Abstract
We present an overview of a comprehensive analysis framework aimed at performing direct extraction of all possible effective Higgs couplings to neutral electroweak gauge bosons in the decay to electrons and muons, the so called ‘golden channel’. Our framework is based primarily on a maximum likelihood method constructed from analytic expressions of the fully differential cross sections for h → 4ℓ and for the dominant irreducible \( q\overline{q} \) → 4ℓ background, where 4ℓ = 2e2μ, 4e, 4μ. Detector effects are included by an explicit convolution of these analytic expressions with the appropriate transfer function over all center of mass variables. Utilizing the full set of observables, we construct an unbinned detector-level likelihood which is continuous in the effective couplings. We consider possible ZZ, Zγ, and γγ couplings simultaneously, allowing for general CP odd/even admixtures. A broad overview is given of how the convolution is performed and we discuss the principles and theoretical basis of the framework. This framework can be used in a variety of ways to study Higgs couplings in the golden channel using data obtained at the LHC and other future colliders.
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].
C.A. Nelson, Correlation between decay planes in Higgs boson decays into W pair (into Z pair), Phys. Rev. D 37 (1988) 1220 [INSPIRE].
A. Soni and R.M. Xu, Probing CP-violation via Higgs decays to four leptons, Phys. Rev. D 48 (1993) 5259 [hep-ph/9301225] [INSPIRE].
D. Chang, W.-Y. Keung and I. Phillips, CP odd correlation in the decay of neutral Higgs boson into ZZ, W + W − , or \( t\overline{t} \), Phys. Rev. D 48 (1993) 3225 [hep-ph/9303226] [INSPIRE].
V.D. Barger, K.-M. Cheung, A. Djouadi, B.A. Kniehl and P.M. Zerwas, Higgs bosons: intermediate mass range at e + e − colliders, Phys. Rev. D 49 (1994) 79 [hep-ph/9306270] [INSPIRE].
T. Arens and L.M. Sehgal, Energy spectra and energy correlations in the decay H →ZZ →μ + μ − μ + μ −, Z. Phys. C 66 (1995) 89 [hep-ph/9409396] [INSPIRE].
S.Y. Choi, D.J. Miller, M.M. Muhlleitner and P.M. Zerwas, Identifying the Higgs spin and parity in decays to Z pairs, Phys. Lett. B 553 (2003) 61 [hep-ph/0210077] [INSPIRE].
C.P. Buszello, I. Fleck, P. Marquard and J.J. van der Bij, Prospective analysis of spin- and CP-sensitive variables in H → ZZ → ℓ +1 ℓ −1 ℓ +2 ℓ −2 at the LHC, Eur. Phys. J. C 32 (2004) 209 [hep-ph/0212396] [INSPIRE].
R.M. Godbole, D.J. Miller and M.M. Muhlleitner, Aspects of CP-violation in the HZZ coupling at the LHC, JHEP 12 (2007) 031 [arXiv:0708.0458] [INSPIRE].
V.A. Kovalchuk, Model-independent analysis of CP-violation effects in decays of the Higgs boson into a pair of the W and Z bosons, J. Exp. Theor. Phys. 107 (2008) 774 [INSPIRE].
Q.-H. Cao, C.B. Jackson, W.-Y. Keung, I. Low and J. Shu, The Higgs mechanism and loop-induced decays of a scalar into two Z bosons, Phys. Rev. D 81 (2010) 015010 [arXiv:0911.3398] [INSPIRE].
Y. Gao et al., Spin determination of single-produced resonances at hadron colliders, Phys. Rev. D 81 (2010) 075022 [arXiv:1001.3396] [INSPIRE].
A. De Rujula, J. Lykken, M. Pierini, C. Rogan and M. Spiropulu, Higgs look-alikes at the LHC, Phys. Rev. D 82 (2010) 013003 [arXiv:1001.5300] [INSPIRE].
J.S. Gainer, K. Kumar, I. Low and R. Vega-Morales, Improving the sensitivity of Higgs boson searches in the golden channel, JHEP 11 (2011) 027 [arXiv:1108.2274] [INSPIRE].
B. Coleppa, K. Kumar and H.E. Logan, Can the 126 GeV boson be a pseudoscalar?, Phys. Rev. D 86 (2012) 075022 [arXiv:1208.2692] [INSPIRE].
S. Bolognesi et al., On the spin and parity of a single-produced resonance at the LHC, Phys. Rev. D 86 (2012) 095031 [arXiv:1208.4018] [INSPIRE].
