Abstract
We study the production of the four-lepton final state ℓ+ℓ−ℓ+ℓ−, predominantly produced by a pair of electroweak Z bosons, ZZ. Using the LoopSim method, we merge NLO QCD results for ZZ and ZZ+jet and obtain approximate NNLO predictions for ZZ production. The exact gluon-fusion loop-squared contribution to the ZZ process is also included. On top of that, we add to our merged sample the gluon-fusion ZZ+jet contributions from the gluon-gluon channel, which is formally of N3LO and provides approximate results at NLO for the gluon-fusion mechanism. The predictions are obtained with the VBFNLO package and include the leptonic decays of the Z bosons with all off-shell and spin-correlation effects, as well as virtual photon contributions. We compare our predictions with existing results for the total inclusive cross section at NNLO and find a very good agreement. Then, we present results for differential distributions for two experimental setups, one used in searches for anomalous triple gauge boson couplings, the other in Higgs analyses in the four charged-lepton final state channel. We find that the approximate NNLO corrections are large, reaching up to 20% at high transverse momentum of the Z boson or the leading lepton, and are not covered by the NLO scale uncertainties. Distributions of the four-lepton invariant mass are, however, stable with respect to QCD corrections at this order.
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References
N. Kauer and G. Passarino, Inadequacy of zero-width approximation for a light Higgs boson signal, JHEP 08 (2012) 116 [arXiv:1206.4803] [INSPIRE].
F. Caola and K. Melnikov, Constraining the Higgs boson width with ZZ production at the LHC, Phys. Rev. D 88 (2013) 054024 [arXiv:1307.4935] [INSPIRE].
J.M. Campbell, R.K. Ellis and C. Williams, Bounding the Higgs width at the LHC using full analytic results for gg → e − e + μ − μ +, JHEP 04 (2014) 060 [arXiv:1311.3589] [INSPIRE].
J.S. Gainer, J. Lykken, K.T. Matchev, S. Mrenna and M. Park, Beyond Geolocating: Constraining Higher Dimensional Operators in H → 4ℓ with Off-Shell Production and More, Phys. Rev. D 91 (2015) 035011 [arXiv:1403.4951] [INSPIRE].
C. Englert and M. Spannowsky, Limitations and Opportunities of Off-Shell Coupling Measurements, Phys. Rev. D 90 (2014) 053003 [arXiv:1405.0285] [INSPIRE].
G. Cacciapaglia, A. Deandrea, G. Drieu La Rochelle and J.-B. Flament, Higgs couplings: disentangling New Physics with off-shell measurements, Phys. Rev. Lett. 113 (2014) 201802 [arXiv:1406.1757] [INSPIRE].
ATLAS collaboration, Measurement of ZZ production in pp collisions at \( \sqrt{s}=7 \) TeV and limits on anomalous ZZZ and ZZγ couplings with the ATLAS detector, JHEP 03 (2013) 128 [arXiv:1211.6096] [INSPIRE].
CMS collaboration, Measurement of the pp → ZZ production cross section and constraints on anomalous triple gauge couplings in four-lepton final states at \( \sqrt{s}=8 \) TeV, Phys. Lett. B 740 (2015)250 [arXiv:1406.0113] [INSPIRE].
R.W. Brown and K.O. Mikaelian, W + W − and Z0 Z0 Pair Production in e + e − , pp, \( p\overline{p} \) Colliding Beams, Phys. Rev. D 19 (1979) 922 [INSPIRE].
B. Mele, P. Nason and G. Ridolfi, QCD radiative corrections to Z boson pair production in hadronic collisions, Nucl. Phys. B 357 (1991) 409 [INSPIRE].
J. Ohnemus and J.F. Owens, An Order α − s calculation of hadronic ZZ production, Phys. Rev. D 43 (1991) 3626 [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].
M. Rubin, G.P. Salam and S. Sapeta, Giant QCD K-factors beyond NLO, JHEP 09 (2010) 084 [arXiv:1006.2144] [INSPIRE].
F. Campanario and S. Sapeta, WZ production beyond NLO for high-pT observables, Phys. Lett. B 718 (2012) 100 [arXiv:1209.4595] [INSPIRE].
F. Campanario, M. Rauch and S. Sapeta, W + W − production at high transverse momenta beyond NLO, Nucl. Phys. B 879 (2014) 65 [arXiv:1309.7293] [INSPIRE].
D.A. Dicus, C. Kao and W.W. Repko, Gluon Production of Gauge Bosons, Phys. Rev. D 36 (1987) 1570 [INSPIRE].
E.W.N. Glover and J.J. van der Bij, Vector boson pair production via gluon fusion, Phys. Lett. B 219 (1989) 488 [INSPIRE].
