CMS-PAS-HIG-23-006

CMS-PAS-HIG-23-006
Constraints on the Higgs boson self-coupling with combination of single and double Higgs boson production
CMS Collaboration
28 November 2023

Abstract: A combination of Higgs boson (H) measurements and searches for the production of Higgs boson pairs (HH) is presented, aiming to constrain the H trilinear self-coupling $\lambda_3$ , using the proton-proton collision data collected by the CMS experiment at $\sqrt{s} =$ 13 TeV. The cross section of the main H production modes and the branching ratios of the principal decay channels depend on $\lambda_3$ because of next-to-leading-order electroweak corrections. On the other hand, the cross section of the HH production via gluon fusion and via vector boson fusion depend on $\lambda_3$ as well as on the H couplings to the top quark, and to vector bosons, respectively. The combination of event categories enriched in single-H and HH events allows the extraction of constraints on $\kappa_\lambda$ , defined as the value of $\lambda_3$ normalized to its standard model prediction, with fewer assumptions on the H couplings to the fermions and vector bosons. Values of $\kappa_\lambda$ outside the interval $-1.2 < \kappa_\lambda <$ 7.5 are excluded at 95% confidence level, which is compatible with the expected range of $-2.0 < \kappa_\lambda <$ 7.7 under the assumption that all the other H couplings are at the standard model predicted values.
Links: CDS record (PDF) ; Physics Briefing ; CADI line (restricted) ; These preliminary results are superseded in this paper, Submitted to PLB. The superseded preliminary plots can be found here.

Figures & Tables	Summary	Additional Figures	References	CMS Publications

Figures
png pdf	Figure 1: Feynman diagrams for the LO HH production via gluon fusion.
png pdf	Figure 2: Feynman diagrams for the LO HH production via vector boson fusion.
png pdf	Figure 2-a: Feynman diagrams for the LO HH production via vector boson fusion.
png pdf	Figure 2-b: Feynman diagrams for the LO HH production via vector boson fusion.
png pdf	Figure 2-c: Feynman diagrams for the LO HH production via vector boson fusion.
png pdf	Figure 3: Feynman diagrams corresponding to the $\kappa_\lambda$ -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 the $\kappa_\lambda$ -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 the $\kappa_\lambda$ -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 the $\kappa_\lambda$ -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 the $\kappa_\lambda$ -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 the $\kappa_\lambda$ -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 the $\kappa_\lambda$ -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 profiled likelihood scans of $\kappa_\lambda$ comparing the full combination of single H and HH to the combinations of only single H or only HH channels.
png pdf	Figure 5: Observed two-dimensional likelihood scans of $(\kappa_\lambda, k_{\mathrm{T}})$ comparing the full combination of single H and HH to the combinations of only single H or only HH 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 to the combinations of only single H or only HH channels. The best fit point for the single H combination can not be calculated because this combination has no sensitivity on the $\kappa_{2\mathrm{V}}$ parameter.
png pdf	Figure 7: Observed likelihood scans of $\kappa_\lambda$ assuming $\kappa_\mathrm{V}$ , $\kappa_{2\mathrm{V}}$ , $k_{\mathrm{T}}$ , $\kappa_\mathrm{b}$ , $\kappa_\tau$ , and $\kappa_\mu$ as unconstrained nuisance parameters.

Tables
png pdf	Table 1: Analyses targeting single H production modes and decay channels included in the combination and the corresponding dataset size, in terms of integrated luminosity. The maximum phase space granularity of the cross section measurements are also reported.
png pdf	Table 2: Analyses targeting HH searches included in this combination and the corresponding HH production modes targeted with dedicated categories.
png pdf	Table 3: Summary of overlaps between the considered single H and HH analyses included in this combination. Non-overlapping analyses are indicated by a $\checkmark$ , overlaps removable with negligible impacts on the combination are indicated by a $\mathcal{X}$ .
png pdf	Table 4: Expected and observed constraints on $\kappa_\lambda$ at 95 $%$ confidence levels 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.

Summary

The combination of single Higgs boson (H) measurements and searches for Higgs boson pair production (HH), to constrain the Higgs boson trilinear self-coupling, is presented in this document. 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 at the CMS experiment. The complementarity of the constraints on the Higgs boson couplings of the single H and HH channels is exploited in the combination. The inclusion of the single H channels improves the constraints on

$\kappa_\lambda$ under minimal assumptions on the Higgs boson couplings to fermions and vector bosons. The observed (expected) confidence interval at 95% on

$\kappa_\lambda$ assuming the other Higgs boson couplings fixed to the SM prediction, is found to be

$-1.2 < \kappa_\lambda <$ 7.5 (

$-2.0 < \kappa_\lambda <$ 7.7). Under minimal assumptions on the Higgs boson couplings to fermions and vector bosons, the observed (expected) exclusion interval at 95% on

$\kappa_\lambda$ is

$-2.3 < \kappa_\lambda <$ 7.8 (

$-1.4 < \kappa_\lambda <$ 7.8).

Additional Figures

png pdf

Additional Figure 1:
Constraints on the Higgs boson trilinear self-coupling modifier from the separate combinations of the single H channels or the HH ones, and from the combination of the two. In case a pair of analysis regions defined in a single H and a HH channel have a non negligible overlap, one of the two is removed from all combinations. The Higgs boson couplings to fermions and vector bosons are assumed to be equal to their SM prediction.

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