D. Stolarski and R. Vega-Morales, Directly measuring the tensor structure of the scalar coupling to gauge bosons, Phys. Rev. D 86 (2012) 117504 [arXiv:1208.4840] [INSPIRE].
Y. Chen, N. Tran and R. Vega-Morales, Scrutinizing the Higgs signal and background in the 2e2μ golden channel, JHEP 01 (2013) 182 [arXiv:1211.1959] [INSPIRE].
R. Boughezal, T.J. LeCompte and F. Petriello, Single-variable asymmetries for measuring the ‘Higgs’ boson spin and CP properties, arXiv:1208.4311 [INSPIRE].
A. Belyaev, N.D. Christensen and A. Pukhov, CalcHEP 3.4 for collider physics within and beyond the standard model, Comput. Phys. Commun. 184 (2013) 1729 [arXiv:1207.6082] [INSPIRE].
P. Avery et al., Precision studies of the Higgs boson decay channel H → ZZ → 4ℓ with MEKD, Phys. Rev. D 87 (2013) 055006 [arXiv:1210.0896] [INSPIRE].
J.M. Campbell, W.T. Giele and C. Williams, Extending the matrix element method to next-to-leading order, arXiv:1205.3434 [INSPIRE].
J.M. Campbell, W.T. Giele and C. Williams, The matrix element method at next-to-leading order, JHEP 11 (2012) 043 [arXiv:1204.4424] [INSPIRE].
CMS collaboration, Search for a Higgs boson in the decay channel H → ZZ (*) → \( q\overline{q}{\ell}^{-}{\ell}^{+} \) in pp collisions at \( \sqrt{s} \) = 7 TeV, JHEP 04 (2012) 036 [arXiv:1202.1416] [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].
CMS collaboration, Study of the mass and spin-parity of the Higgs boson candidate via its decays to Z boson pairs, Phys. Rev. Lett. 110 (2013) 081803 [arXiv:1212.6639] [INSPIRE].
A. Menon, T. Modak, D. Sahoo, R. Sinha and H.-Y. Cheng, Inferring the nature of the boson at 125-126 GeV, Phys. Rev. D 89 (2014) 095021 [arXiv:1301.5404] [INSPIRE].
Y. Sun, X.-F. Wang and D.-N. Gao, CP mixed property of the Higgs-like particle in the decay channel h → ZZ * → 4ℓ, Int. J. Mod. Phys. A 29 (2014) 1450086 [arXiv:1309.4171] [INSPIRE].
J.S. Gainer, J. Lykken, K.T. Matchev, S. Mrenna and M. Park, Geolocating the Higgs boson candidate at the LHC, Phys. Rev. Lett. 111 (2013) 041801 [arXiv:1304.4936] [INSPIRE].
P. Artoisenet et al., A framework for Higgs characterisation, JHEP 11 (2013) 043 [arXiv:1306.6464] [INSPIRE].
I. Anderson et al., Constraining anomalous HVV interactions at proton and lepton colliders, Phys. Rev. D 89 (2014) 035007 [arXiv:1309.4819] [INSPIRE].
M. Chen et al., The role of interference in unraveling the ZZ-couplings of the newly discovered boson at the LHC, Phys. Rev. D 89 (2014) 034002 [arXiv:1310.1397] [INSPIRE].
G. Buchalla, O. Catà and G. D’Ambrosio, Nonstandard Higgs couplings from angular distributions in h → Zℓ + ℓ −, Eur. Phys. J. C 74 (2014) 2798 [arXiv:1310.2574] [INSPIRE].
Y. Chen and R. Vega-Morales, Extracting effective Higgs couplings in the golden channel, JHEP 04 (2014) 057 [arXiv:1310.2893] [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, arXiv:1403.4951 [INSPIRE].
Y. Chen, R. Harnik and R. Vega-Morales, Probing the Higgs couplings to photons in h → 4ℓ at the LHC, Phys. Rev. Lett. 113 (2014) 191801 [arXiv:1404.1336] [INSPIRE].
CMS collaboration, Constraints on anomalous HVV interactions using H → 4ℓ decays, CMS-PAS-HIG-14-014, CERN, Geneva Switzerland (2014).
CMS collaboration, Constraints on the spin-parity and anomalous HVV couplings of the Higgs boson in proton collisions at 7 and 8 TeV, arXiv:1411.3441 [INSPIRE].
