# Fiducial cross sections for the four-lepton decay mode in Higgs-plus-jet production up to NNLO QCD

- 23 Downloads

## Abstract

The four-lepton decay mode of the Higgs boson allows for a clean kinematic reconstruction, thereby enabling precision studies of the Higgs boson properties and of its production dynamics. We compute the NNLO QCD corrections to fiducial cross sections relevant to this decay mode in the gluon-fusion channel producing a Higgs boson in association with a hadronic jet, and study the impact of the QCD corrections on the fiducial acceptance factors in inclusive Higgs and Higgs-plus-jet production. We investigate in detail the different definitions used in the ATLAS and CMS measurements to define the fiducial cross sections. Differences in the lepton isolation prescription are found to have a sizeable impact on the higher order corrections to the fiducial acceptance factors.

## Keywords

Higgs Physics Perturbative QCD## Notes

### **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.

## References

- [1]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]. - [2]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]. - [3]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]. - [4]H.M. Georgi, S.L. Glashow, M.E. Machacek and D.V. Nanopoulos,
*Higgs bosons from two gluon annihilation in proton proton collisions*,*Phys. Rev. Lett.***40**(1978) 692 [INSPIRE].ADSGoogle Scholar - [5]M. Spira, A. Djouadi, D. Graudenz and P.M. Zerwas,
*Higgs boson production at the LHC*,*Nucl. Phys.***B 453**(1995) 17 [hep-ph/9504378] [INSPIRE]. - [6]R. Harlander and P. Kant,
*Higgs production and decay: Analytic results at next-to-leading order QCD*,*JHEP***12**(2005) 015 [hep-ph/0509189] [INSPIRE]. - [7]U. Aglietti, R. Bonciani, G. Degrassi and A. Vicini,
*Analytic results for virtual QCD corrections to Higgs production and decay*,*JHEP***01**(2007) 021 [hep-ph/0611266] [INSPIRE]. - [8]C. Anastasiou, S. Bucherer and Z. Kunszt,
*HPro: a NLO Monte-Carlo for Higgs production via gluon fusion with finite heavy quark masses*,*JHEP***10**(2009) 068 [arXiv:0907.2362] [INSPIRE].ADSGoogle Scholar - [9]S. Dawson,
*Radiative corrections to Higgs boson production*,*Nucl. Phys.***B 359**(1991) 283 [INSPIRE].ADSGoogle Scholar - [10]C. Anastasiou and K. Melnikov,
*Higgs boson production at hadron colliders in NNLO QCD*,*Nucl. Phys.***B 646**(2002) 220 [hep-ph/0207004] [INSPIRE]. - [11]R.V. Harlander and W.B. Kilgore,
*Next-to-next-to-leading order Higgs production at hadron colliders*,*Phys. Rev. Lett.***88**(2002) 201801 [hep-ph/0201206] [INSPIRE]. - [12]V. Ravindran, J. Smith and W.L. van Neerven,
*NNLO corrections to the total cross-section for Higgs boson production in hadron hadron collisions*,*Nucl. Phys.***B 665**(2003) 325 [hep-ph/0302135] [INSPIRE]. - [13]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]. - [14]M. Grazzini,
*NNLO predictions for the Higgs boson signal in the H*→*WW*→*l*ν*l*ν*and H*→*ZZ*→ 4*l decay channels*,*JHEP***02**(2008) 043 [arXiv:0801.3232] [INSPIRE].ADSGoogle Scholar - [15]M. Grazzini and H. Sargsyan,
*Heavy-quark mass effects in Higgs boson production at the LHC*,*JHEP***09**(2013) 129 [arXiv:1306.4581] [INSPIRE].ADSGoogle Scholar - [16]C. Anastasiou et al.,
*Higgs boson gluon-fusion production in QCD at three loops*,*Phys. Rev. Lett.***114**(2015) 212001 [arXiv:1503.06056] [INSPIRE].ADSGoogle Scholar - [17]B. Mistlberger,
*Higgs boson production at hadron colliders at N*^{3}*LO in QCD*,*JHEP***05**(2018) 028 [arXiv:1802.00833] [INSPIRE].ADSGoogle Scholar - [18]L. Cieri et al.,