T. Matsuura and J.J. van der Bij, Characteristics of leptonic signals for Z boson pairs at hadron colliders, Z. Phys. C 51 (1991) 259 [INSPIRE].
C. Zecher, T. Matsuura and J.J. van der Bij, Leptonic signals from off-shell Z boson pairs at hadron colliders, Z. Phys. C 64 (1994) 219 [hep-ph/9404295] [INSPIRE].
N.E. Adam et al., Higgs Working Group Summary Report, arXiv:0803.1154 [INSPIRE].
T. Binoth, N. Kauer and P. Mertsch, Gluon-induced QCD corrections to \( pp\to ZZ\to l\overline{l}l^{\prime}\overline{l}^{\prime } \), arXiv:0807.0024 [INSPIRE].
F. Campanario, Q. Li, M. Rauch and M. Spira, ZZ+jet production via gluon fusion at the LHC, JHEP 06 (2013) 069 [arXiv:1211.5429] [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 gluon fusion, JHEP 06 (2015) 129 [arXiv:1503.08759] [INSPIRE].
A. von Manteuffel and L. Tancredi, The two-loop helicity amplitudes for gg → V_1V_2 → 4 leptons, JHEP 06 (2015) 197 [arXiv:1503.08835] [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, Full NLO massive gauge boson pair production at the LHC, arXiv:1310.3972 [INSPIRE].
T. Binoth, T. Gleisberg, S. Karg, N. Kauer and G. Sanguinetti, NLO QCD corrections to ZZ+jet production at hadron colliders, Phys. Lett. B 683 (2010) 154 [arXiv:0911.3181] [INSPIRE].
F. Campanario, M. Kerner, L.D. Ninh and D. Zeppenfeld, Next-to-leading order QCD corrections to ZZ production in association with two jets, JHEP 07 (2014) 148 [arXiv:1405.3972] [INSPIRE].
T. Gehrmann, A. von Manteuffel, L. Tancredi and E. Weihs, The two-loop master integrals for \( q\overline{q}\to VV \), JHEP 06 (2014) 032 [arXiv:1404.4853] [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].
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, arXiv:1503.04812 [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].
F. Cascioli et al., ZZ production at hadron colliders in NNLO QCD, Phys. Lett. B 735 (2014) 311 [arXiv:1405.2219] [INSPIRE].
M. Rubin, G.P. Salam and S. Sapeta, https://loopsim.hepforge.org.
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].
K. Arnold et al., VBFNLO: A Parton Level Monte Carlo for Processes with Electroweak Bosons – Manual for Version 2.5.0, arXiv:1107.4038 [INSPIRE].
J. Baglio et al., Release Note - VBFNLO 2.7.0, arXiv:1404.3940 [INSPIRE].
D. Maître and S. Sapeta, Simulated NNLO for high-p_T observables in vector boson + jets production at the LHC, Eur. Phys. J. C 73 (2013) 2663 [arXiv:1307.2252] [INSPIRE].
CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].
L.D. Landau, On the angular momentum of a two-photon system, Dokl. Akad. Nauk Ser. Fiz. 60 (1948) 207.
C.-N. Yang, Selection Rules for the Dematerialization of a Particle Into Two Photons, Phys. Rev. 77 (1950) 242 [INSPIRE].
F. Campanario, C. Englert, M. Rauch and D. Zeppenfeld, Precise predictions for Wγγ +jet production at hadron colliders, Phys. Lett. B 704 (2011) 515 [arXiv:1106.4009] [INSPIRE].
K. Hagiwara and D. Zeppenfeld, Amplitudes for Multiparton Processes Involving a Current at e + e − , e ± p, and Hadron Colliders, Nucl. Phys. B 313 (1989) 560 [INSPIRE].
F. Campanario, Towards pp → VVjj at NLO QCD: Bosonic contributions to triple vector boson production plus jet, JHEP 10 (2011) 070 [arXiv:1105.0920] [INSPIRE].
G. ’t Hooft and M.J.G. Veltman, Regularization and Renormalization of Gauge Fields, Nucl. Phys. B 44 (1972) 189 [INSPIRE].
M.S. Chanowitz, M. Furman and I. Hinchliffe, The Axial Current in Dimensional Regularization, Nucl. Phys. B 159 (1979) 225 [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].
G. ’t Hooft and M.J.G. Veltman, Scalar One Loop Integrals, Nucl. Phys. B 153 (1979) 365 [INSPIRE].
Z. Bern, L.J. Dixon and D.A. Kosower, Dimensionally regulated pentagon integrals, Nucl. Phys. B 412 (1994) 751 [hep-ph/9306240] [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].
