbative consistency between the two observables.
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18 October 2018
We correct an error in the implementation of the NNLO corrections, which modifies the numerical predictions. In the light of these modifications, we re-assess the kinematical range of applicability of the fixed-order NNLO predictions.
18 October 2018
We correct an error in the implementation of the NNLO corrections, which modifies the numerical predictions. In the light of these modifications, we re-assess the kinematical range of applicability of the fixed-order NNLO predictions.
References
ATLAS collaboration, Measurement of the Z/γ ∗ boson transverse momentum distribution in pp collisions at \( \sqrt{s}=7 \) TeV with the ATLAS detector, JHEP 09 (2014) 145 [arXiv:1406.3660] [INSPIRE].
ATLAS collaboration, Measurement of the transverse momentum and \( {\phi}_{{}^{\eta}}^{\ast } \) distributions of Drell-Yan lepton pairs in proton-proton collisions at \( \sqrt{s}=8 \) TeV with the ATLAS detector, Eur. Phys. J. C 76 (2016) 291 [arXiv:1512.02192] [INSPIRE].
CMS collaboration, Measurement of the rapidity and transverse momentum distributions of Z bosons in pp collisions at \( \sqrt{s}=7 \) TeV, Phys. Rev. D 85 (2012) 032002 [arXiv:1110.4973] [INSPIRE].
CMS collaboration, Measurement of the Z boson differential cross section in transverse momentum and rapidity in proton-proton collisions at 8 TeV, Phys. Lett. B 749 (2015) 187 [arXiv:1504.03511] [INSPIRE].
LHCb collaboration, Measurement of the forward Z boson production cross-section in pp collisions at \( \sqrt{s}=7 \) TeV, JHEP 08 (2015) 039 [arXiv:1505.07024] [INSPIRE].
LHCb collaboration, Measurement of forward W and Z boson production in pp collisions at \( \sqrt{s}=8 \) TeV, JHEP 01(2016) 155 [arXiv:1511.08039] [INSPIRE].
R. Hamberg, W.L. van Neerven and T. Matsuura, A complete calculation of the order α 2 s correction to the Drell-Yan K factor, Nucl. Phys. B 359 (1991) 343 [Erratum ibid. B 644 (2002) 403] [INSPIRE].
W.L. van Neerven and E.B. Zijlstra, The O(α 2 s ) corrected Drell-Yan K factor in the DIS and MS scheme, Nucl. Phys. B 382 (1992) 11 [Erratum ibid. B 680 (2004) 513] [INSPIRE].
C. Anastasiou, L.J. Dixon, K. Melnikov and F. Petriello, Dilepton rapidity distribution in the Drell-Yan process at NNLO in QCD, Phys. Rev. Lett. 91 (2003) 182002 [hep-ph/0306192] [INSPIRE].
K. Melnikov and F. Petriello, The W boson production cross section at the LHC through O(α 2 s ), Phys. Rev. Lett. 96 (2006) 231803 [hep-ph/0603182] [INSPIRE].
K. Melnikov and F. Petriello, Electroweak gauge boson production at hadron colliders through O(α 2 s ), Phys. Rev. D 74 (2006) 114017 [hep-ph/0609070] [INSPIRE].
S. Catani, G. Ferrera and M. Grazzini, W boson production at hadron colliders: the lepton charge asymmetry in NNLO QCD, JHEP 05 (2010) 006 [arXiv:1002.3115] [INSPIRE].
S. Catani, L. Cieri, G. Ferrera, D. de Florian and M. Grazzini, Vector boson production at hadron colliders: a fully exclusive QCD calculation at NNLO, Phys. Rev. Lett. 103 (2009) 082001 [arXiv:0903.2120] [INSPIRE].
R. Gavin, Y. Li, F. Petriello and S. Quackenbush, FEWZ 2.0: a code for hadronic Z production at next-to-next-to-leading order, Comput. Phys. Commun. 182 (2011) 2388 [arXiv:1011.3540] [INSPIRE].
C. Anastasiou, L.J. Dixon, K. Melnikov and F. Petriello, High precision QCD at hadron colliders: electroweak gauge boson rapidity distributions at NNLO, Phys. Rev. D 69 (2004) 094008 [hep-ph/0312266] [INSPIRE].
J.C. Collins, D.E. Soper and G.F. Sterman, Transverse momentum distribution in Drell-Yan pair and W and Z boson production, Nucl. Phys. B 250 (1985) 199 [INSPIRE].
G. Bozzi, S. Catani, G. Ferrera, D. de Florian and M. Grazzini, Transverse-momentum resummation: a perturbative study of Z production at the Tevatron, Nucl. Phys. B 815 (2009) 174 [arXiv:0812.2862] [INSPIRE].