*Higgs boson production at the LHC using the q*_{T}*subtraction formalism at N*^{3}*LO QCD*,*JHEP***02**(2019) 096 [arXiv:1807.11501] [INSPIRE].ADSGoogle Scholar - [19]F. Dulat, B. Mistlberger and A. Pelloni,
*Precision predictions at N*^{3}*LO for the Higgs boson rapidity distribution at the LHC*,*Phys. Rev.***D 99**(2019) 034004 [arXiv:1810.09462] [INSPIRE].ADSGoogle Scholar - [20]R. Boughezal et al.,
*Higgs boson production in association with a jet at next-to-next-to-leading order*,*Phys. Rev. Lett.***115**(2015) 082003 [arXiv:1504.07922] [INSPIRE].ADSGoogle Scholar - [21]X. Chen et al.,
*NNLO QCD corrections to Higgs boson production at large transverse momentum*,*JHEP***10**(2016) 066 [arXiv:1607.08817] [INSPIRE].ADSGoogle Scholar - [22]R. Boughezal et al.,
*Higgs boson production in association with a jet at NNLO using jettiness subtraction*,*Phys. Lett.***B 748**(2015) 5 [arXiv:1505.03893] [INSPIRE].ADSGoogle Scholar - [23]F. Caola, K. Melnikov and M. Schulze,
*Fiducial cross sections for Higgs boson production in association with a jet at next-to-next-to-leading order in QCD*,*Phys. Rev.***D 92**(2015) 074032 [arXiv:1508.02684] [INSPIRE].ADSGoogle Scholar - [24]J.M. Lindert, K. Kudashkin, K. Melnikov and C. Wever,
*Higgs bosons with large transverse momentum at the LHC*,*Phys. Lett.***B 782**(2018) 210 [arXiv:1801.08226] [INSPIRE].ADSGoogle Scholar - [25]S.P. Jones, M. Kerner and G. Luisoni,
*Next-to-leading-order QCD corrections to Higgs boson plus jet production with full top-quark mass dependence*,*Phys. Rev. Lett.***120**(2018) 162001 [arXiv:1802.00349] [INSPIRE].ADSGoogle Scholar - [26]ATLAS collaboration,
*Fiducial and differential cross sections of Higgs boson production measured in the four-lepton decay channel in pp collisions at*\( \sqrt{s} \) = 8*TeV with the ATLAS detector*,*Phys. Lett.***B 738**(2014) 234 [arXiv:1408.3226] [INSPIRE]. - [27]CMS collaboration,
*Measurement of differential and integrated fiducial cross sections for Higgs boson production in the four-lepton decay channel in pp collisions at*\( \sqrt{s} \) = 7*and*8*TeV*,*JHEP***04**(2016) 005 [arXiv:1512.08377] [INSPIRE]. - [28]ATLAS collaboration,
*Study of the spin and parity of the Higgs boson in diboson decays with the ATLAS detector*,*Eur. Phys. J.***C 75**(2015) 476 [*Erratum ibid.***C 76**(2016) 152] [arXiv:1506.05669] [INSPIRE]. - [29]CMS collaboration,
*Constraints on the spin-parity and anomalous HVV couplings of the Higgs boson in proton collisions at*7*and*8*TeV*,*Phys. Rev.***D 92**(2015) 012004 [arXiv:1411.3441] [INSPIRE]. - [30]ATLAS collaboration,
*Measurement of inclusive and differential cross sections in the H*→*ZZ*^{*}→ 4*ℓ decay channel in pp collisions at*\( \sqrt{s} \) = 13*TeV with the ATLAS detector*,*JHEP***10**(2017) 132 [arXiv:1708.02810] [INSPIRE]. - [31]ATLAS collaboration,
*Measurements of the Higgs boson production, fiducial and differential cross sections in the*4*ℓ decay channel at*\( \sqrt{s} \) = 13*TeV with the ATLAS detector*, ATLAS-CONF-2018-018 (2018). - [32]CMS collaboration,
*Measurements of properties of the Higgs boson decaying into the four-lepton final state in pp collisions at*\( \sqrt{s} \) = 13*TeV*,*JHEP***11**(2017) 047 [arXiv:1706.09936] [INSPIRE]. - [33]CMS Collaboration,
*Measurements of properties of the Higgs boson in the four-lepton final state in proton-proton collisions at*\( \sqrt{s} \) = 13*TeV*, CMS-PAS-HIG-19-001 (2019). - [34]F. Wilczek,