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].
T. Hahn and M. Rauch, News from FormCalc and LoopTools, Nucl. Phys. Proc. Suppl. 157 (2006) 236 [hep-ph/0601248] [INSPIRE].
T. Binoth, J.P. Guillet, G. Heinrich, E. Pilon and C. Schubert, An algebraic/numerical formalism for one-loop multi-leg amplitudes, JHEP 10 (2005) 015 [hep-ph/0504267] [INSPIRE].
A. Denner and S. Dittmaier, Reduction schemes for one-loop tensor integrals, Nucl. Phys. B 734 (2006) 62 [hep-ph/0509141] [INSPIRE].
T. Hahn, Automatic loop calculations with FeynArts, FormCalc and LoopTools, Nucl. Phys. Proc. Suppl. 89 (2000) 231 [hep-ph/0005029] [INSPIRE].
T. Hahn, A Mathematica interface for FormCalc-generated code, Comput. Phys. Commun. 178 (2008) 217 [hep-ph/0611273] [INSPIRE].
M. Rauch, Quantum Effects in Higgs-Boson Production Processes at Hadron Colliders, arXiv:0804.2428 [INSPIRE].
C. Groß, T. Hahn, S. Heinemeyer, F. von der Pahlen, H. Rzehak and C. Schappacher, New Developments in FormCalc 8.4, PoS(LL2014)035 arXiv:1407.0235.
T. Gleisberg et al., Event generation with SHERPA 1.1, JHEP 02 (2009) 007 [arXiv:0811.4622] [INSPIRE].
J.M. Campbell and R.K. Ellis, MCFM for the Tevatron and the LHC, Nucl. Phys. Proc. Suppl. 205-206 (2010) 10 [arXiv:1007.3492] [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].
J. Alwall et al., A standard format for Les Houches event files, Comput. Phys. Commun. 176 (2007) 300 [hep-ph/0609017] [INSPIRE].
Y.L. Dokshitzer, G.D. Leder, S. Moretti and B.R. Webber, Better jet clustering algorithms, JHEP 08 (1997) 001 [hep-ph/9707323] [INSPIRE].
M. Wobisch and T. Wengler, Hadronization corrections to jet cross sections in deep-inelastic scattering, hep-ph/9907280 [INSPIRE].
M. Cacciari and G.P. Salam, Dispelling the N 3 myth for the k_t jet-finder, Phys. Lett. B 641 (2006) 57 [hep-ph/0512210] [INSPIRE].
M. Cacciari, G.P. Salam and G. Soyez, http://fastjet.fr/.
S. Catani, Y.L. Dokshitzer, M. Olsson, G. Turnock and B.R. Webber, New clustering algorithm for multijet cross-sections in e + e − annihilation, Phys. Lett. B 269 (1991) 432 [INSPIRE].
S.D. Ellis and D.E. Soper, Successive combination jet algorithm for hadron collisions, Phys. Rev. D 48 (1993) 3160 [hep-ph/9305266] [INSPIRE].
A.D. Martin, W.J. Stirling, R.S. Thorne and G. Watt, Parton distributions for the LHC, Eur. Phys. J. C 63 (2009) 189 [arXiv:0901.0002] [INSPIRE].
M. Cacciari, G.P. Salam and G. Soyez, The anti-k t jet clustering algorithm, JHEP 04 (2008) 063 [arXiv:0802.1189] [INSPIRE].
M. Cacciari, G.P. Salam and G. Soyez, FastJet User Manual, Eur. Phys. J. C 72 (2012) 1896 [arXiv:1111.6097] [INSPIRE].
M.R. Whalley, D. Bourilkov and R.C. Group, The Les Houches accord PDFs (LHAPDF) and LHAGLUE, hep-ph/0508110 [INSPIRE]
S. Frixione, P. Nason and G. Ridolfi, Strong corrections to W Z production at hadron colliders, Nucl. Phys. B 383 (1992) 3 [INSPIRE].
F. Campanario, R. Roth and D. Zeppenfeld, QCD radiation in W H and W Z production and anomalous coupling measurements, Phys. Rev. D 91 (2015) 054039 [arXiv:1410.4840] [INSPIRE].
CMS collaboration, Properties of the Higgs-like boson in the decay H to ZZ to 4l in pp collisions at \( \sqrt{s}=7 \) and 8 TeV, CMS-PAS-HIG-13-002.
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Campanario, F., Rauch, M. & Sapeta, S. ZZ production at high transverse momenta beyond NLO QCD. J. High Energ. Phys. 2015, 70 (2015). https://doi.org/10.1007/JHEP08(2015)070
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DOI: https://doi.org/10.1007/JHEP08(2015)070