Abstract
We compute the QCD corrections at next-to-leading order for the process gg → ZH, including both the virtual two-loop terms and real-emission contributions. The two-loop box diagrams in the virtual corrections are approximated analytically over the complete phase space, combining the results of an expansion in the limit of small transverse momentum and an expansion in the regime of high energy. We obtain both inclusive and differential results for the cross section. We find that the NLO QCD corrections are of the same size as the LO contribution up to ZH invariant masses close to 1 TeV, but they increase significantly when higher energies are considered, due to a class of real-emission diagrams in which the Z boson is radiated from an open quark line. Finally, we estimate the uncertainty due to the renormalization scheme used for the top-quark mass both on the total and differential cross section.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [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].
G. Heinrich, Collider physics at the precision frontier, Phys. Rept. 922 (2021) 1 [arXiv:2009.00516] [INSPIRE].
ATLAS collaboration, Observation of H → \( b\overline{b} \) decays and VH production with the ATLAS detector, Phys. Lett. B 786 (2018) 59 [arXiv:1808.08238] [INSPIRE].
CMS collaboration, Observation of Higgs boson decay to bottom quarks, Phys. Rev. Lett. 121 (2018) 121801 [arXiv:1808.08242] [INSPIRE].
ATLAS collaboration, Measurements of WH and ZH production in the H→ \( b\overline{b} \) decay channel in pp collisions at 13 TeV with the ATLAS detector, Eur. Phys. J. C 81 (2021) 178 [arXiv:2007.02873] [INSPIRE].
ATLAS collaboration, Direct constraint on the Higgs-charm coupling from a search for Higgs boson decays into charm quarks with the ATLAS detector, arXiv:2201.11428 [INSPIRE].
LHC Higgs Cross Section Working Group collaboration, Handbook of LHC Higgs cross sections: 4. Deciphering the nature of the Higgs sector, arXiv:1610.07922 [INSPIRE].
T. Han and S. Willenbrock, QCD correction to the pp → WH and ZH total cross-sections, Phys. Lett. B 273 (1991) 167 [INSPIRE].
O. Brein, A. Djouadi and R. Harlander, NNLO QCD corrections to the Higgs-strahlung processes at hadron colliders, Phys. Lett. B 579 (2004) 149 [hep-ph/0307206] [INSPIRE].
O. Brein, R. Harlander, M. Wiesemann and T. Zirke, Top-quark mediated effects in hadronic Higgs-strahlung, Eur. Phys. J. C 72 (2012) 1868 [arXiv:1111.0761] [INSPIRE].
M.L. Ciccolini, S. Dittmaier and M. Krämer, Electroweak radiative corrections to associated WH and ZH production at hadron colliders, Phys. Rev. D 68 (2003) 073003 [hep-ph/0306234] [INSPIRE].
A. Denner, S. Dittmaier, S. Kallweit and A. Muck, Electroweak corrections to Higgs-strahlung off W/Z bosons at the Tevatron and the LHC with HAWK, JHEP 03 (2012) 075 [arXiv:1112.5142] [INSPIRE].
B.A. Kniehl, Associated production of Higgs and Z bosons from gluon fusion in hadron collisions, Phys. Rev. D 42 (1990) 2253 [INSPIRE].
D.A. Dicus and C. Kao, Higgs boson-Z0 production from gluon fusion, Phys. Rev. D 38 (1988) 1008 [Erratum ibid. 42 (1990) 2412] [INSPIRE].
G. Ferrera, M. Grazzini and F. Tramontano, Associated ZH production at hadron colliders: the fully differential NNLO QCD calculation, Phys. Lett. B 740 (2015) 51 [arXiv:1407.4747] [INSPIRE].
B. Hespel, F. Maltoni and E. Vryonidou, Higgs and Z boson associated production via gluon fusion in the SM and the 2HDM, JHEP 06 (2015) 065 [arXiv:1503.01656] [INSPIRE].
R.V. Harlander, J. Klappert, S. Liebler and L. Simon, vh@nnlo-v2: new physics in Higgs strahlung, JHEP 05 (2018) 089 [arXiv:1802.04817] [INSPIRE].