*Decays of heavy vector mesons into Higgs particles*,*Phys. Rev. Lett.***39**(1977) 1304 [INSPIRE].ADSGoogle Scholar - [35]M.A. Shifman, A.I. Vainshtein and V.I. Zakharov,
*Remarks on Higgs boson interactions with nucleons*,*Phys. Lett.***78B**(1978) 443 [INSPIRE].ADSGoogle Scholar - [36]T. Inami, T. Kubota and Y. Okada,
*Effective gauge theory and the effect of heavy quarks in Higgs boson decays*,*Z. Phys.***C 18**(1983) 69 [INSPIRE].ADSGoogle Scholar - [37]K.G. Chetyrkin, B.A. Kniehl and M. Steinhauser,
*Decoupling relations to O*(*α*_{S}^{3})*and their connection to low-energy theorems*,*Nucl. Phys.***B 510**(1998) 61 [hep-ph/9708255] [INSPIRE]. - [38]M. Krämer, E. Laenen and M. Spira,
*Soft gluon radiation in Higgs boson production at the LHC*,*Nucl. Phys.***B 511**(1998) 523 [hep-ph/9611272] [INSPIRE]. - [39]Y. Schröder and M. Steinhauser,
*Four-loop decoupling relations for the strong coupling*,*JHEP***01**(2006) 051 [hep-ph/0512058] [INSPIRE]. - [40]K.G. Chetyrkin, J.H. Kuhn and C. Sturm,
*QCD decoupling at four loops*,*Nucl. Phys.***B 744**(2006) 121 [hep-ph/0512060] [INSPIRE]. - [41]B.A. Kniehl, A.V. Kotikov, A.I. Onishchenko and O.L. Veretin,
*Strong-coupling constant with flavor thresholds at five loops in the anti-MS scheme*,*Phys. Rev. Lett.***97**(2006) 042001 [hep-ph/0607202] [INSPIRE]. - [42]M. Spira,
*Effective multi-Higgs couplings to gluons*,*JHEP***10**(2016) 026 [arXiv:1607.05548] [INSPIRE].ADSGoogle Scholar - [43]M. Gerlach, F. Herren and M. Steinhauser,
*Wilson coefficients for Higgs boson production and decoupling relations to*\( \mathcal{O}\left({\alpha}_s^4\right) \),*JHEP***11**(2018) 141 [arXiv:1809.06787] [INSPIRE]. - [44]R. Boughezal et al.,
*Higgs boson production in association with a jet at next-to-next-to-leading order in perturbative QCD*,*JHEP***06**(2013) 072 [arXiv:1302.6216] [INSPIRE].ADSGoogle Scholar - [45]X. Chen, T. Gehrmann, E.W.N. Glover and M. Jaquier,
*Precise QCD predictions for the production of Higgs + jet final states*,*Phys. Lett.***B 740**(2015) 147 [arXiv:1408.5325] [INSPIRE].ADSGoogle Scholar - [46]T. Gehrmann, M. Jaquier, E.W.N. Glover and A. Koukoutsakis,
*Two-loop QCD corrections to the helicity amplitudes for H*→ 3*partons*,*JHEP***02**(2012) 056 [arXiv:1112.3554] [INSPIRE].ADSzbMATHGoogle Scholar - [47]L.J. Dixon and Y. Sofianatos,
*Analytic one-loop amplitudes for a Higgs boson plus four partons*,*JHEP***08**(2009) 058 [arXiv:0906.0008] [INSPIRE].ADSMathSciNetGoogle Scholar - [48]S. Badger et al.,
*One-loop Higgs plus four gluon amplitudes: full analytic results*,*JHEP***01**(2010) 036 [arXiv:0909.4475] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar - [49]S. Badger, J.M. Campbell, R.K. Ellis and C. Williams,
*Analytic results for the one-loop NMHV Hqqgg amplitude*,*JHEP***12**(2009) 035 [arXiv:0910.4481] [INSPIRE].ADSGoogle Scholar - [50]V. Del Duca, A. Frizzo and F. Maltoni,
*Higgs boson production in association with three jets*,*JHEP***05**(2004) 064 [hep-ph/0404013] [INSPIRE]. - [51]L.J. Dixon, E.W.N. Glover and V.V. Khoze,
*MHV rules for Higgs plus multi-gluon amplitudes*,*JHEP***12**(2004) 015 [hep-th/0411092] [INSPIRE].ADSMathSciNetGoogle Scholar - [52]S.D. Badger, E.W.N. Glover and V.V. Khoze,
*MHV rules for Higgs plus multi-parton amplitudes*,*JHEP***03**(2005) 023 [hep-th/0412275] [INSPIRE].ADSMathSciNetGoogle Scholar - [53]A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover,
