Abstract
We report on the first fully differential calculation for W ± Z production in hadron collisions up to next-to-next-to-leading order (NNLO) in QCD perturbation theory. Leptonic decays of the W and Z bosons are consistently taken into account, i.e. we include all resonant and non-resonant diagrams that contribute to the process pp → ℓ ′± ν ℓ ′ ℓ + ℓ − +X both in the same-flavour (ℓ ′ = ℓ) and the different-flavour (ℓ ′ ≠ ℓ) channel. Fiducial cross sections and distributions are presented in the presence of standard selection cuts applied in the experimental W ± Z analyses by ATLAS and CMS at centre-of-mass energies of 8 and 13 TeV. As previously shown for the inclusive cross section, NNLO corrections increase the NNLO result by about 10%, thereby leading to an improved agreement with experimental data. The importance of NNLO accurate predictions is also shown in the case of new-physics scenarios, where, especially in high-p T categories, their impact can reach \( \mathcal{O}\left(20\%\right) \). The availability of differential NNLO predictions will play a crucial role in the rich physics programme that is based on precision studies of W ± Z signatures at the LHC.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
D.E. Morrissey, T. Plehn and T.M.P. Tait, Physics searches at the LHC, Phys. Rept. 515 (2012) 1 [arXiv:0912.3259] [INSPIRE].
CDF collaboration, T. Aaltonen et al., Measurement of the W Z Cross section and Triple Gauge Couplings in \( p\overline{p} \) Collisions at \( \sqrt{s}=1.96 \) TeV, Phys. Rev. D 86 (2012) 031104 [arXiv:1202.6629] [INSPIRE].
D0 collaboration, V.M. Abazov et al., A measurement of the W Z and ZZ production cross sections using leptonic final states in 8.6 fb −1 of pp collisions, Phys. Rev. D 85 (2012) 112005 [arXiv:1201.5652] [INSPIRE].
ATLAS collaboration, Measurement of W Z production in proton-proton collisions at \( \sqrt{s}=7 \) TeV with the ATLAS detector, Eur. Phys. J. C 72 (2012) 2173 [arXiv:1208.1390] [INSPIRE].
CMS collaboration, Measurement of the WZ production cross section in pp collisions at \( \sqrt{s}=7 \) and 8TeV and search for anomalous triple gauge couplings at \( \sqrt{s}=8 \) TeV, Eur. Phys. J. C 77 (2017) 236 [arXiv:1609.05721] [INSPIRE].
ATLAS collaboration, Measurements of W ± Z production cross sections in pp collisions at \( \sqrt{s}=8 \) TeV with the ATLAS detector and limits on anomalous gauge boson self-couplings, Phys. Rev. D 93 (2016) 092004 [arXiv:1603.02151] [INSPIRE].
ATLAS collaboration, Measurement of the W ± Z boson pair-production cross section in pp collisions at \( \sqrt{s}=13 \) TeV with the ATLAS Detector, Phys. Lett. B 762 (2016) 1 [arXiv:1606.04017] [INSPIRE].
CMS collaboration, Measurement of the WZ production cross section in pp collisions at \( \sqrt{s}=13 \) TeV, Phys. Lett. B 766 (2017) 268 [arXiv:1607.06943] [INSPIRE].
J. Ohnemus, An Order α − s calculation of hadronic W ± Z production, Phys. Rev. D 44 (1991) 3477.
J. Ohnemus, Hadronic ZZ, W − W + and W ± Z production with QCD corrections and leptonic decays, Phys. Rev. D 50 (1994) 1931 [hep-ph/9403331] [INSPIRE].
J.M. Campbell and R.K. Ellis, An Update on vector boson pair production at hadron colliders, Phys. Rev. D 60 (1999) 113006 [hep-ph/9905386] [INSPIRE].
L.J. Dixon, Z. Kunszt and A. Signer, Vector boson pair production in hadronic collisions at order α s : Lepton correlations and anomalous couplings, Phys. Rev. D 60 (1999) 114037 [hep-ph/9907305] [INSPIRE].
J.M. Campbell, R.K. Ellis and C. Williams, Vector boson pair production at the LHC, JHEP 07 (2011) 018 [arXiv:1105.0020] [INSPIRE].
L.J. Dixon, Z. Kunszt and A. Signer, Helicity amplitudes for O(α s ) production of W + W − , W ± Z, ZZ, W ± γ, or Zγ pairs at hadron colliders, Nucl. Phys. B 531 (1998) 3 [hep-ph/9803250] [INSPIRE].
F. Campanario, C. Englert, S. Kallweit, M. Spannowsky and D. Zeppenfeld, NLO QCD corrections to WZ+jet production with leptonic decays, JHEP 07 (2010) 076 [arXiv:1006.0390] [INSPIRE].
A. Bierweiler, T. Kasprzik and J.H. Kühn, Vector-boson pair production at the LHC to \( \mathcal{O}\left({\alpha}^3\right) \) accuracy, JHEP 12 (2013) 071 [arXiv:1305.5402] [INSPIRE].
