CMS-PAS-HIG-24-012

CMS-PAS-HIG-24-012
Search for nonresonant triple Higgs boson production in the six b-quark final state in proton-proton collisions at $ \sqrt{s} = $ 13 TeV
CMS Collaboration
2025-10-07

Abstract: A search for nonresonant triple Higgs boson production in the six b-quark final state is performed using data from proton-proton collisions at a center-of-mass energy of 13 TeV collected by the CMS experiment, and corresponding to an integrated luminosity of 138 fb$^{-1} $. The search targets final states in which the b quarks from the decays of the Higgs bosons are reconstructed in small-radius or large-radius jets, resulting in topologies that are fully boosted, partially boosted, partially resolved, or fully resolved. The analysis employs symmetry-preserving attention networks to categorize events in the respective topologies, and to classify signal and background events. The data are found to be compatible with the standard model predictions, and upper limits on the triple Higgs boson production cross section are set. The observed (expected) upper limit, at 95% confidence level, on the production rate times branching fraction, relative to the standard model prediction, is 588 (572), corresponding to an upper limit of 44 (43) fb on the cross section. The observed (expected) 95% confidence level intervals for the trilinear and quartic Higgs boson self-interaction coupling modifiers are $ [-7,12] ([-6,11]) $ for $ \kappa_{3} $, and $ [-190,190] ([-190,190]) $ for $ \kappa_{4} $. This result represents the best limit of triple Higgs boson production at the LHC and the most stringent constraint on the quartic coupling modifier $ \kappa_4 $ to date.
Links: CDS record (PDF) ; CADI line (restricted) ;

Figures	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Post-fit yields in the signal-region categories with three reconstructed Higgs bosons (left) and two (right). Bins correspond to ten bins per category intervals of the SPANET score ProbMultiH in the high-score range 0.8-1.0, ordered by increasing score. The HH contribution and the data-driven background are stacked.
png pdf	Figure 1-a: Post-fit yields in the signal-region categories with three reconstructed Higgs bosons (left) and two (right). Bins correspond to ten bins per category intervals of the SPANET score ProbMultiH in the high-score range 0.8-1.0, ordered by increasing score. The HH contribution and the data-driven background are stacked.
png pdf	Figure 1-b: Post-fit yields in the signal-region categories with three reconstructed Higgs bosons (left) and two (right). Bins correspond to ten bins per category intervals of the SPANET score ProbMultiH in the high-score range 0.8-1.0, ordered by increasing score. The HH contribution and the data-driven background are stacked.
png pdf	Figure 2: Breakdown of the upper limits on the HHH signal for the SM hypothesis across different topology categories compared for the combination of categories with three and two reconstructed Higgs bosons (3H and 2H respectively) as well as the combination with all categories.
png pdf	Figure 3: Constraints on the coupling modifiers $ \kappa_3 $ and $ \kappa_4 $ from a profile-likelihood scan in the $ (\kappa_3,\kappa_4) $ plane using the combination of all signal regions. Observed and expected 68% and 95% CL contours are shown. The region of parameter space allowed by perturbative unitarity in $ \mathrm{H}\mathrm{H}\!\to\!\mathrm{H}\mathrm{H} $ scattering is indicated in gray, following Ref. [45].

Summary

A search for nonresonant triple Higgs boson production HHH is presented, using the data collected by the CMS experiment from proton-proton collision at a center-of-mass energy $ \sqrt{s} = $ 13 TeV. The analysis targets final states in which three Higgs bosons decay to $ \mathrm{b}\overline{\mathrm{b}} $ quark pairs and are reconstructed across fully resolved, partially resolved, partially boosted, and fully boosted topologies. To maximize sensitivity across this diverse phase space, the analysis exploits advanced machine learning techniques for the identification of heavy-flavor jets, separation of signal from background events, and classification of the signal event candidates. For the latter, symmetry-preserving attention networks SPANET are employed. The observed (expected) upper limit on the HHH production rate times branching fraction is 588 (572) at 95% CL, which corresponds to an upper limit on the cross section of 44 (43) fb. Constraints on the Higgs boson self-coupling parameters are obtained, yielding $ \kappa_3 \in [-7,12] $ and $ \kappa_4 \in [-190,190] $, setting the most stringent bound to date on the quartic self-coupling modifier $ \kappa_4 $. This result constitutes the most sensitive probe of nonresonant HHH production at the LHC to date. Whereas the sensitivity is currently limited by the overwhelming QCD multijet background inherent to fully hadronic final states, the analysis demonstrates that topological and flavor-based discriminants powered by machine learning can improve the sensitivity to rare signals in challenging environments. The HHH process provides direct access to the quartic term in the Higgs potential, offering a unique and complementary window to the HH searches. Together, these channels form a coherent experimental program for probing the structure of the Higgs potential and testing the mechanism of electroweak symmetry breaking. The methods presented here lay the groundwork for a broader HHH search strategy at the LHC and the upcoming HL-LHC era.