W. Bizoń, F. Caola, K. Melnikov and R. Röntsch, Anomalous couplings in associated VH production with Higgs boson decay to massive b quarks at NNLO in QCD, Phys. Rev. D 105 (2022) 014023 [arXiv:2106.06328] [INSPIRE].
C. Englert, M. McCullough and M. Spannowsky, Gluon-initiated associated production boosts Higgs physics, Phys. Rev. D 89 (2014) 013013 [arXiv:1310.4828] [INSPIRE].
C. Englert, R. Rosenfeld, M. Spannowsky and A. Tonero, New physics and signal-background interference in associated pp → HZ production, EPL 114 (2016) 31001 [arXiv:1603.05304] [INSPIRE].
B. Yan and C.P. Yuan, Anomalous \( Zb\overline{b} \) couplings: from LEP to LHC, Phys. Rev. Lett. 127 (2021) 051801 [arXiv:2101.06261] [INSPIRE].
B.A. Kniehl and C.P. Palisoc, Associated production of Z and neutral Higgs bosons at the CERN Large Hadron Collider, Phys. Rev. D 85 (2012) 075027 [arXiv:1112.1575] [INSPIRE].
L. Altenkamp, S. Dittmaier, R.V. Harlander, H. Rzehak and T.J.E. Zirke, Gluon-induced Higgs-strahlung at next-to-leading order QCD, JHEP 02 (2013) 078 [arXiv:1211.5015] [INSPIRE].
O. Brein, R.V. Harlander and T.J.E. Zirke, vh@nnlo — Higgs strahlung at hadron colliders, Comput. Phys. Commun. 184 (2013) 998 [arXiv:1210.5347] [INSPIRE].
A. Hasselhuhn, T. Luthe and M. Steinhauser, On top quark mass effects to gg → ZH at NLO, JHEP 01 (2017) 073 [arXiv:1611.05881] [INSPIRE].
R. Gröber, A. Maier and T. Rauh, Reconstruction of top-quark mass effects in Higgs pair production and other gluon-fusion processes, JHEP 03 (2018) 020 [arXiv:1709.07799] [INSPIRE].
G. Wang, X. Xu, Y. Xu and L.L. Yang, Next-to-leading order corrections for gg → ZH with top quark mass dependence, Phys. Lett. B 829 (2022) 137087 [arXiv:2107.08206] [INSPIRE].
L. Chen et al., ZH production in gluon fusion at NLO in QCD, arXiv:2204.05225 [INSPIRE].
J. Davies, G. Mishima and M. Steinhauser, Virtual corrections to gg → ZH in the high-energy and large-mt limits, JHEP 03 (2021) 034 [arXiv:2011.12314] [INSPIRE].
L. Chen, G. Heinrich, S.P. Jones, M. Kerner, J. Klappert and J. Schlenk, ZH production in gluon fusion: two-loop amplitudes with full top quark mass dependence, JHEP 03 (2021) 125 [arXiv:2011.12325] [INSPIRE].
S. Alioli, A. Broggio, S. Kallweit, M.A. Lim and L. Rottoli, Higgsstrahlung at NNLL’+NNLO matched to parton showers in GENEVA, Phys. Rev. D 100 (2019) 096016 [arXiv:1909.02026] [INSPIRE].
S. Zanoli, M. Chiesa, E. Re, M. Wiesemann and G. Zanderighi, Next-to-next-to-leading order event generation for VH production with H → \( b\overline{b} \) decay, JHEP 07 (2022) 008 [arXiv:2112.04168] [INSPIRE].
R.V. Harlander, A. Kulesza, V. Theeuwes and T. Zirke, Soft gluon resummation for gluon-induced Higgs strahlung, JHEP 11 (2014) 082 [arXiv:1410.0217] [INSPIRE].
L. Alasfar, G. Degrassi, P.P. Giardino, R. Gröber and M. Vitti, Virtual corrections to gg → ZH via a transverse momentum expansion, JHEP 05 (2021) 168 [arXiv:2103.06225] [INSPIRE].