G. Bozzi, S. Catani, G. Ferrera, D. de Florian and M. Grazzini, Production of Drell-Yan lepton pairs in hadron collisions: Transverse-momentum resummation at next-to-next-to-leading logarithmic accuracy, Phys. Lett. B 696 (2011) 207 [arXiv:1007.2351] [INSPIRE].
T. Becher and M. Neubert, Drell-Yan production at small q T , transverse parton distributions and the collinear anomaly, Eur. Phys. J. C 71 (2011) 1665 [arXiv:1007.4005] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover, A. Huss and T.A. Morgan, The NNLO QCD corrections to Z boson production at large transverse momentum, JHEP 07 (2016) 133 [arXiv:1605.04295] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover, A. Huss and T.A. Morgan, Precise QCD predictions for the production of a Z boson in association with a hadronic jet, Phys. Rev. Lett. 117 (2016) 022001 [arXiv:1507.02850] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover, A. Huss and T.A. Morgan, NNLO QCD corrections for Z boson plus jet production, arXiv:1601.04569 [INSPIRE].
A. Banfi, S. Redford, M. Vesterinen, P. Waller and T.R. Wyatt, Optimisation of variables for studying dilepton transverse momentum distributions at hadron colliders, Eur. Phys. J. C 71 (2011) 1600 [arXiv:1009.1580] [INSPIRE].
D0 collaboration, V.M. Abazov et al., Precise study of the Z/γ ∗ boson transverse momentum distribution in pp collisions using a novel technique, Phys. Rev. Lett. 106 (2011) 122001 [arXiv:1010.0262] [INSPIRE].
ATLAS collaboration, Measurement of angular correlations in Drell-Yan lepton pairs to probe Z/γ ∗ boson transverse momentum at \( \sqrt{s}=7 \) TeV with the ATLAS detector, Phys. Lett. B 720 (2013) 32 [arXiv:1211.6899] [INSPIRE].
LHCb collaboration, Measurement of the forward Z boson production cross-section in pp collisions at \( \sqrt{s}=13 \) TeV, JHEP 09 (2016) 136 [arXiv:1607.06495] [INSPIRE].
C. Balázs and C.P. Yuan, Soft gluon effects on lepton pairs at hadron colliders, Phys. Rev. D 56 (1997) 5558 [hep-ph/9704258] [INSPIRE].
M. Guzzi, P.M. Nadolsky and B. Wang, Nonperturbative contributions to a resummed leptonic angular distribution in inclusive neutral vector boson production, Phys. Rev. D 90 (2014) 014030 [arXiv:1309.1393] [INSPIRE].
A. Banfi, M. Dasgupta, S. Marzani and L. Tomlinson, Predictions for Drell-Yan ϕ ∗ and Q T observables at the LHC, Phys. Lett. B 715 (2012) 152 [arXiv:1205.4760] [INSPIRE].
S. Catani, D. de Florian, G. Ferrera and M. Grazzini, Vector boson production at hadron colliders: transverse-momentum resummation and leptonic decay, JHEP 12 (2015) 047 [arXiv:1507.06937] [INSPIRE].
S. Alioli, P. Nason, C. Oleari and E. Re, A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX, JHEP 06 (2010) 043 [arXiv:1002.2581] [INSPIRE].
T. Sjöstrand, S. Mrenna and P.Z. Skands, A brief introduction to PYTHIA 8.1, Comput. Phys. Commun. 178 (2008) 852 [arXiv:0710.3820] [INSPIRE].
T. Gleisberg et al., Event generation with SHERPA 1.1, JHEP 02 (2009) 007 [arXiv:0811.4622] [INSPIRE].
S. Frixione and B.R. Webber, Matching NLO QCD computations and parton shower simulations, JHEP 06 (2002) 029 [hep-ph/0204244] [INSPIRE].
M. Vesterinen and T.R. Wyatt, A novel technique for studying the Z boson transverse momentum distribution at hadron colliders, Nucl. Instrum. Meth. A 602 (2009) 432 [arXiv:0807.4956] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Antenna subtraction at NNLO, JHEP 09 (2005) 056 [hep-ph/0505111] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Gluon-gluon antenna functions from Higgs boson decay, Phys. Lett. B 612 (2005) 49 [hep-ph/0502110] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Quark-gluon antenna functions from neutralino decay, Phys. Lett. B 612 (2005) 36 [hep-ph/0501291] [INSPIRE].
A. Daleo, T. Gehrmann and D. Maître, Antenna subtraction with hadronic initial states, JHEP 04 (2007) 016 [hep-ph/0612257] [INSPIRE].