References
1	F. Englert and R. Brout	Broken Symmetry and the Mass of Gauge Vector Mesons	PRL 13 (1964) 321
2	P. W. Higgs	Broken symmetries, massless particles and gauge fields	PL 12 (1964) 132
3	P. W. Higgs	Broken symmetries and the masses of gauge bosons	PRL 13 (1964) 508
4	G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble	Global conservation laws and massless particles	PRL 13 (1964) 585
5	P. W. Higgs	Spontaneous symmetry breakdown without massless bosons	PR 145 (1966) 1156
6	T. W. B. Kibble	Symmetry breaking in non-abelian gauge theories	PR 155 (1967) 1554
7	ATLAS Collaboration	Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC	PLB 716 (2012) 1	1207.7214
8	CMS Collaboration	Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC	PLB 716 (2012) 30	CMS-HIG-12-028 1207.7235
9	B. Horn	The Higgs field and early universe cosmology: a (brief) review	MDPI Physics 2 (2020) 503	2007.10377
10	M. Reichert et al.	Probing baryogenesis through the higgs boson self-coupling	PRD 97 (2018) 075008
11	A. Noble and M. Perelstein	Higgs self-coupling as a probe of the electroweak phase transition	PRD 78 (2008) 063518
12	T. Markkanen, A. Rajantie, and S. Stopyra	Cosmological Aspects of Higgs Vacuum Metastability	Front. Astron. Space Sci. 5 (2018) 40	1809.06923
13	LHCSW Group	LHC HH Cross Section Working Group — References	link
14	M. Grazzini et al.	Higgs boson pair production at NNLO with top quark mass effects	JHEP 05 (2018) 059	1803.02463
15	S. Dawson, S. Dittmaier, and M. Spira	Neutral higgs-boson pair production at hadron colliders: Qcd corrections	PRD 58 (1998) 115012
16	S. Borowka et al.	Higgs boson pair production in gluon fusion at next-to-leading order with full top-quark mass dependence	PRL 117 (2016) 012001
17	J. Baglio et al.	Gluon fusion into Higgs pairs at NLO QCD and the top mass scheme	EPJC 79 (2019) 459	1811.05692
18	D. de Florian and J. Mazzitelli	Higgs boson pair production at next-to-next-to-leading order in qcd	PRL 111 (2013) 201801
19	D. Y. Shao, C. S. Li, H. T. Li, and J. Wang	Threshold resummation effects in Higgs boson pair production at the LHC	JHEP 07 (2013) 169	1301.1245
20	D. de Florian and J. Mazzitelli	Higgs pair production at next-to-next-to-leading logarithmic accuracy at the LHC	JHEP 09 (2015) 053	1505.07122
21	J. Baglio et al.	$ gg \rightarrow hh $: Combined uncertainties	PRD 103 (2021) 056002
22	G. Heinrich, J. Lang, and L. Scyboz	SMEFT predictions for $ gg \rightarrow hh $ at full NLO QCD and truncation uncertainties	JHEP 08 (2022) 079	2204.13045
23	E. Bagnaschi, G. Degrassi, and R. Grober	Higgs boson pair production at NLO in the POWHEG approach and the top quark mass uncertainties	EPJC 83 (2023) 1054	2309.10525
24	F. Maltoni, E. Vryonidou, and M. Zaro	Top-quark mass effects in double and triple Higgs production in gluon-gluon fusion at NLO	JHEP 11 (2014) 079	1408.6542
25	A. Papaefstathiou and G. Tetlalmatzi-Xolocotzi	Multi-Higgs boson production with anomalous interactions at current and future proton colliders	JHEP 06 (2024) 124	2312.13562
26	D. de Florian, I. Fabre, and J. Mazzitelli	Triple Higgs production at hadron colliders at NNLO in QCD	JHEP 03 (2020) 155	1912.02760
27	H. e. a. Abouabid	HHH whitepaper	EPJC 84 (2024) 1183	2407.03015
