CMS-HIG-23-006

CMS-HIG-23-006 ; CERN-EP-2024-145
Constraints on the Higgs boson self-coupling from the combination of single and double Higgs boson production in proton-proton collisions at $\sqrt{s} =$ 13 TeV
CMS Collaboration
18 July 2024
Phys. Lett. B 861 (2025) 139210
Abstract: The Higgs boson (H) trilinear self-coupling, $\lambda_3$ , is constrained via its measured properties and limits on the HH pair production using the proton-proton collision data collected by the CMS experiment at $\sqrt{s} =$ 13 TeV. The combination of event categories enriched in single-H and HH events is used to measure $\kappa_\lambda$ , defined as the value of $\lambda_3$ normalized to its standard model prediction, while simultaneously constraining the Higgs boson couplings to fermions and vector bosons. Values of $\kappa_\lambda$ outside the interval $-$ 1.2 $< \kappa_\lambda <$ 7.5 are excluded at 2 $\sigma$ confidence level, which is compatible with the expected range of $-$ 2.0 $< \kappa_\lambda <$ 7.7 under the assumption that all other Higgs boson couplings are equal to their standard model predicted values. Relaxing the assumption on the Higgs couplings to fermions and vector bosons the observed (expected) $\kappa_\lambda$ interval is constrained to be within $-$ 1.4 $< \kappa_\lambda <$ 7.8 ( $-$ 2.3 $< \kappa_\lambda <$ 7.8) at 2 $\sigma$ confidence level.
Links: e-print arXiv:2407.13554 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; Physics Briefing ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Feynman diagrams for the LO HH production via gluon fusion. $\kappa_{f}$ corresponds to the modifier of the Higgs boson coupling strength (Section 4) to fermions.
png pdf	Figure 1-a: Feynman diagrams for the LO HH production via gluon fusion. $\kappa_{f}$ corresponds to the modifier of the Higgs boson coupling strength (Section 4) to fermions.
png pdf	Figure 1-b: Feynman diagrams for the LO HH production via gluon fusion. $\kappa_{f}$ corresponds to the modifier of the Higgs boson coupling strength (Section 4) to fermions.
png pdf	Figure 2: Feynman diagrams for the LO HH production via vector boson fusion. $\kappa_\mathrm{V}$ and $\kappa_{2\mathrm{V}}$ correspond to the modifiers of the Higgs boson coupling strength (Section 4) to one and a pair of vector bosons, respectively.
png pdf	Figure 2-a: Feynman diagrams for the LO HH production via vector boson fusion. $\kappa_\mathrm{V}$ and $\kappa_{2\mathrm{V}}$ correspond to the modifiers of the Higgs boson coupling strength (Section 4) to one and a pair of vector bosons, respectively.
png pdf	Figure 2-b: Feynman diagrams for the LO HH production via vector boson fusion. $\kappa_\mathrm{V}$ and $\kappa_{2\mathrm{V}}$ correspond to the modifiers of the Higgs boson coupling strength (Section 4) to one and a pair of vector bosons, respectively.
png pdf	Figure 2-c: Feynman diagrams for the LO HH production via vector boson fusion. $\kappa_\mathrm{V}$ and $\kappa_{2\mathrm{V}}$ correspond to the modifiers of the Higgs boson coupling strength (Section 4) to one and a pair of vector bosons, respectively.
png pdf	Figure 3: Feynman diagrams corresponding to $\kappa_\lambda$ -dependent NLO corrections to the main single-H production mechanisms (in the two top rows), to the $\mathrm{H}\to\mathrm{V}\mathrm{V}$ decay width (bottom left) and to the Higgs boson propagator (bottom right).
png pdf	Figure 3-a: Feynman diagrams corresponding to $\kappa_\lambda$ -dependent NLO corrections to the main single-H production mechanisms (in the two top rows), to the $\mathrm{H}\to\mathrm{V}\mathrm{V}$ decay width (bottom left) and to the Higgs boson propagator (bottom right).
png pdf	Figure 3-b: Feynman diagrams corresponding to $\kappa_\lambda$ -dependent NLO corrections to the main single-H production mechanisms (in the two top rows), to the $\mathrm{H}\to\mathrm{V}\mathrm{V}$ decay width (bottom left) and to the Higgs boson propagator (bottom right).
png pdf	Figure 3-c: Feynman diagrams corresponding to $\kappa_\lambda$ -dependent NLO corrections to the main single-H production mechanisms (in the two top rows), to the $\mathrm{H}\to\mathrm{V}\mathrm{V}$ decay width (bottom left) and to the Higgs boson propagator (bottom right).
png pdf	Figure 3-d: Feynman diagrams corresponding to $\kappa_\lambda$ -dependent NLO corrections to the main single-H production mechanisms (in the two top rows), to the $\mathrm{H}\to\mathrm{V}\mathrm{V}$ decay width (bottom left) and to the Higgs boson propagator (bottom right).
png pdf	Figure 3-e: Feynman diagrams corresponding to $\kappa_\lambda$ -dependent NLO corrections to the main single-H production mechanisms (in the two top rows), to the $\mathrm{H}\to\mathrm{V}\mathrm{V}$ decay width (bottom left) and to the Higgs boson propagator (bottom right).
png pdf	Figure 3-f: Feynman diagrams corresponding to $\kappa_\lambda$ -dependent NLO corrections to the main single-H production mechanisms (in the two top rows), to the $\mathrm{H}\to\mathrm{V}\mathrm{V}$ decay width (bottom left) and to the Higgs boson propagator (bottom right).
png pdf	Figure 4: Observed profile likelihood scans of $\kappa_\lambda$ comparing the full combination of single-H and HH (red) to the combinations of only single-H (blue) or only HH (yellow) channels. The legend includes the best-fit values and the 1 $\sigma$ uncertainties.
png pdf	Figure 5: Observed two-dimensional likelihood scans of $(\kappa_\lambda, \kappa_{\mathrm{t}})$ comparing the full combination of single-H and HH (red) to the combinations of only single-H (blue) or only HH (yellow) channels.
png pdf	Figure 6: Observed two-dimensional likelihood scans of $(\kappa_\mathrm{V}, \kappa_{2\mathrm{V}})$ comparing the full combination of single-H and HH (red) to the combinations of only single-H (blue) or only HH (yellow) channels. The single-H combination has no sensitivity on the $\kappa_{2\mathrm{V}}$ parameter.
png pdf	Figure 7: Observed likelihood scans of $\kappa_\lambda$ assuming $\kappa_\mathrm{V}$ , $\kappa_{2\mathrm{V}}$ , $\kappa_{\mathrm{t}}$ , $\kappa_\mathrm{b}$ , $\kappa_\tau$ , and $\kappa_\mu$ as unconstrained nuisance parameters. The legend includes the best-fit value and the 1 $\sigma$ uncertainty.

