Abstract
The production of a neutral and a charged vector boson with subsequent decays into three charged leptons and a neutrino is a very important process for precision tests of the Standard Model of elementary particles and in searches for anomalous triple-gauge-boson couplings. In this article, the first computation of next-to-leading-order electroweak corrections to the production of the four-lepton final states μ + μ −e+ ν e, \( {\mu}^{+}{\mu}^{-}{\mathrm{e}}^{-}{\overline{\nu}}_{\mathrm{e}} \), μ + μ − μ + ν μ , and \( {\mu}^{+}{\mu}^{-}{\mu}^{-}{\overline{\nu}}_{\mu } \) at the Large Hadron Collider is presented. We use the complete matrix elements at leading and next-to-leading order, including all off-shell effects of intermediate massive vector bosons and virtual photons. The relative electroweak corrections to the fiducial cross sections from quark-induced partonic processes vary between −3% and −6%, depending significantly on the event selection. At the level of differential distributions, we observe large negative corrections of up to −30% in the high-energy tails of distributions originating from electroweak Sudakov logarithms. Photon-induced contributions at next-to-leading order raise the leading-order fiducial cross section by +2%. Interference effects in final states with equal-flavour leptons are at the permille level for the fiducial cross section, but can lead to sizeable effects in off-shell sensitive phase-space regions.
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
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].
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].
CMS collaboration, Measurement of the WZ production cross section in pp collisions at \( \sqrt{s}=7 \) and 8 TeV 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, Measurement of W ± Z boson pair-production in pp collisions at \( \sqrt{s}=13 \) TeV with the ATLAS Detector and confidence intervals for anomalous triple gauge boson couplings, ATLAS-CONF-2016-043 (2016).
J. Ohnemus, An order α S calculation of hadronic W ± Z production, Phys. Rev. D 44 (1991) 3477 [INSPIRE].
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].
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 and R.K. Ellis, An update on vector boson pair production at hadron colliders, Phys. Rev. D 60 (1999) 113006 [hep-ph/9905386] [INSPIRE].
K. Hamilton, A positive-weight next-to-leading order simulation of weak boson pair production, JHEP 01 (2011) 009 [arXiv:1009.5391] [INSPIRE].
T. Melia, P. Nason, R. Röntsch and G. Zanderighi, W + W − , WZ and ZZ production in the POWHEG BOX, JHEP 11 (2011) 078 [arXiv:1107.5051] [INSPIRE].
P. Nason and G. Zanderighi, W + W − , W Z and ZZ production in the POWHEG-BOX-V2, Eur. Phys. J. C 74 (2014) 2702 [arXiv:1311.1365] [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].
M. Grazzini, S. Kallweit, D. Rathlev and M. Wiesemann, W ± Z production at the LHC: fiducial cross sections and distributions in NNLO QCD, JHEP 05 (2017) 139 [arXiv:1703.09065] [INSPIRE].
W. Beenakker, A. Denner, S. Dittmaier, R. Mertig and T. Sack, High-energy approximation for on-shell W pair production, Nucl. Phys. B 410 (1993) 245 [INSPIRE].
M. Beccaria, G. Montagna, F. Piccinini, F.M. Renard and C. Verzegnassi, Rising bosonic electroweak virtual effects at high-energy e + e − colliders, Phys. Rev. D 58 (1998) 093014 [hep-ph/9805250] [INSPIRE].
P. Ciafaloni and D. Comelli, Sudakov enhancement of electroweak corrections, Phys. Lett. B 446 (1999) 278 [hep-ph/9809321] [INSPIRE].
J.H. Kühn and A.A. Penin, Sudakov logarithms in electroweak processes, hep-ph/9906545 [INSPIRE].
V.S. Fadin, L.N. Lipatov, A.D. Martin and M. Melles, Resummation of double logarithms in electroweak high-energy processes, Phys. Rev. D 61 (2000) 094002 [hep-ph/9910338] [INSPIRE].
A. Denner and S. Pozzorini, One loop leading logarithms in electroweak radiative corrections. 1. Results, Eur. Phys. J. C 18 (2001) 461 [hep-ph/0010201] [INSPIRE].
E. Accomando, A. Denner and A. Kaiser, Logarithmic electroweak corrections to gauge-boson pair production at the LHC, Nucl. Phys. B 706 (2005) 325 [hep-ph/0409247] [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].
B. Biedermann, A. Denner, S. Dittmaier, L. Hofer and B. Jäger, Electroweak corrections to pp → μ + μ − e + e − + X at the LHC: a Higgs background study, Phys. Rev. Lett. 116 (2016) 161803 [arXiv:1601.07787] [INSPIRE].
B. Biedermann, A. Denner, S. Dittmaier, L. Hofer and B. Jäger, Next-to-leading-order electroweak corrections to the production of four charged leptons at the LHC, JHEP 01 (2017) 033 [arXiv:1611.05338] [INSPIRE].