J. Baglio, L.D. Ninh and M.M. Weber, Massive gauge boson pair production at the LHC: a next-to-leading order story, Phys. Rev. D 88 (2013) 113005 [arXiv:1307.4331] [INSPIRE].
M. Grazzini, S. Kallweit, D. Rathlev and M. Wiesemann, W ± Z production at hadron colliders in NNLO QCD, Phys. Lett. B 761 (2016) 179 [arXiv:1604.08576] [INSPIRE].
T. Gehrmann, A. von Manteuffel and L. Tancredi, The two-loop helicity amplitudes for \( q{\overline{q}}^{\prime}\to\ {V}_1{V}_2\to 4 \) leptons, JHEP 09 (2015) 128 [arXiv:1503.04812] [INSPIRE].
F. Caola, J.M. Henn, K. Melnikov, A.V. Smirnov and V.A. Smirnov, Two-loop helicity amplitudes for the production of two off-shell electroweak bosons in quark-antiquark collisions, JHEP 11 (2014) 041 [arXiv:1408.6409] [INSPIRE].
A. Denner, S. Dittmaier, M. Roth and L.H. Wieders, Electroweak corrections to charged-current e + e − → 4 fermion processes: Technical details and further results, Nucl. Phys. B 724 (2005) 247 [Erratum ibid. B 854 (2012) 504] [hep-ph/0505042] [INSPIRE].
S. Catani and M. Grazzini, An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC, Phys. Rev. Lett. 98 (2007) 222002 [hep-ph/0703012] [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].
S. Catani and M.H. Seymour, The Dipole formalism for the calculation of QCD jet cross-sections at next-to-leading order, Phys. Lett. B 378 (1996) 287 [hep-ph/9602277] [INSPIRE].
S. Catani and M.H. Seymour, A General algorithm for calculating jet cross-sections in NLO QCD, Nucl. Phys. B 485 (1997) 291 [Erratum ibid. B 510 (1998) 503] [hep-ph/9605323] [INSPIRE].
F. Cascioli, P. Maierhöfer and S. Pozzorini, Scattering Amplitudes with Open Loops, Phys. Rev. Lett. 108 (2012) 111601 [arXiv:1111.5206] [INSPIRE].
A. Denner, S. Dittmaier and L. Hofer, COLLIER — A fortran-library for one-loop integrals, PoS (LL2014) 071 [arXiv:1407.0087] [INSPIRE].
A. Denner, S. Dittmaier and L. Hofer, Collier: a fortran-based Complex One-Loop LIbrary in Extended Regularizations, Comput. Phys. Commun. 212 (2017) 220 [arXiv:1604.06792] [INSPIRE].
M. Grazzini, S. Kallweit, D. Rathlev and M. Wiesemann, Transverse-momentum resummation for vector-boson pair production at NNLL+NNLO, JHEP 08 (2015) 154 [arXiv:1507.02565] [INSPIRE].
M. Wiesemann, Transverse-momentum resummation of colorless final states at the NNLL+NNLO, PoS (RADCOR2015) 026 [arXiv:1602.03401] [INSPIRE].
S. Catani, L. Cieri, D. de Florian, G. Ferrera and M. Grazzini, Universality of transverse-momentum resummation and hard factors at the NNLO, Nucl. Phys. B 881 (2014) 414 [arXiv:1311.1654] [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].
T. Gehrmann, T. Lübbert and L.L. Yang, Transverse parton distribution functions at next-to-next-to-leading order: the quark-to-quark case, Phys. Rev. Lett. 109 (2012) 242003 [arXiv:1209.0682] [INSPIRE].
T. Gehrmann, T. Lübbert and L.L. Yang, Calculation of the transverse parton distribution functions at next-to-next-to-leading order, JHEP 06 (2014) 155 [arXiv:1403.6451] [INSPIRE].
T. Matsuura, S.C. van der Marck and W. van Neerven, The Calculation of the Second Order Soft and Virtual Contributions to the Drell-Yan Cross-Section, Nucl. Phys. B 319 (1989) 570.
T. Gehrmann and L. Tancredi, Two-loop QCD helicity amplitudes for \( q\overline{q}\to {W}^{\pm}\gamma \) and \( q\overline{q}\to {Z}^0\gamma \), JHEP 02 (2012) 004 [arXiv:1112.1531] [INSPIRE].
M. Grazzini, S. Kallweit, D. Rathlev and A. Torre, Zγ production at hadron colliders in NNLO QCD, Phys. Lett. B 731 (2014) 204 [arXiv:1309.7000] [INSPIRE].
M. Grazzini, S. Kallweit and D. Rathlev, W γ and Zγ production at the LHC in NNLO QCD, JHEP 07 (2015) 085 [arXiv:1504.01330] [INSPIRE].
F. Cascioli et al., ZZ production at hadron colliders in NNLO QCD, Phys. Lett. B 735 (2014) 311 [arXiv:1405.2219] [INSPIRE].
M. Grazzini, S. Kallweit and D. Rathlev, ZZ production at the LHC: fiducial cross sections and distributions in NNLO QCD, Phys. Lett. B 750 (2015) 407 [arXiv:1507.06257] [INSPIRE].