L. Bellafronte, G. Degrassi, P.P. Giardino, R. Gröber and M. Vitti, Gluon fusion production at NLO: merging the transverse momentum and the high-energy expansions, JHEP 07 (2022) 069 [arXiv:2202.12157] [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. 510 (1998) 503] [hep-ph/9605323] [INSPIRE].
K. Melnikov and T.v. Ritbergen, The three loop relation between the MS-bar and the pole quark masses, Phys. Lett. B 482 (2000) 99 [hep-ph/9912391] [INSPIRE].
K.G. Chetyrkin, Quark mass anomalous dimension to O(\( {\alpha}_S^4 \)), Phys. Lett. B 404 (1997) 161 [hep-ph/9703278] [INSPIRE].
R. Bonciani, G. Degrassi, P.P. Giardino and R. Gröber, Analytical method for next-to-leading-order QCD corrections to double-Higgs production, Phys. Rev. Lett. 121 (2018) 162003 [arXiv:1806.11564] [INSPIRE].
R.N. Lee, LiteRed 1.4: a powerful tool for reduction of multiloop integrals, J. Phys. Conf. Ser. 523 (2014) 012059 [arXiv:1310.1145] [INSPIRE].
R.N. Lee, Presenting LiteRed: a tool for the Loop InTEgrals REDuction, arXiv:1212.2685 [INSPIRE].
L. Naterop, A. Signer and Y. Ulrich, handyG — rapid numerical evaluation of generalised polylogarithms in fortran, Comput. Phys. Commun. 253 (2020) 107165 [arXiv:1909.01656] [INSPIRE].
R. Bonciani, G. Degrassi, P.P. Giardino and R. Gröber, A numerical routine for the crossed vertex diagram with a massive-particle loop, Comput. Phys. Commun. 241 (2019) 122 [arXiv:1812.02698] [INSPIRE].
S. Actis, A. Denner, L. Hofer, A. Scharf and S. Uccirati, Recursive generation of one-loop amplitudes in the Standard Model, JHEP 04 (2013) 037 [arXiv:1211.6316] [INSPIRE].
A. Denner, J.-N. Lang and S. Uccirati, Recola2: REcursive Computation of One-Loop Amplitudes 2, Comput. Phys. Commun. 224 (2018) 346 [arXiv:1711.07388] [INSPIRE].
J. Alwall et al., The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations, JHEP 07 (2014) 079 [arXiv:1405.0301] [INSPIRE].
NNPDF collaboration, Parton distributions from high-precision collider data, Eur. Phys. J. C 77 (2017) 663 [arXiv:1706.00428] [INSPIRE].
M. Ciafaloni, P. Ciafaloni and D. Comelli, Bloch-Nordsieck violating electroweak corrections to inclusive TeV scale hard processes, Phys. Rev. Lett. 84 (2000) 4810 [hep-ph/0001142] [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].
J.M. Campbell, R.K. Ellis and W.T. Giele, A multi-threaded version of MCFM, Eur. Phys. J. C 75 (2015) 246 [arXiv:1503.06182] [INSPIRE].
R. Boughezal et al., Color singlet production at NNLO in MCFM, Eur. Phys. J. C 77 (2017) 7 [arXiv:1605.08011] [INSPIRE].
B.A. Kniehl, On the decay mode Z → Hgg, Phys. Rev. D 42 (1990) 3100 [INSPIRE].
J. Baglio et al., Higgs-pair production via gluon fusion at hadron colliders: NLO QCD corrections, JHEP 04 (2020) 181 [arXiv:2003.03227] [INSPIRE].
J. Baglio, F. Campanario, S. Glaus, M. Mühlleitner, M. Spira and J. Streicher, Gluon fusion into Higgs pairs at NLO QCD and the top mass scheme, Eur. Phys. J. C 79 (2019) 459 [arXiv:1811.05692] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2205.02769
Rights and permissions
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.
About this article
Cite this article
Degrassi, G., Gröber, R., Vitti, M. et al. On the NLO QCD corrections to gluon-initiated ZH production. J. High Energ. Phys. 2022, 9 (2022). https://doi.org/10.1007/JHEP08(2022)009
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2022)009