A. Daleo, A. Gehrmann-De Ridder, T. Gehrmann and G. Luisoni, Antenna subtraction at NNLO with hadronic initial states: initial-final configurations, JHEP 01 (2010) 118 [arXiv:0912.0374] [INSPIRE].
T. Gehrmann and P.F. Monni, Antenna subtraction at NNLO with hadronic initial states: real-virtual initial-initial configurations, JHEP 12 (2011) 049 [arXiv:1107.4037] [INSPIRE].
R. Boughezal, A. Gehrmann-De Ridder and M. Ritzmann, Antenna subtraction at NNLO with hadronic initial states: double real radiation for initial-initial configurations with two quark flavours, JHEP 02 (2011) 098 [arXiv:1011.6631] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann and M. Ritzmann, Antenna subtraction at NNLO with hadronic initial states: double real initial-initial configurations, JHEP 10 (2012) 047 [arXiv:1207.5779] [INSPIRE].
J. Currie, E.W.N. Glover and S. Wells, Infrared structure at NNLO using antenna subtraction, JHEP 04 (2013) 066 [arXiv:1301.4693] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, Infrared structure of e + e − → 3 jets at NNLO, JHEP 11 (2007) 058 [arXiv:0710.0346] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, EERAD3: event shapes and jet rates in electron-positron annihilation at order α 3 s , Comput. Phys. Commun. 185 (2014) 3331 [arXiv:1402.4140] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and J. Pires, Second order QCD corrections to jet production at hadron colliders: the all-gluon contribution, Phys. Rev. Lett. 110 (2013) 162003 [arXiv:1301.7310] [INSPIRE].
J. Currie, A. Gehrmann-De Ridder, E.W.N. Glover and J. Pires, NNLO QCD corrections to jet production at hadron colliders from gluon scattering, JHEP 01 (2014) 110 [arXiv:1310.3993] [INSPIRE].
X. Chen, T. Gehrmann, E.W.N. Glover and M. Jaquier, Precise QCD predictions for the production of Higgs + jet final states, Phys. Lett. B 740 (2015) 147 [arXiv:1408.5325] [INSPIRE].
X. Chen, J. Cruz-Martinez, T. Gehrmann, E.W.N. Glover and M. Jaquier, NNLO QCD corrections to Higgs boson production at large transverse momentum, JHEP 10 (2016) 066 [arXiv:1607.08817] [INSPIRE].
G. Abelof, A. Gehrmann-De Ridder and I. Majer, Top quark pair production at NNLO in the quark-antiquark channel, JHEP 12 (2015) 074 [arXiv:1506.04037] [INSPIRE].
J. Currie, T. Gehrmann and J. Niehues, Precise QCD predictions for the production of dijet final states in deep inelastic scattering, Phys. Rev. Lett. 117 (2016) 042001 [arXiv:1606.03991] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover, A. Huss and T.A. Morgan, Z+jet production at NNLO, PoS (LL2016) 056 [arXiv:1607.01749] [INSPIRE].
NNPDF collaboration, R.D. Ball et al., Parton distributions for the LHC Run II, JHEP 04 (2015) 040 [arXiv:1410.8849] [INSPIRE].
S. Catani, L. Cieri, D. de Florian, G. Ferrera and M. Grazzini, Vector boson production at hadron colliders: hard-collinear coefficients at the NNLO, Eur. Phys. J. C 72 (2012) 2195 [arXiv:1209.0158] [INSPIRE].
G. Bozzi, S. Catani, D. de Florian and M. Grazzini, Transverse-momentum resummation and the spectrum of the Higgs boson at the LHC, Nucl. Phys. B 737 (2006) 73 [hep-ph/0508068] [INSPIRE].
A. Banfi, M. Dasgupta and S. Marzani, QCD predictions for new variables to study dilepton transverse momenta at hadron colliders, Phys. Lett. B 701 (2011) 75 [arXiv:1102.3594] [INSPIRE].
A. Banfi, M. Dasgupta and R.M. Duran Delgado, The a T distribution of the Z boson at hadron colliders, JHEP 12 (2009) 022 [arXiv:0909.5327] [INSPIRE].
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Gehrmann-De Ridder, A., Gehrmann, T., Glover, E. et al. NNLO QCD corrections for Drell-Yan p ZT and \( {\phi}_{{}^{\eta}}^{\ast } \) observables at the LHC. J. High Energ. Phys. 2016, 94 (2016). https://doi.org/10.1007/JHEP11(2016)094
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DOI: https://doi.org/10.1007/JHEP11(2016)094