Measurements of the Higgs boson production and decay rates and coupling strengths using pp collision data at [Formula: see text] and 8 TeV in the ATLAS experiment

Abstract

Combined analyses of the Higgs boson production and decay rates as well as its coupling strengths to vector bosons and fermions are presented. The combinations include the results of the analyses of the [Formula: see text] and [Formula: see text] decay modes, and the constraints on the associated production with a pair of top quarks and on the off-shell coupling strengths of the Higgs boson. The results are based on the LHC proton-proton collision datasets, with integrated luminosities of up to 4.7 [Formula: see text] at [Formula: see text] TeV and 20.3 [Formula: see text] at [Formula: see text] TeV, recorded by the ATLAS detector in 2011 and 2012. Combining all production modes and decay channels, the measured signal yield, normalised to the Standard Model expectation, is [Formula: see text]. The observed Higgs boson production and decay rates are interpreted in a leading-order coupling framework, exploring a wide range of benchmark coupling models both with and without assumptions on the Higgs boson width and on the Standard Model particle content in loop processes. The data are found to be compatible with the Standard Model expectations for a Higgs boson at a mass of 125.36 GeV for all models considered.

Fig. 1

Summary of the signal-strength measurements, as published, from individual analyses that are inputs to the combinations. The Higgs boson mass column indicates the $m_H$ value at which the result is quoted. The overall signal strength of each analysis (black) is the combined result of the measurements for different production processes (blue) assuming SM values for their cross-section ratios. The error bars represent $\pm 1\mathit{\sigma }$ total uncertainties, combining statistical and systematic contributions. The green shaded bands indicate the uncertainty on the overall signal strength obtained by each analysis. The combined signal strength of the $H\to \mathit{\gamma }\mathit{\gamma }$ analysis also includes the ttH contribution which is listed separately under ttH production

Fig. 2

The observed signal strengths and uncertainties for different Higgs boson decay channels and their combination for $m_H=125.36$ GeV. Higgs boson signals corresponding to the same decay channel are combined together for all analyses, assuming SM values for the cross-section ratios of different production processes. The best-fit values are shown by the solid vertical lines. The total $\pm 1\mathit{\sigma }$ uncertainties are indicated by green shaded bands, with the individual contributions from the statistical uncertainty (top), the total (experimental and theoretical) systematic uncertainty (middle), and the signal theoretical uncertainty (bottom) on the signal strength shown as horizontal error bars

Fig. 3

The best-fit signal-strength values of different production modes determined from the combined fit to the $\sqrt{s}=7$ and 8 TeV data. Higgs boson signals corresponding to the same production process but from different decay channels are combined together, assuming SM values for the ratios of the branching ratios of different Higgs boson decay channels. The inner and outer error bars correspond to 68  and 95 % CL intervals. Total uncertainties combining statistical, experimental and theoretical systematic uncertainties are shown

Fig. 4

Likelihood contours in the $({\mathit{\mu }}_{\mathrm{ggF}+ttH}^f,{\mathit{\mu }}_{\mathrm{VBF}+VH}^f)$ plane for a Higgs boson mass $m_H=125.36$ GeV measured separately for $H\to W{W}^{\ast },Z{Z}^{\ast },b\overline{b},\mathit{\gamma }\mathit{\gamma }$ and $\mathit{\tau }\mathit{\tau }$ decays. SM values are assumed for the relative contributions between ggF and ttH and between VBF and VH production. The straight lower portions of the $H\to \mathit{\gamma }\mathit{\gamma }$ and $H\to Z{Z}^{\ast }\to 4\ell$ contours are due to the small numbers of events in these channels and the requirement of a positive probability density function. The best-fit values to the data (plus symbol) and the $68\%$ (full) and $95\%$ (dashed) CL contours are indicated, as well as the SM expectation $(\ast )$

Fig. 5

The ratios of cross sections for the vector-boson- and fermion-mediated processes relative to their SM values at $m_H=125.36$ GeV, measured in the individual Higgs boson decay final states and their combination, $R_{\mathrm{Combined}}$ (see text). The inner and outer error bars represent 68 and 95 % CL intervals, combining statistical and systematic uncertainties. These measurements are independent of Higgs boson decay branching ratios

Fig. 6

The $gg\to H\to W{W}^{\ast }$ cross section, ratios of cross sections and of partial decay widths relative to their SM values at $m_H=125.36$ GeV from the combined analyses of the $\sqrt{s}=7$ and 8 TeV data. The inner and outer error bars on the measurements are 68 and 95 % CL intervals. The SM predictions are shown as the vertical line at unity with grey bands representing theoretical uncertainties on the ratios of inclusive cross sections and of partial decay widths

Fig. 7

Feynman diagrams of Higgs boson production via a the ggF and b VBF production processes

Fig. 8

Feynman diagrams of Higgs boson production via a the $q\overline{q}\to VH$ and b, c $gg\to ZH$ production processes

Fig. 9

Feynman diagrams of Higgs boson production via a the ttH (bbH) and b, c $tH{q}^{\prime }b$ and d, e WtH processes

Fig. 10

Feynman diagrams of Higgs boson decays a to W and Z bosons and b to fermions

Fig. 11

Feynman diagrams of Higgs boson decays to a pair of photons, or to a photon and a Z boson