B. Biedermann et al., Next-to-leading-order electroweak corrections to pp → W + W − → 4 leptons at the LHC, JHEP 06 (2016) 065 [arXiv:1605.03419] [INSPIRE].
S. Kallweit, J.M. Lindert, S. Pozzorini and M. Schönherr, NLO QCD+EW predictions for 2ℓ2ν diboson signatures at the LHC, arXiv:1705.00598 [INSPIRE].
A. Denner, S. Dittmaier, M. Roth and D. Wackeroth, Predictions for all processes e + e − → 4 fermions + γ, Nucl. Phys. B 560 (1999) 33 [hep-ph/9904472] [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].
A. Denner and S. Dittmaier, The complex-mass scheme for perturbative calculations with unstable particles, Nucl. Phys. Proc. Suppl. 160 (2006) 22 [hep-ph/0605312] [INSPIRE].
S. Dittmaier, A general approach to photon radiation off fermions, Nucl. Phys. B 565 (2000) 69 [hep-ph/9904440] [INSPIRE].
S. Dittmaier, A. Kabelschacht and T. Kasprzik, Polarized QED splittings of massive fermions and dipole subtraction for non-collinear-safe observables, Nucl. Phys. B 800 (2008) 146 [arXiv:0802.1405] [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].
B. Biedermann, A. Denner and M. Pellen, Large electroweak corrections to vector-boson scattering at the Large Hadron Collider, Phys. Rev. Lett. 118 (2017) 261801 [arXiv:1611.02951] [INSPIRE].
B. Biedermann, A. Denner and M. Pellen, Complete NLO corrections to W+W+ scattering and its irreducible background at the LHC, arXiv:1708.00268 [INSPIRE].
S. Actis, A. Denner, L. Hofer, J.-N. Lang, A. Scharf and S. Uccirati, RECOLA: REcursive Computation of One-Loop Amplitudes, Comput. Phys. Commun. 214 (2017) 140 [arXiv:1605.01090] [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].
G. ’t Hooft and M.J.G. Veltman, Scalar One Loop Integrals, Nucl. Phys. B 153 (1979) 365 [INSPIRE].
W. Beenakker and A. Denner, Infrared Divergent Scalar Box Integrals With Applications in the Electroweak Standard Model, Nucl. Phys. B 338 (1990) 349 [INSPIRE].
S. Dittmaier, Separation of soft and collinear singularities from one loop N point integrals, Nucl. Phys. B 675 (2003) 447 [hep-ph/0308246] [INSPIRE].
A. Denner and S. Dittmaier, Scalar one-loop 4-point integrals, Nucl. Phys. B 844 (2011) 199 [arXiv:1005.2076] [INSPIRE].
G. Passarino and M.J.G. Veltman, One Loop Corrections for e + e − Annihilation Into μ + μ − in the Weinberg Model, Nucl. Phys. B 160 (1979) 151 [INSPIRE].
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].
E. Accomando, A. Denner and C. Meier, Electroweak corrections to W γ and Zγ production at the LHC, Eur. Phys. J. C 47 (2006) 125 [hep-ph/0509234] [INSPIRE].
J. Küblbeck, M. Böhm and A. Denner, Feyn Arts: Computer Algebraic Generation of Feynman Graphs and Amplitudes, Comput. Phys. Commun. 60 (1990) 165 [INSPIRE].
T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260] [INSPIRE].
T. Hahn and M. Pérez-Victoria, Automatized one loop calculations in four-dimensions and D-dimensions, Comput. Phys. Commun. 118 (1999) 153 [hep-ph/9807565] [INSPIRE].
F.A. Berends, R. Pittau and R. Kleiss, All electroweak four fermion processes in electron-positron collisions, Nucl. Phys. B 424 (1994) 308 [hep-ph/9404313] [INSPIRE].
S. Dittmaier and M. Roth, LUSIFER: A LUcid approach to six FERmion production, Nucl. Phys. B 642 (2002) 307 [hep-ph/0206070] [INSPIRE].
Particle Data Group collaboration, C. Patrignani et al., Review of Particle Physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].
D. Yu. Bardin, A. Leike, T. Riemann and M. Sachwitz, Energy-dependent width effects in e + e − annihilation near the Z boson pole, Phys. Lett. B 206 (1988) 539 [INSPIRE].
A. Manohar, P. Nason, G.P. Salam and G. Zanderighi, How bright is the proton? A precise determination of the photon parton distribution function, Phys. Rev. Lett. 117 (2016) 242002 [arXiv:1607.04266] [INSPIRE].
J. Butterworth et al., PDF4LHC recommendations for LHC Run II, J. Phys. G 43 (2016) 023001 [arXiv:1510.03865] [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: 1708.06938
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
Biedermann, B., Denner, A. & Hofer, L. Next-to-leading-order electroweak corrections to the production of three charged leptons plus missing energy at the LHC. J. High Energ. Phys. 2017, 43 (2017). https://doi.org/10.1007/JHEP10(2017)043
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2017)043