A detailed map of Higgs boson interactions by the ATLAS experiment ten years after the discovery

The Higgs boson production rates are probed by the likelihood fit to observed signal yields described earlier. Because the production cross-section σi and the branching fraction Bf for a specific production process i and decay mode f cannot be measured separately without further assumptions, the observed signal yield for a given process is expressed in terms of a single signal strength modifier μif=(σi/σiSM)(Bf/BfSM), where the superscript ‘SM’ denotes the corresponding standard model prediction. Assuming that all production and decay processes scale with the same global signal strength μ = μif, the inclusive Higgs boson production rate relative to the standard model prediction is measured to be

The total measurement uncertainty is decomposed into components for statistical uncertainties, experimental systematic uncertainties, and theory uncertainties in both signal and background modelling. Both the experimental and the theoretical uncertainties are almost a factor of two lower than in the Run 1 result. The presented measurement supersedes the previous ATLAS combination with a partial Run 2 dataset, decreasing the latest total measurement uncertainty by about 30%.

Higgs boson production is also studied per individual process. As opposed to the top quark decay products from tt¯H production, the identification efficiency of b jets from the bb¯H production is low, making the bb¯H process experimentally indistinguishable from ggF production. The bb¯H and ggF processes are therefore grouped together, with bb¯H contributing a relatively small amount: of the order of 1% to the total ggF+bb¯H production. In cases where several processes are combined, the combination assumes the relative fractions of the components to be those from the standard model within corresponding theory uncertainties. Results are obtained from the fit to the data, where the cross-section of each production process is a free parameter of the fit. Higgs boson decay branching fractions are set to their standard model values, within the uncertainties specified previously. The results are shown in Fig. 2a.

All measurement results are compatible with the standard model predictions. For the ggF and VBF production processes, which were previously observed in Run 1 data, the cross-sections are measured with a precision of 7% and 12%, respectively. The following production processes are now also observed: WH with an observed (expected) signal significance of 5.8 (5.1) standard deviations (σ), ZH with 5.0σ (5.5σ) and the combined tt¯H and tH production processes with 6.4σ (6.6σ), where the expected signal significances are obtained under the standard model hypothesis. The separate tt¯H and tH measurements lead to an observed (expected) upper limit on tH production of 15 (7) times the standard model prediction at the 95% confidence level (CL), with a relatively large negative correlation coefficient of 56% between the two measurements. This is due to cross-contamination between the tt¯H and tH processes in the set of reconstructed events that provide the highest sensitivity to these production processes.

Branching fractions of individual Higgs boson decay modes are measured by setting the cross-sections for Higgs boson production processes to their respective standard model values. The results are shown in Fig. 2b. The branching fractions of the γγ, ZZ, W±W∓ and τ+τ− decays, which were already observed in the Run 1 data, are measured with a precision ranging from 10% to 12%. The bb¯ decay mode is observed with a signal significance of 7.0σ (expected 7.7σ), and the observed (expected) signal significances for the H → μ+μ− and H → Zγ decays are 2.0σ (1.7σ) and 2.3σ (1.1σ), respectively.

The assumptions about the relative contributions of different decay or production processes in the above measurements are relaxed by directly measuring the product of production cross-section and branching fraction for different combinations of production and decay processes. The corresponding results are shown in Fig. 3. The measurements are in agreement with the standard model prediction.

To determine the value of a particular Higgs boson coupling strength, a simultaneous fit of many individual production times branching fraction measurements is required. The coupling fit presented here is performed within the κ framework with a set of parameters κ that affect the Higgs boson coupling strengths without altering any kinematic distributions of a given process.

Within this framework, the cross-section times the branching fraction for an individual measurement is parameterized in terms of the multiplicative coupling strength modifiers κ. A coupling strength modifier κp for a production or decay process via the coupling to a given particle p is defined as κp2=σp/σpSM or κp2=Γp/ΓpSM, respectively, where Γp is the partial decay width into a pair of particles p. The parameterization takes into account that the total decay width depends on all decay modes included in the present measurements, as well as currently undetected or invisible, direct or indirect decays predicted by the standard model (such as those to gluons, light quarks or neutrinos) and the hypothetical decays into non-standard model particles. The decays to non-standard model particles are divided into decays to invisible particles and other decays that would be undetected owing to large backgrounds. The corresponding branching fractions for the two are denoted by Binv. and Bu., respectively.

In the following, three classes of models with progressively fewer assumptions about coupling strength modifiers are considered. Standard model values are assumed for the coupling strength modifiers of first-generation fermions, and the modifiers of the second-generation quarks are set to those of the third generation, except where κc is left free-floating in the fit. Owing to their small sizes, these couplings are not expected to noticeably affect any of the results. The ggF production and the H → γγ and H → Zγ decays are loop-induced processes. They are either expressed in terms of the more fundamental coupling strength scale factors corresponding to the particles that contribute to the loop-induced processes in the standard model, or treated using effective coupling strength modifiers κg, κγ and κZγ, respectively. The latter scenario accounts for possible loop contributions from particles beyond the standard model. The small contribution from the loop-induced gg → ZH process is always parameterized in terms of the couplings to the corresponding standard model particles.