*Antenna subtraction at NNLO*,*JHEP***09**(2005) 056 [hep-ph/0505111] [INSPIRE]. - [54]A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover,
*Gluon-gluon antenna functions from Higgs boson decay*,*Phys. Lett.***B 612**(2005) 49 [hep-ph/0502110] [INSPIRE]. - [55]A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover,
*quark-gluon antenna functions from neutralino decay*,*Phys. Lett.***B 612**(2005) 36 [hep-ph/0501291] [INSPIRE]. - [56]A. Daleo, T. Gehrmann and D. Maître,
*Antenna subtraction with hadronic initial states*,*JHEP***04**(2007) 016 [hep-ph/0612257] [INSPIRE]. - [57]A. Daleo, A. Gehrmann-De Ridder, T. Gehrmann and G. Luisoni,
*Antenna subtraction at NNLO with hadronic initial states: initial-final configurations*,*JHEP***01**(2010) 118 [arXiv:0912.0374] [INSPIRE].ADSzbMATHGoogle Scholar - [58]T. Gehrmann and P.F. Monni,
*Antenna subtraction at NNLO with hadronic initial states: real-virtual initial-initial configurations*,*JHEP***12**(2011) 049 [arXiv:1107.4037] [INSPIRE].ADSzbMATHGoogle Scholar - [59]R. Boughezal, A. Gehrmann-De Ridder and M. Ritzmann,
*Antenna subtraction at NNLO with hadronic initial states: double real radiation for initial-initial configurations with two quark flavours*,*JHEP***02**(2011) 098 [arXiv:1011.6631] [INSPIRE].ADSzbMATHGoogle Scholar - [60]A. Gehrmann-De Ridder, T. Gehrmann and M. Ritzmann,
*Antenna subtraction at NNLO with hadronic initial states: double real initial-initial configurations*,*JHEP***10**(2012) 047 [arXiv:1207.5779] [INSPIRE].ADSzbMATHGoogle Scholar - [61]J. Currie, E.W.N. Glover and S. Wells,
*Infrared structure at NNLO using antenna subtraction*,*JHEP***04**(2013) 066 [arXiv:1301.4693] [INSPIRE].ADSGoogle Scholar - [62]J.F. Gunion, G.L. Kane and J. Wudka,
*Search techniques for charged and neutral intermediate mass Higgs bosons*,*Nucl. Phys.***B 299**(1988) 231 [INSPIRE].ADSGoogle Scholar - [63]
- [64]J.M. Campbell, R.K. Ellis and C. Williams,
*Vector boson pair production at the LHC*,*JHEP***07**(2011) 018 [arXiv:1105.0020] [INSPIRE].ADSGoogle Scholar - [65]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]. - [66]NNPDF collaboration,
*Parton distributions for the LHC Run II*,*JHEP***04**(2015) 040 [arXiv:1410.8849] [INSPIRE]. - [67]ATLAS collaboration,
*Combined measurement of differential and total cross sections in the H*→*γγ and the H*→*ZZ*^{*}→ 4*ℓ decay channels at*\( \sqrt{s} \) = 13*TeV with the ATLAS detector*,*Phys. Lett.***B 786**(2018) 114 [arXiv:1805.10197] [INSPIRE]. - [68]CMS collaboration,
*Combined measurement and interpretation of differential Higgs boson production cross sections at*\( \sqrt{s} \) = 13*TeV*, CMS-PAS-HIG-17-028 (2017). - [69]R.K. Ellis et al.,
*Higgs decay to τ*^{+}*τ*^{−}*: a possible signature of intermediate mass Higgs bosons at the SSC*,*Nucl. Phys.***B 297**(1988) 221 [INSPIRE].ADSGoogle Scholar - [70]U. Baur and E.W.N. Glover,
*Higgs boson production at large transverse momentum in hadronic collisions*,*Nucl. Phys.***B 339**(1990) 38 [INSPIRE].ADSGoogle Scholar - [71]Z. Li, J. Wang, Q.-S. Yan and X. Zhao,
*Efficient numerical evaluation of Feynman integrals*,*Chin. Phys.***C 40**(2016) 033103 [arXiv:1508.02512] [INSPIRE].ADSGoogle Scholar - [72]S. Borowka et al.,
*SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop*,*Comput. Phys. Commun.***196**(2015) 470 [arXiv:1502.06595] [INSPIRE]. - [73]S. Borowka et al.,
*pySecDec: a toolbox for the numerical evaluation of multi-scale integrals*,*Comput. Phys. Commun.***222**(2018) 313 [arXiv:1703.09692] [INSPIRE]. - [74]K. Melnikov, L. Tancredi and C. Wever,