Y. Chen et al., Technical note for 8D likelihood effective Higgs couplings extraction framework in the golden channel, arXiv:1410.4817 [INSPIRE].
Y. Chen, Precision measurement of the 125 GeV Higgs boson discovered in proton-proton collisions at \( \sqrt{s} \) = 7, 8 TeV with the CMS detector at the LHC, thesis in preparation for Ph.D., California Institute of Technology, U.S.A.
R. Vega-Morales, The Higgs boson as a window to beyond the standard model, thesis in fulfillment of Ph.D. requirements, Northwestern University, U.S.A. (2013) [INSPIRE].
B. Bradie, A friendly introduction to numerical analysis: with C and MATLAB materials on website; int. ed., Prentice-Hall, Englewood Cliffs U.S.A. (2006).
P. Artoisenet and O. Mattelaer, MadWeight: automatic event reweighting with matrix elements, PoS(CHARGED2008)025 [INSPIRE].
P. Artoisenet, V. Lemaitre, F. Maltoni and O. Mattelaer, Automation of the matrix element reweighting method, JHEP 12 (2010) 068 [arXiv:1007.3300] [INSPIRE].
P. Artoisenet, P. de Aquino, F. Maltoni and O. Mattelaer, Unravelling \( t\overline{t}h \) via the matrix element method, Phys. Rev. Lett. 111 (2013) 091802 [arXiv:1304.6414] [INSPIRE].
A. Falkowski and R. Vega-Morales, Exotic Higgs decays in the golden channel, JHEP 12 (2014) 037 [arXiv:1405.1095] [INSPIRE].
A. Bredenstein, A. Denner, S. Dittmaier and M.M. Weber, Precise predictions for the Higgs-boson decay H → WW/ZZ → 4ℓ, Phys. Rev. D 74 (2006) 013004 [hep-ph/0604011] [INSPIRE].
A. Bredenstein, A. Denner, S. Dittmaier and M.M. Weber, Precision calculations for the Higgs decays H → ZZ/WW → 4ℓ, Nucl. Phys. Proc. Suppl. 160 (2006) 131 [hep-ph/0607060] [INSPIRE].
N.E. Adam et al., Higgs working group summary report, arXiv:0803.1154 [INSPIRE].
J. Neyman and E.S. Pearson, On the problem of the most efficient tests of statistical hypotheses, Phil. Trans. Roy. Soc. Lond. A 231 (1933) 289.
CMS collaboration, CMS physics: technical design report volume 1: detector performance and software, CERN-LHCC-2006-001, CERN, Geneva Switzerland (2006).
CMS collaboration, CMS 2013 public electron performance results webpage, https://twiki.cern.ch/twiki/bin/view/CMSPublic/EGMElectronsMoriond2013.
CMS collaboration, Electron performance with 19.6 fb−1 of data collected at \( \sqrt{s} \) = 8 TeV with the CMS detector, CMS-DP-2013-003, CERN, Geneva Switzerland (2013).
Y. Chen and R. Vega-Morales, Scrutinizing the golden channel webpage, http://yichen.me/project/GoldenChannel/.
N.D. Christensen and C. Duhr, FeynRules — Feynman rules made easy, Comput. Phys. Commun. 180 (2009) 1614 [arXiv:0806.4194] [INSPIRE].
J. Alwall et al., MadGraph/MadEvent v4: the new web generation, JHEP 09 (2007) 028 [arXiv:0706.2334] [INSPIRE].
A. Falkowski, F. Riva and A. Urbano, Higgs at last, JHEP 11 (2013) 111 [arXiv:1303.1812] [INSPIRE].
J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer and T. Stelzer, MadGraph 5: going beyond, JHEP 06 (2011) 128 [arXiv:1106.0522] [INSPIRE].
T. Melia, P. Nason, R. Rontsch and G. Zanderighi, W + W − , WZ and ZZ production in the POWHEG BOX, JHEP 11 (2011) 078 [arXiv:1107.5051] [INSPIRE].
F. James, MINUIT function minimization and error analysis: reference manual version 94.1, CERN, Geneva Switzerland (1994) [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: 1401.2077
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
Chen, Y., Di Marco, E., Lykken, J. et al. 8D likelihood effective Higgs couplings extraction framework in h → 4ℓ . J. High Energ. Phys. 2015, 125 (2015). https://doi.org/10.1007/JHEP01(2015)125
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2015)125
Keywords
- Hadron-Hadron Scattering
- Higgs physics