The first model tests one scale factor for the vector bosons, κV = κW = κZ, and a second, κF, which applies to all fermions. In general, the standard model prediction of κV = κF = 1 does not hold in extensions of the standard model. For example, the values of κV and κF would be less than 1 in models in which the Higgs boson is a composite particle. The effective couplings corresponding to the ggF, H → γγ and H → Zγ loop-induced processes are parameterized in terms of the fundamental standard model couplings. It is assumed that there are no invisible or undetected Higgs boson decays beyond the standard model, that is, Binv. = Bu. = 0. As only the relative sign between κV and κF is physical and a negative relative sign has been excluded with a high level of confidence, κV ≥ 0 and κF ≥ 0 are assumed. Figure 4 shows the results of a combined fit in the (κV, κF) plane. The best-fit values and their uncertainties from the combined fit are κV = 1.035 ± 0.031 and κF = 0.95 ± 0.05, compatible with the standard model predictions. A relatively large positive correlation of 39% is observed between the two fit parameters, because some of the most sensitive input measurements involve the ggF production process (that is, via couplings to fermions) with subsequent Higgs boson decays into vector bosons.

In the second class of models, the coupling strength modifiers for W, Z, t, b, c, τ and μ are treated independently. All modifiers are assumed to be positive. It is assumed that only standard model particles contribute to the loop-induced processes, and modifications of the fermion and vector boson couplings are propagated through the loop calculations. Invisible or undetected non-standard model Higgs boson decays are not considered. These models enable testing of the predicted scaling of the couplings of the Higgs boson to the standard model particles as a function of their mass using the reduced coupling strength modifiers κVgV/2vev=κV(mV/vev) for weak bosons with a mass mV and κFgF = κFmF/vev for fermions with a mass mF, where gV and gF are the corresponding absolute coupling strengths and ‘vev’ is the vacuum expectation value of the Higgs field. Figure 5 shows the results for two scenarios: one with the coupling to c quarks constrained by κc = κt in order to cope with the low sensitivity to this coupling; and the other with κc left as a free parameter in the fit. All measured coupling strength modifiers are found to be compatible with their standard model prediction. When the coupling strength modifier κc is left unconstrained in the fit, an upper limit of κc < 5.7 (7.6) times the standard model prediction is observed (expected) at 95% CL and the uncertainty in each of the other parameters increases because of the resulting weaker constraint on the total decay width. This improves the current observed (expected) limit of κc < 8.5 (12.4) at 95% CL from the individual measurement of H→cc¯ decays despite the relaxed assumptions on other coupling strength modifiers, through constraints coming from the parameterization of the total Higgs boson decay width that impacts all measurements.

The third class of models in the κ framework closely follows the previous one, but allows for the presence of non-standard model particles in the loop-induced processes. These processes are parameterized by the effective coupling strength modifiers κg, κγ and κZγ instead of propagating modifications of the standard model particle couplings through the loop calculations. It is also assumed that any potential effect beyond the standard model does not substantially affect the kinematic properties of the Higgs boson decay products. The fit results for the scenario in which invisible or undetected non-standard model Higgs boson decays are assumed not to contribute to the total Higgs decay width, that is, Binv. = Bu. = 0, are shown in Fig. 6 together with the results for the scenario allowing such decays. To avoid degenerate solutions, the latter constrains Bu. ≥ 0 and imposes the additional constraint κV ≤ 1 that naturally arises in various scenarios of physics beyond the standard model. All measured coupling strength modifiers are compatible with their standard model predictions.

When allowing invisible or undetected non-standard model Higgs boson decays to contribute to the total Higgs boson decay width, the previously measured coupling strength modifiers do not change significantly, and upper limits of Bu. < 0.12 (expected 0.21) and Binv. < 0.13 (expected 0.08) are set at 95% CL on the corresponding branching fraction. The latter improves on the current best limit of Binv. < 0.145 (expected 0.103) from direct ATLAS searches.

In all tested scenarios, the statistical and the systematic uncertainty contribute almost equally to the total uncertainty in most of the κ parameter measurements. The exceptions are the κμ, κZγ, κc and Bu. measurements, for which the statistical uncertainty still dominates.

Kinematic properties of Higgs boson production probing the internal structure of its couplings are studied in the framework of simplified template cross-sections. The framework partitions the phase space of standard model Higgs boson production processes into a set of regions defined by the specific kinematic properties of the Higgs boson and, where relevant, of the associated jets, W bosons, or Z bosons, as described in Methods. The regions are defined so as to provide experimental sensitivity to deviations from the standard model predictions, to avoid large theory uncertainties in these predictions, and to minimize the model-dependence of their extrapolations to the experimentally accessible signal regions. Signal cross-sections measured in each of the introduced kinematic regions are compared with those predicted when assuming that the branching fractions and kinematic properties of the Higgs boson decay are described by the standard model.

The results of the simultaneous measurement in 36 kinematic regions are presented in Fig. 7. Compared to previous results with a smaller dataset, a much larger number of regions are probed, particularly at high Higgs boson transverse momenta, where in many cases the sensitivity to new phenomena beyond the standard model is expected to be enhanced. All measurements are consistent with the standard model predictions.