28	ATLAS Collaboration	Studies of new Higgs boson interactions through nonresonant HH production in the $ b\overline{b}\gamma \gamma $ final state in pp collisions at $ \sqrt{s} = $ 13 TeV with the ATLAS detector	JHEP 01 (2024) 066	2310.12301
29	ATLAS Collaboration	Search for nonresonant pair production of higgs bosons in the $ b\overline{b}b\overline{b} $ final state in $ pp $ collisions at $ \sqrt{s}= $ 13 TeV with the atlas detector	PRD 108 (2023) 052003	2301.03212
30	ATLAS Collaboration	Search for the nonresonant production of higgs boson pairs via gluon fusion and vector-boson fusion in the $ b\bar{b}\tau^{+}\tau^{-} $ final state in proton-proton collisions at $ \sqrt{s}= $ 13 TeV with the atlas detector	PRD 110 (2024) 032012	2404.12660
31	ATLAS Collaboration	Search for non-resonant Higgs boson pair production in final states with leptons, taus, and photons in pp collisions at $ \sqrt{s} = $ 13 TeV with the ATLAS detector	JHEP 08 (2024) 164	2405.20040
32	ATLAS Collaboration	Search for non-resonant Higgs boson pair production in the 2 $ b+2\ell +{E}_{\textrm{T}}^{\textrm{miss}} $ final state in pp collisions at $ \sqrt{s} = $ 13 TeV with the ATLAS detector	JHEP 02 (2024) 037	2310.11286
33	CMS Collaboration	Search for nonresonant Higgs boson pair production in final state with two bottom quarks and two tau leptons in proton-proton collisions at $ \sqrt{s}= $ 13 TeV	PLB 842 (2023) 137531	CMS-HIG-20-010 2206.09401
34	CMS Collaboration	Search for Higgs boson pair production with one associated vector boson in proton-proton collisions at $ \sqrt{s} = $ 13 TeV	JHEP 10 (2024) 061	CMS-HIG-22-006 2404.08462
35	CMS Collaboration	Search for Higgs boson pairs decaying to WWWW, WW*$ \tau\tau $, and $ \tau\tau\tau\tau $ in proton-proton collisions at $ \sqrt{s} = $ 13 TeV	JHEP 07 (2023) 095	CMS-HIG-21-002 2206.10268
36	CMS Collaboration	Search for Higgs boson pair production in the $ \textrm{b}\overline{\textrm{b}}{\textrm{W}}^{+}{\textrm{W}}^{-} $ decay mode in proton-proton collisions at $ \sqrt{s} = $ 13 TeV	JHEP 07 (2024) 293	CMS-HIG-21-005 2403.09430
37	A. Hayrapetyan et al.	Combination of searches for higgs boson pair production in $ pp $ collisions at $ \sqrt{s}= $ 13 TeV with the atlas detector	PRL 133 (2024) 101801	2406.09971
38	CMS Collaboration	A portrait of the Higgs boson by the CMS experiment ten years after the discovery.	Nature 607 (2022) 60	CMS-HIG-22-001 2207.00043
39	ATLAS Collaboration	Search for pair production of boosted Higgs bosons via vector-boson fusion in the bbbb final state using pp collisions at $ \sqrt{s}= $ 13 TeV with the ATLAS detector	PLB 858 (2024) 139007	2404.17193
40	A. Tumasyan et al.	Search for higgs boson pair production in the four $ b $ quark final state in proton-proton collisions at $ \sqrt{s}= $ 13 TeV	PRL 129 (2022) 081802	2202.09617
41	CMS Collaboration	Search for Nonresonant Pair Production of Highly Energetic Higgs Bosons Decaying to Bottom Quarks	PRL 131 (2023) 041803	2205.06667
42	CMS Collaboration	Combination of searches for nonresonant Higgs boson pair production in proton-proton collisions at $ \sqrt{s}= $ 13 TeV	technical report, CERN, Geneva, 2024 CDS
43	G. Aad et al.	Search for triple higgs boson production in the 6 $ b $ final state using $ pp $ collisions at $ \sqrt{s}= $ 13 TeV with the atlas detector	PRD 111 (2025) 032006	2411.02040
