A global view on the Higgs self-coupling

TL;DR

The paper analyzes how to constrain the Higgs trilinear self-coupling κλ within a model-independent EFT framework by combining inclusive single-Higgs data, double-Higgs production, and differential observables in associated Higgs processes. It demonstrates that single-Higgs measurements alone contain a flat direction that prevents robust bounds on individual couplings, including κλ, but that incorporating double-Higgs production and differential distributions breaks these degeneracies and yields meaningful κλ constraints at the HL-LHC. The study also examines EFT validity, highlighting scenarios (e.g., non-linear EFT or Higgs portals) where large κλ deviations can occur and how they affect the fit, as well as robustness against experimental and theoretical uncertainties. Overall, the work provides a detailed strategy showing that, with HL-LHC data and a global EFT treatment, κλ can be probed with sensitivity comparable to or surpassing expectations from double-Higgs channels, while emphasizing the importance of including multiple observables to ensure robust bounds.

Abstract

The Higgs self-coupling is notoriously intangible at the LHC. It was recently proposed to probe the trilinear Higgs interaction through its radiative corrections to single-Higgs processes. This approach however requires to disentangle these effects from those associated to deviations of other Higgs-couplings to fermions and gauge bosons. We show that a global fit exploiting only single-Higgs inclusive data suffers from degeneracies that prevent one from extracting robust bounds on each individual coupling. We show how the inclusion of double-Higgs production via gluon fusion, and the use of differential measurements in the associated single-Higgs production channels WH, ZH and ttH, can help to overcome the deficiencies of a global Higgs-couplings fit. In particular, we bound the variations of the Higgs trilinear self-coupling relative to its SM value to the interval [0.1, 2.3] at 68% confidence level at the high-luminosity LHC, and we discuss the robustness of our results against various assumptions on the experimental uncertainties and the underlying new physics dynamics. We also study how to obtain a parametrically enhanced deviation of the Higgs self-couplings and we estimate how large this deviation can be in a self-consistent effective field theory framework.

Figures (6)

• Figure 1: Variation of the Higgs basis parameters along the flat direction as a function of the Higgs trilinear coupling $\kappa_\lambda$. The gray bands correspond to the $1\sigma$ error bands at the high-luminosity LHC (see eq. (\ref{['eq:1sigmaunc']})).
• Figure 2: $\chi^2$ as a function of the Higgs trilinear coupling $\kappa_\lambda$ obtained by performing a global fit including the constraints coming from TGC's measurements and the bound on the $h\to Z\gamma$ decay rate. The results are obtained by assuming an integrated luminosity of $3/{\rm ab}$ at $14$ TeV. The dotted curve corresponds to the result obtained by setting to zero all the other the Higgs-coupling parameters, while the solid curve is obtained by profiling and is multiplied by a factor $20$ to improve its visibility. To compare with previous literature (ref. Degrassi:2016wml), we also display the exclusive fit performed assuming the uncertainty projections from the more optimistic 'Scenario 2' of CMS CMS:2013xfa (dashed curve).
• Figure 3: Constraints in the planes $(\delta y_t, \hat{c}_{gg})$ (left panel) and $(\delta y_b, \hat{c}_{\gamma\gamma})$ (right panel) obtained from a global fit on the single-Higgs processes. The darker regions are obtained by fixing the Higgs trilinear to the SM value $\kappa_\lambda = 1$, while the lighter ones are obtained through profiling by restricting $\delta \kappa_\lambda$ in the ranges $|\delta \kappa_\lambda| \leq 10$ and $|\delta \kappa_\lambda| \leq 20$ respectively. The regions correspond to $68\%$ confidence level (defined in the Gaussian limit corresponding to $\Delta \chi^2 = 2.3$).
• Figure 4: Left: The solid curve shows the global $\chi^2$ as a function of the corrections to the Higgs trilinear self-coupling obtained from a fit exploiting inclusive single Higgs and inclusive double Higgs observables. The dashed line shows the fit obtained by neglecting the dependence on $\delta \kappa_\lambda$ in single-Higgs observables. The dotted line is obtained by exclusive fit in which all the EFT parameters, except for $\delta \kappa_\lambda$, are set to zero. Right: The same but using differential observables for double Higgs.
• Figure 5: Left:$\chi^2$ as a function of the Higgs trilinear self-coupling. The green bands are obtained from the differential analysis on single-Higgs observables and are delimited by the fits corresponding to the optimistic and pessimistic estimates of the experimental uncertainties. The dotted green curves correspond to a fit performed exclusively on $\delta \kappa_\lambda$ setting to zero all the other parameters, while the solid green lines are obtained by a global fit profiling over the single-Higgs coupling parameters. Right: The red lines show the fits obtained by a combination of single-Higgs and double-Higgs differential observables. In both panels the dark blue curves are obtained by considering only double-Higgs differential observables and coincide with the results shown in fig. \ref{['fig:chi2c3_hh']}.