T. Gehrmann et al., W + W − Production at Hadron Colliders in Next to Next to Leading Order QCD, Phys. Rev. Lett. 113 (2014) 212001 [arXiv:1408.5243] [INSPIRE].
M. Grazzini, S. Kallweit, S. Pozzorini, D. Rathlev and M. Wiesemann, W + W − production at the LHC: fiducial cross sections and distributions in NNLO QCD, JHEP 08 (2016) 140 [arXiv:1605.02716] [INSPIRE].
U. Baur, T. Han and J. Ohnemus, Amplitude zeros in W ± Z production, Phys. Rev. Lett. 72 (1994) 3941 [hep-ph/9403248] [INSPIRE].
CMS collaboration, Search for electroweak SUSY production in multilepton final states in pp collisions at \( \sqrt{s}=13 \) TeV with 12.9/fb, CMS-PAS-SUS-16-024 (2016).
F. Cascioli, J. Lindert, P. Maierhöfer and S. Pozzorini, The OpenLoops one-loop generator, is publicly available at http://openloops.hepforge.org.
A. Denner, S. Dittmaier and L. Hofer, Collier — A Complex One-Loop LIbrary with Extended Regularizations, is publicly available at http://collier.hepforge.org.
A. Denner and S. Dittmaier, Reduction of one loop tensor five point integrals, Nucl. Phys. B 658 (2003) 175 [hep-ph/0212259] [INSPIRE].
A. Denner and S. Dittmaier, Reduction schemes for one-loop tensor integrals, Nucl. Phys. B 734 (2006) 62 [hep-ph/0509141] [INSPIRE].
A. Denner and S. Dittmaier, Scalar one-loop 4-point integrals, Nucl. Phys. B 844 (2011) 199 [arXiv:1005.2076] [INSPIRE].
G. Ossola, C.G. Papadopoulos and R. Pittau, CutTools: A Program implementing the OPP reduction method to compute one-loop amplitudes, JHEP 03 (2008) 042 [arXiv:0711.3596] [INSPIRE].
A. van Hameren, OneLOop: For the evaluation of one-loop scalar functions, Comput. Phys. Commun. 182 (2011) 2427 [arXiv:1007.4716] [INSPIRE].
T. Gehrmann, A. von Manteuffel and L. Tancredi, The VVamp project, is publicly available at http://vvamp.hepforge.org.
J. Vollinga and S. Weinzierl, Numerical evaluation of multiple polylogarithms, Comput. Phys. Commun. 167 (2005) 177 [hep-ph/0410259] [INSPIRE].
C.W. Bauer, A. Frink and R. Kreckel, Introduction to the GiNaC framework for symbolic computation within the C++ programming language, J. Symb. Comput. 33 (2000) 1.
S. Catani, S. Dittmaier, M.H. Seymour and Z. Trócsányi, The Dipole formalism for next-to-leading order QCD calculations with massive partons, Nucl. Phys. B 627 (2002) 189 [hep-ph/0201036] [INSPIRE].
S. Kallweit, J.M. Lindert, P. Maierhöfer, S. Pozzorini and M. Schönherr, NLO electroweak automation and precise predictions for W+multijet production at the LHC, JHEP 04 (2015) 012 [arXiv:1412.5157] [INSPIRE].
S. Kallweit, J.M. Lindert, P. Maierhöfer, S. Pozzorini and M. Schönherr, NLO QCD+EW predictions for V + jets including off-shell vector-boson decays and multijet merging, JHEP 04 (2016) 021 [arXiv:1511.08692] [INSPIRE].
D. de Florian and M. Grazzini, The Structure of large logarithmic corrections at small transverse momentum in hadronic collisions, Nucl. Phys. B 616 (2001) 247 [hep-ph/0108273] [INSPIRE].
S. Catani and M. Grazzini, Higgs Boson Production at Hadron Colliders: Hard-Collinear Coefficients at the NNLO, Eur. Phys. J. C 72 (2012) 2013 [Erratum ibid. C 72 (2012) 2132] [arXiv:1106.4652] [INSPIRE].
Particle Data Group collaboration, K.A. Olive et al., Review of Particle Physics, Chin. Phys. C 38 (2014) 090001
NNPDF collaboration, R.D. Ball et al., Parton distributions for the LHC Run II, JHEP 04 (2015) 040 [arXiv:1410.8849] [INSPIRE].
M. Cacciari, G.P. Salam and G. Soyez, The Anti-k(t) jet clustering algorithm, JHEP 04 (2008) 063 [arXiv:0802.1189] [INSPIRE].
F. Campanario, M. Kerner, L.D. Ninh and D. Zeppenfeld, WZ Production in Association with Two Jets at Next-to-Leading Order in QCD, Phys. Rev. Lett. 111 (2013) 052003 [arXiv:1305.1623] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1703.09065
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Grazzini, M., Kallweit, S., Rathlev, D. et al. W ± Z production at the LHC: fiducial cross sections and distributions in NNLO QCD. J. High Energ. Phys. 2017, 139 (2017). https://doi.org/10.1007/JHEP05(2017)139
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2017)139