Abstract
We present a study at next-to-leading-order (NLO) of the process pp → W±Z → ℓνlℓ′+ℓ′−, where ℓ, ℓ′ = e, μ, at the Large Hadron Collider. We include the full NLO QCD corrections and the NLO electroweak (EW) corrections in the double-pole approximation. We define eight fiducial polarization coefficients directly constructed from the polar-azimuthal angular distribution of the decay leptons. These coefficients depend strongly on the kinematical cuts on the transverse momentum or rapidity of the individual leptons. Similarly, fiducial polarization fractions are also defined and they can be directly related to the fiducial coefficients. We perform a detailed analysis of the NLO QCD+EW fiducial polarization observables including theoretical uncertainties stemming from the scale variation and parton distribution function uncertainties, using the fiducial phase space defined by the ATLAS and CMS experiments. We provide results in the helicity coordinate system and in the Collins-Soper coordinate system, at a center-of-mass energy of 13 TeV. The EW corrections are found to be important in two of the angular coefficients related to the Z boson, irrespective of the kinematical cuts or the coordinate system. Meanwhile, those EW corrections are very small for the W± bosons.
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References
ATLAS collaboration, Measurement of the W boson polarization in top quark decays with the ATLAS detector, JHEP 06 (2012) 088 [arXiv:1205.2484] [INSPIRE].
CMS collaboration, Measurement of the W boson helicity fractions in the decays of top quark pairs to lepton + jets final states produced in pp collisions at \( \sqrt{s} \) = 8TeV, Phys. Lett. B 762 (2016) 512 [arXiv:1605.09047] [INSPIRE].
CMS collaboration, Measurement of the Polarization of W Bosons with Large Transverse Momenta in W+Jets Events at the LHC, Phys. Rev. Lett. 107 (2011) 021802 [arXiv:1104.3829] [INSPIRE].
ATLAS collaboration, Measurement of the polarisation of W bosons produced with large transverse momentum in pp collisions at \( \sqrt{s} \) = 7 TeV with the ATLAS experiment, Eur. Phys. J. C 72 (2012) 2001 [arXiv:1203.2165] [INSPIRE].
CMS collaboration, Angular coefficients of Z bosons produced in pp collisions at \( \sqrt{s} \) = 8 TeV and decaying to μ + μ − as a function of transverse momentum and rapidity, Phys. Lett. B 750 (2015) 154 [arXiv:1504.03512] [INSPIRE].
ATLAS collaboration, Measurement of the angular coefficients in Z-boson events using electron and muon pairs from data taken at \( \sqrt{s} \) = 8 TeV with the ATLAS detector, JHEP 08 (2016) 159 [arXiv:1606.00689] [INSPIRE].
Z. Bern et al., Left-Handed W Bosons at the LHC, Phys. Rev. D 84 (2011) 034008 [arXiv:1103.5445] [INSPIRE].
W.J. Stirling and E. Vryonidou, Electroweak gauge boson polarisation at the LHC, JHEP 07 (2012) 124 [arXiv:1204.6427] [INSPIRE].
J.C. Collins and D.E. Soper, Angular Distribution of Dileptons in High-Energy Hadron Collisions, Phys. Rev. D 16 (1977) 2219 [INSPIRE].
C.S. Lam and W.-K. Tung, A Parton Model Relation Sans QCD Modifications in Lepton Pair Productions, Phys. Rev. D 21 (1980) 2712 [INSPIRE].
E. Mirkes, Angular decay distribution of leptons from W bosons at NLO in hadronic collisions, Nucl. Phys. B 387 (1992) 3 [INSPIRE].
J.A. Aguilar-Saavedra and J. Bernabéu, Breaking down the entire W boson spin observables from its decay, Phys. Rev. D 93 (2016) 011301 [arXiv:1508.04592] [INSPIRE].
E. Mirkes and J. Ohnemus, W and Z polarization effects in hadronic collisions, Phys. Rev. D 50 (1994) 5692 [hep-ph/9406381] [INSPIRE].
J.A. Aguilar-Saavedra, J. Bernabéu, V.A. Mitsou and A. Segarra, The Z boson spin observables as messengers of new physics, Eur. Phys. J. C 77 (2017) 234 [arXiv:1701.03115] [INSPIRE].
K. Hagiwara, K.-i. Hikasa and N. Kai, Parity Odd Asymmetries in W Jet Events at Hadron Colliders, Phys. Rev. Lett. 52 (1984) 1076 [INSPIRE].
K. Hagiwara, K.-i. Hikasa and H. Yokoya, Parity-Odd Asymmetries in W − Jet Events at the Tevatron, Phys. Rev. Lett. 97 (2006) 221802 [hep-ph/0604208] [INSPIRE].
A. Karlberg, E. Re and G. Zanderighi, NNLOPS accurate Drell-Yan production, JHEP 09 (2014) 134 [arXiv:1407.2940] [INSPIRE].
J. Ohnemus, An order α s calculation of hadronic W ± Z production, Phys. Rev. D 44 (1991) 3477 [INSPIRE].
S. Frixione, P. Nason and G. Ridolfi, Strong corrections to W Z production at hadron colliders, Nucl. Phys. B 383 (1992) 3 [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 [Erratum ibid. D 94 (2016) 099902] [arXiv:1307.4331] [INSPIRE].
A. Bierweiler, T. Kasprzik and J.H. Kühn, Vector-boson pair production at the LHC to \( \mathcal{O} \)(α 3) accuracy, JHEP 12 (2013) 071 [arXiv:1305.5402] [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].
B. Biedermann, A. Denner and L. Hofer, Next-to-leading-order electroweak corrections to the production of three charged leptons plus missing energy at the LHC, JHEP 10 (2017) 043 [arXiv:1708.06938] [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. Arnold et al., VBFNLO: A parton level Monte Carlo for processes with electroweak bosons, Comput. Phys. Commun. 180 (2009) 1661 [arXiv:0811.4559] [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].