44	CMS Collaboration	Search for triple Higgs production in Run2 data of CMS using 4b2gamma final state.
45	P. Stylianou and G. Weiglein	Constraints on the trilinear and quartic Higgs couplings from triple Higgs production at the LHC and beyond	EPJC 84 (2024) 366	2312.04646
46	CMS Collaboration	Precision luminosity measurement in proton--proton collisions at $ \sqrt{s}= $ 13 TeV in 2015 and 2016 at CMS	EPJC 81 (2021) 800	CMS-LUM-17-003 2104.01927
47	CMS Collaboration	CMS luminosity measurement for the 2017 data-taking period at $ \sqrt{s}= $ 13 TeV
48	CMS Collaboration	CMS luminosity measurement for the 2018 data-taking period at $ \sqrt{s}= $ 13 TeV
49	CMS Collaboration	The CMS experiment at the CERN LHC	JINST 3 (2008) S08004
50	CMS Collaboration	Development of the CMS detector for the CERN LHC Run 3	JINST 19 (2024) P05064	CMS-PRF-21-001 2309.05466
51	CMS Collaboration	Performance of the CMS Level-1 trigger in proton-proton collisions at $ \sqrt{s} = $ 13 TeV	JINST 15 (2020) P10017	CMS-TRG-17-001 2006.10165
52	CMS Collaboration	The CMS trigger system	JINST 12 (2017) P01020	CMS-TRG-12-001 1609.02366
53	CMS Collaboration	Performance of the CMS high-level trigger during LHC run 2	JINST 19 (2024) P11021	CMS-TRG-19-001 2410.17038
54	CMS Collaboration	Electron and photon reconstruction and identification with the CMS experiment at the CERN LHC	JINST 16 (2021) P05014	CMS-EGM-17-001 2012.06888
55	CMS Collaboration	Performance of the CMS muon detector and muon reconstruction with proton-proton collisions at $ \sqrt{s}= $ 13 TeV	JINST 13 (2018) P06015	CMS-MUO-16-001 1804.04528
56	CMS Collaboration	Description and performance of track and primary-vertex reconstruction with the CMS tracker	JINST 9 (2014) P10009	CMS-TRK-11-001 1405.6569
57	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	1405.0301
58	P. Nason	A new method for combining NLO QCD with shower Monte Carlo algorithms	JHEP 11 (2004) 040	hep-ph/0409146
59	S. Frixione, P. Nason, and C. Oleari	Matching NLO QCD computations with parton shower simulations: the POWHEG method	JHEP 11 (2007) 070	0709.2092
60	S. Alioli, P. Nason, C. Oleari, and E. Re	A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX	JHEP 06 (2010) 043	1002.2581
61	E. Bagnaschi, G. Degrassi, P. Slavich, and A. Vicini	Higgs production via gluon fusion in the POWHEG approach in the SM and in the MSSM	JHEP 02 (2012) 088	1111.2854
62	G. Heinrich et al.	NLO predictions for Higgs boson pair production with full top quark mass dependence matched to parton showers	JHEP 08 (2017) 088	1703.09252
63	S. Jones and S. Kuttimalai	Parton shower and NLO-matching uncertainties in Higgs boson pair production	JHEP 02 (2018) 176	1711.03319
64	G. Buchalla et al.	Higgs boson pair production in non-linear effective field theory with full $ m_\mathrm{t} $-dependence at NLO QCD	JHEP 09 (2018) 057	1806.05162
65	G. Heinrich et al.	Probing the trilinear Higgs boson coupling in di-Higgs production at NLO QCD including parton shower effects	JHEP 06 (2019) 066	1903.08137
66	G. Heinrich, S. P. Jones, M. Kerner, and L. Scyboz	A non-linear EFT description of $ \mathrm{g}\mathrm{g}\to\mathrm{H}\mathrm{H} $ at NLO interfaced to POWHEG	JHEP 10 (2020) 021	2006.16877
67	J. Davies et al.	Double Higgs boson production at NLO: Combining the exact numerical result and high-energy expansion	JHEP 11 (2019) 024	1907.06408
68	S. Frixione, P. Nason, and G. Ridolfi	A positive-weight next-to-leading-order Monte Carlo for heavy flavour hadroproduction	JHEP 09 (2007) 126	0707.3088
69	T. Jezo et al.	An NLO+PS generator for $ {\mathrm{t}\overline{\mathrm{t}}} $ and $ \mathrm{W}\mathrm{t} $ production and decay including non-resonant and interference effects	EPJC 76 (2016) 691	1607.04538