*Two-loop gg*→*Hg amplitude mediated by a nearly massless quark*,*JHEP***11**(2016) 104 [arXiv:1610.03747] [INSPIRE].ADSGoogle Scholar - [75]K. Melnikov, L. Tancredi and C. Wever,
*Two-loop amplitudes for qg*→*Hq and*\( q\overline{q}\to Hg \)*mediated by a nearly massless quark*,*Phys. Rev.***D 95**(2017) 054012 [arXiv:1702.00426] [INSPIRE].ADSGoogle Scholar - [76]K. Kudashkin, K. Melnikov and C. Wever,
*Two-loop amplitudes for processes gg*→*Hg, qg*→*Hq and*\( q\overline{q}\to Hg \)*at large Higgs transverse momentum*,*JHEP***02**(2018) 135 [arXiv:1712.06549] [INSPIRE]. - [77]T. Neumann,
*NLO Higgs+jet production at large transverse momenta including top quark mass effects*,*J. Phys. Comm.***2**(2018) 095017 [arXiv:1802.02981] [INSPIRE].ADSGoogle Scholar - [78]J.M. Lindert, K. Melnikov, L. Tancredi and C. Wever,
*Top-bottom interference effects in Higgs plus jet production at the LHC*,*Phys. Rev. Lett.***118**(2017) 252002 [arXiv:1703.03886] [INSPIRE].ADSGoogle Scholar - [79]F. Caola et al.,
*Bottom-quark effects in Higgs production at intermediate transverse momentum*,*JHEP***09**(2018) 035 [arXiv:1804.07632] [INSPIRE].ADSGoogle Scholar - [80]M. Grazzini et al.,
*Higgs boson pair production at NNLO with top quark mass effects*,*JHEP***05**(2018) 059 [arXiv:1803.02463] [INSPIRE].ADSGoogle Scholar - [81]A. Banfi, P.F. Monni, G.P. Salam and G. Zanderighi,
*Higgs and Z-boson production with a jet veto*,*Phys. Rev. Lett.***109**(2012) 202001 [arXiv:1206.4998] [INSPIRE].ADSGoogle Scholar - [82]T. Becher, M. Neubert and L. Rothen,
*Factorization and N*^{3}*LL*_{p}*+NNLO predictions for the Higgs cross section with a jet veto*,*JHEP***10**(2013) 125 [arXiv:1307.0025] [INSPIRE].ADSGoogle Scholar - [83]I.W. Stewart, F.J. Tackmann, J.R. Walsh and S. Zuberi,
*Jet p*_{T}*resummation in Higgs production at NNLL*′ +*NNLO*,*Phys. Rev.***D 89**(2014) 054001 [arXiv:1307.1808] [INSPIRE]. - [84]A. Banfi et al.,
*Jet-vetoed Higgs cross section in gluon fusion at N*^{3}*LO+NNLL with small-R resummation*,*JHEP***04**(2016) 049 [arXiv:1511.02886] [INSPIRE].ADSGoogle Scholar - [85]J.K.L. Michel, P. Pietrulewicz and F.J. Tackmann,
*Jet veto resummation with jet rapidity cuts*,*JHEP***04**(2019) 142 [arXiv:1810.12911] [INSPIRE].ADSGoogle Scholar - [86]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]. - [87]D. de Florian, G. Ferrera, M. Grazzini and D. Tommasini,
*Transverse-momentum resummation: Higgs boson production at the Tevatron and the LHC*,*JHEP***11**(2011) 064 [arXiv:1109.2109] [INSPIRE].Google Scholar - [88]D. de Florian, G. Ferrera, M. Grazzini and D. Tommasini,
*Higgs boson production at the LHC: transverse momentum resummation effects in the H*→ 2*γ, H*→*WW*→*lνlν and H*→*ZZ*→ 4*l decay modes*,*JHEP***06**(2012) 132 [arXiv:1203.6321] [INSPIRE]. - [89]T. Becher, M. Neubert and D. Wilhelm,
*Higgs-boson production at small transverse momentum*,*JHEP***05**(2013) 110 [arXiv:1212.2621] [INSPIRE].ADSGoogle Scholar - [90]D. Neill, I.Z. Rothstein and V. Vaidya,
*The Higgs transverse momentum distribution at NNLL and its theoretical errors*,*JHEP***12**(2015) 097 [arXiv:1503.00005] [INSPIRE].ADSGoogle Scholar - [91]X. Chen et al.,
*Precise QCD description of the Higgs boson transverse momentum spectrum*,*Phys. Lett.***B 788**(2019) 425 [arXiv:1805.00736] [INSPIRE].ADSGoogle Scholar - [92]W. Bizoń et al.,
*Fiducial distributions in Higgs and Drell-Yan production at N*^{3}*LL+NNLO*,*JHEP***12**(2018) 132 [arXiv:1805.05916] [INSPIRE].ADSGoogle Scholar