Tables
png pdf	Table 1: Analyses targeting single-H production modes and decay channels included in the combination and the corresponding data set sizes, in terms of integrated luminosity. The production modes targeted with dedicated analysis categories and the maximum phase space granularity of each cross section measurement are also reported.
png pdf	Table 2: The HH searches included in the combination and the corresponding data set sizes, in terms of integrated luminosity. The HH production modes targeted with dedicated event categories are also reported.
png pdf	Table 3: Expected and observed constraints on $\kappa_\lambda$ at 2 $\sigma$ and best fit values from the combination of the single-H and HH channels under different assumptions on the Higgs boson couplings to fermions and vector bosons. The floating coupling parameters are either treated as POIs or as unconstrained nuisance parameters in the fit. The parameters that are not listed as floating are always assumed fixed to the SM prediction.

Summary

A combination of Higgs boson (H) measurements and searches for Higgs boson pair production (HH) to constrain the Higgs boson trilinear self-coupling has been presented. Proton-proton collision data at

$\sqrt{s} =$ 13 TeV, collected by the CMS experiment between 2016 and 2018, were analyzed. This is the first combination of single-H and HH channels from the CMS Collaboration. The complementarity of the constraints on the Higgs boson couplings of the single-H and HH channels is employed in the combination. The single-H channels lessen the assumptions on the measurements on the modifier of the Higgs boson trilinear self-coupling

$\kappa_\lambda$ , allowing for simultaneous constraint of the Higgs boson couplings to fermions and vector bosons. The observed (expected) interval at 2

$\sigma$ confidence level on

$\kappa_\lambda$ under the assumption that the other Higgs boson couplings are fixed to the standard model prediction, is found to be

$-$ 1.2

$< \kappa_\lambda <$ 7.5 (

$-$ 2.0

$< \kappa_\lambda <$ 7.7). Relaxing the assumption on the Higgs couplings to fermions and vector bosons the corresponding observed (expected) interval on

$\kappa_\lambda$ is

$-$ 1.4

$< \kappa_\lambda <$ 7.8 (

$-$ 2.3

$< \kappa_\lambda <$ 7.8).

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