70	R. Frederix and S. Frixione	Merging meets matching in MC@NLO	JHEP 12 (2012) 061	1209.6215
71	M. Czakon and A. Mitov	Top++: A program for the calculation of the top-pair cross-section at hadron colliders	Comput. Phys. Commun. 185 (2014) 2930	1112.5675
72	M. Czakon et al.	Top-pair production at the LHC through NNLO QCD and NLO EW	JHEP 10 (2017) 186	1705.04105
73	T. Sjostrand et al.	An introduction to PYTHIA 8.2	Comput. Phys. Commun. 191 (2015) 159	1410.3012
74	CMS Collaboration	Extraction and validation of a new set of CMS PYTHIA8 tunes from underlying-event measurements	EPJC 80 (2020) 4	CMS-GEN-17-001 1903.12179
75	NNPDF Collaboration	Parton distributions from high-precision collider data	EPJC 77 (2017) 663	1706.00428
76	GEANT4 Collaboration	GEANT 4---a simulation toolkit	NIM A 506 (2003) 250
77	CMS Collaboration	Particle-flow reconstruction and global event description with the CMS detector	JINST 12 (2017) P10003	CMS-PRF-14-001 1706.04965
78	M. Cacciari, G. P. Salam, and G. Soyez	The anti-$ k_{\mathrm{T}} $ jet clustering algorithm	JHEP 04 (2008) 063	0802.1189
79	M. Cacciari, G. P. Salam, and G. Soyez	FastJet user manual	EPJC 72 (2012) 1896	1111.6097
80	CMS Collaboration	Pileup Removal Algorithms	technical report, CERN, Geneva, 2014 CDS
81	D. Bertolini, P. Harris, M. Low, and N. Tran	Pileup per particle identification	JHEP 10 (2014) 059	1407.6013
82	CMS Collaboration	Pileup mitigation at CMS in 13 TeV data	JINST 15 (2020) P09018	CMS-JME-18-001 2003.00503
83	CMS Collaboration	Jet energy scale and resolution in the CMS experiment in pp collisions at 8 TeV	JINST 12 (2017) P02014	CMS-JME-13-004 1607.03663
84	CMS Collaboration	Performance of missing transverse momentum reconstruction in proton-proton collisions at $ \sqrt{s} = $ 13 TeV using the CMS detector	JINST 14 (2019) P07004	CMS-JME-17-001 1903.06078
85	CMS Collaboration	Performance of electron reconstruction and selection with the CMS detector in proton-proton collisions at $ \sqrt{s} = $ 8 TeV	JINST 10 (2015) P06005	CMS-EGM-13-001 1502.02701
86	CMS Collaboration	Search for supersymmetry in pp collisions at $ \sqrt{s}= $ 13 TeV in the single-lepton final state using the sum of masses of large-radius jets	JHEP 08 (2016) 122	CMS-SUS-15-007 1605.04608
87	H. Qu and L. Gouskos	Jet tagging via particle clouds	PRD 101 (2020) 056019	1902.08570
88	CMS Collaboration	Performance of the ParticleNet b and bb-tagging algorithms in the CMS High-Level Trigger in Run 3	CDS
89	CMS Collaboration	Search for Higgs boson decay to a charm quark-antiquark pair via ttH production
90	CMS Collaboration	Search for $ \gamma $H production and constraints on the Yukawa couplings of light quarks to the Higgs boson		CMS-HIG-23-011 2502.05665
91	A. Shmakov et al.	SPANet: Generalized permutationless set assignment for particle physics using symmetry preserving attention	SciPost Phys. 12 (2022) 178	2106.03898
92	C.-W. Chiang, F.-Y. Hsieh, S.-C. Hsu, and I. Low	Deep learning to improve the sensitivity of Di-Higgs searches in the 4b channel	JHEP 09 (2024) 139	2401.14198
93	H. Li et al.	Reconstruction of boosted and resolved multi-Higgs-boson events with symmetry-preserving attention networks		2412.03819
94	G. Degrassi, P. P. Giardino, F. Maltoni, and D. Pagani	Probing the Higgs self coupling via single Higgs production at the LHC	JHEP 12 (2016) 080	1607.04251
95	F. Maltoni, D. Pagani, A. Shivaji, and X. Zhao	Trilinear Higgs coupling determination via single-Higgs differential measurements at the LHC	EPJC 77 (2017) 887	1709.08649
96	U. Haisch, A. Sankar, and G. Zanderighi	A new probe of the quartic Higgs self-coupling		2505.20463
97	J. M. Campbell, G. De Laurentis, and R. K. Ellis	An analytic result for the 0 $ \to gghhh $ amplitude	link	2507.19313