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].
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].
C.L. Bilchak, R.W. Brown and J.D. Stroughair, W ± and Z 0 polarization in pair production: Dominant helicities, Phys. Rev. D 29 (1984) 375 [INSPIRE].
S.S.D. Willenbrock, Pair Production of W and Z Bosons and the Goldstone Boson Equivalence Theorem, Annals Phys. 186 (1988) 15 [INSPIRE].
ATLAS collaboration, Measurement of W ± Z production cross sections and gauge boson polarisation in pp collisions at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, ATLAS-CONF-2018-034 (2018).
ATLAS collaboration, Measurement of W ± Z production cross sections and gauge boson polarisation in pp collisions at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, arXiv:1902.05759 [INSPIRE].
J. Baglio et al., VBFNLO: A Parton Level Monte Carlo for Processes with Electroweak Bosons — Manual for Version 2.7.0, arXiv:1107.4038 [INSPIRE].
J. Baglio et al., Release Note — VBFNLO 2.7.0, arXiv:1404.3940 [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, 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].
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].
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].
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].
A.V. Manohar, P. Nason, G.P. Salam and G. Zanderighi, The Photon Content of the Proton, JHEP 12 (2017) 046 [arXiv:1708.01256] [INSPIRE].
J. Butterworth et al., PDF4LHC recommendations for LHC Run II, J. Phys. G 43 (2016) 023001 [arXiv:1510.03865] [INSPIRE].
S. Dulat et al., New parton distribution functions from a global analysis of quantum chromodynamics, Phys. Rev. D 93 (2016) 033006 [arXiv:1506.07443] [INSPIRE].
L.A. Harland-Lang, A.D. Martin, P. Motylinski and R.S. Thorne, Parton distributions in the LHC era: MMHT 2014 PDFs, Eur. Phys. J. C 75 (2015) 204 [arXiv:1412.3989] [INSPIRE].
NNPDF collaboration, Parton distributions for the LHC Run II, JHEP 04 (2015) 040 [arXiv:1410.8849] [INSPIRE].
J. Gao and P. Nadolsky, A meta-analysis of parton distribution functions, JHEP 07 (2014) 035 [arXiv:1401.0013] [INSPIRE].
S. Carrazza, S. Forte, Z. Kassabov, J.I. Latorre and J. Rojo, An Unbiased Hessian Representation for Monte Carlo PDFs, Eur. Phys. J. C 75 (2015) 369 [arXiv:1505.06736] [INSPIRE].
G. Watt and R.S. Thorne, Study of Monte Carlo approach to experimental uncertainty propagation with MSTW 2008 PDFs, JHEP 08 (2012) 052 [arXiv:1205.4024] [INSPIRE].
D. de Florian, G.F.R. Sborlini and G. Rodrigo, QED corrections to the Altarelli-Parisi splitting functions, Eur. Phys. J. C 76 (2016) 282 [arXiv:1512.00612] [INSPIRE].
A. Buckley et al., LHAPDF6: parton density access in the LHC precision era, Eur. Phys. J. C 75 (2015) 132 [arXiv:1412.7420] [INSPIRE].
A. Denner, S. Dittmaier, M. Roth and D. Wackeroth, Electroweak radiative corrections to e + e − → WW → 4 fermions in double pole approximation: The RACOONWW approach, Nucl. Phys. B 587 (2000) 67 [hep-ph/0006307] [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].
T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260] [INSPIRE].
W. Beenakker, A.P. Chapovsky and F.A. Berends, Nonfactorizable corrections to W pair production, Phys. Lett. B 411 (1997) 203 [hep-ph/9706339] [INSPIRE].
A. Denner, S. Dittmaier and M. Roth, Nonfactorizable photonic corrections to e + e − → WW → 4 fermions, Nucl. Phys. B 519 (1998) 39 [hep-ph/9710521] [INSPIRE].
A. Denner, S. Dittmaier and M. Roth, Further numerical results on nonfactorizable corrections to e + e − → 4 fermions, Phys. Lett. B 429 (1998) 145 [hep-ph/9803306] [INSPIRE].
S. Dittmaier, A general approach to photon radiation off fermions, Nucl. Phys. B 565 (2000) 69 [hep-ph/9904440] [INSPIRE].
L. Basso, S. Dittmaier, A. Huss and L. Oggero, Techniques for the treatment of IR divergences in decay processes at NLO and application to the top-quark decay, Eur. Phys. J. C 76 (2016) 56 [arXiv:1507.04676] [INSPIRE].
A. Ballestrero, E. Maina and G. Pelliccioli, W boson polarization in vector boson scattering at the LHC, JHEP 03 (2018) 170 [arXiv:1710.09339] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, Chin. Phys. C 38 (2014) 090001 [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].
A. Denner, S. Dittmaier, M. Roth and L.H. Wieders, Complete electroweak \( \mathcal{O} \)(α) corrections to charged-current e + e − → 4 fermion processes, Phys. Lett. B 612 (2005) 223 [Erratum ibid. B 704 (2011) 667] [hep-ph/0502063] [INSPIRE].
LHC Higgs Cross Section Working Group collaboration, Handbook of LHC Higgs Cross Sections: 1. Inclusive Observables, arXiv:1101.0593 [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].
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Baglio, J., Ninh, L.D. Fiducial polarization observables in hadronic WZ production: a next-to-leading order QCD+EW study. J. High Energ. Phys. 2019, 65 (2019). https://doi.org/10.1007/JHEP04(2019)065
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DOI: https://doi.org/10.1007/JHEP04(2019)065