Fig. 12

Results of fits for the two-parameter benchmark model defined in Sect. 5.2.1 that probes different coupling-strength scale factors for fermions and vector bosons, assuming only SM contributions to the total width: a results of the two-dimensional fit to ${\mathit{\kappa }}_F$ and ${\mathit{\kappa }}_V$, including $68\%$ and $95\%$ CL contours; overlaying the $68\%$ CL contours derived from the individual channels and their combination; b the same measurement, without the overlays of the individual channels; c the profile likelihood ratio as a function of the coupling-strength scale factors ${\mathit{\kappa }}_F$ (${\mathit{\kappa }}_V$ is profiled) and d as a function of  ${\mathit{\kappa }}_V$ (${\mathit{\kappa }}_F$ is profiled). The dashed curves in c and d show the SM expectations. In d the sign of the chosen profiled solution for ${\mathit{\kappa }}_F$ changes at ${\mathit{\kappa }}_V\approx 0.8$ , causing a kink in the likelihood. The profile likelihood curves restricting ${\mathit{\kappa }}_F$ to be either positive or negative are also shown to illustrate that this sign change in the unrestricted profile likelihood is the origin of the kink. The red (green) horizontal line indicates the value of the profile likelihood ratio corresponding to a 68 % (95 %) confidence interval for the parameter of interest, assuming the asymptotic ${\mathit{\chi }}^2$ distribution for the test statistic

Fig. 13

Results of fits for benchmark models that probe for potential extra contributions to the total width, but do not allow contributions from non-SM particles in the $H\to \mathit{\gamma }\mathit{\gamma }$, $gg\to H$ and $H\to Z\mathit{\gamma }$ loops, with free gauge and fermion coupling-strength scale factors ${\mathit{\kappa }}_V,{\mathit{\kappa }}_F$. The estimated values of each parameter under the constraint ${\mathit{\kappa }}_V<1$, ${\mathit{\kappa }}_{\mathrm{on}}={\mathit{\kappa }}_{\mathrm{off}}$ or ${\mathrm{BR}}_{\mathrm{i}.,\mathrm{u}.}=0$ are shown with markers in the shape of box, circle, or diamond, respectively. The inner and outer bars correspond to 68 and 95 % CL intervals. The confidence intervals of ${\mathrm{BR}}_{\mathrm{i}.,\mathrm{u}.}$ and, in the benchmark model with the constraint ${\mathit{\kappa }}_V<1$, also ${\mathit{\kappa }}_V$, are estimated with respect to their physical bounds, as described in the text. The numerical values of the fit under the constraint ${\mathit{\kappa }}_V<1$ are shown on the left. Values for the two alternative constraints are also shown (in a reduced font size due to space constraints)

Fig. 14

Results of fits for the two-parameter benchmark model defined in Sect. 5.2.3 that probes different coupling-strength scale factors for fermions and vector bosons without assumptions about the total width: a profile likelihood ratio as a function of the coupling-strength scale factor ratio ${\mathit{\lambda }}_{FV}$ (${\mathit{\kappa }}_{VV}$ is profiled). The dashed curve shows the SM expectation. The red (green) horizontal line indicates the value of the profile likelihood ratio corresponding to a 68 % (95 %) confidence interval for the parameter of interest, assuming the asymptotic ${\mathit{\chi }}^2$ distribution for the test statistic. b Results of the two-dimensional fit to ${\mathit{\kappa }}_{VV}$ and ${\mathit{\lambda }}_{FV}$, including 68 and 95 % CL contours

Fig. 15

Results of fits for the benchmark model described in Sect. 5.3.1 that probes the ratio of scale factors between down- and up-type fermions: profile likelihood ratios as functions of the coupling-strength scale factor ratios a ${\mathit{\lambda }}_{du}$ (${\mathit{\lambda }}_{Vu}$ and ${\mathit{\kappa }}_{uu}$ are profiled), b ${\mathit{\lambda }}_{Vu}$ (${\mathit{\lambda }}_{du}$ and ${\mathit{\kappa }}_{uu}$ are profiled), and c the overall scale factor ${\mathit{\kappa }}_{uu}$ (${\mathit{\lambda }}_{du}$ and ${\mathit{\lambda }}_{Vu}$ are profiled). The dashed curves show the SM expectations. The red (green) horizontal line indicates the value on the profile likelihood ratio corresponding to a 68 % (95 %) confidence interval for the parameter of interest, assuming the asymptotic ${\mathit{\chi }}^2$ distribution for the test statistic

Fig. 16

Results of fits for the benchmark model described in Sect. 5.3.2 that probes the symmetry between quarks and leptons: profile likelihood ratios as functions of the coupling-strength scale factor ratios a ${\mathit{\lambda }}_{\ell q}$ (${\mathit{\lambda }}_{Vq}$ and ${\mathit{\kappa }}_{qq}$ are profiled), b ${\mathit{\lambda }}_{Vq}$ (${\mathit{\lambda }}_{\ell q}$ and ${\mathit{\kappa }}_{qq}$ are profiled), and c the overall scale factor ${\mathit{\kappa }}_{qq}$ (${\mathit{\lambda }}_{\ell q}$ and ${\mathit{\lambda }}_{Vq}$ are profiled). The dashed curves show the SM expectations. The red (green) horizontal line indicates the value of the profile likelihood ratio corresponding to a 68 % (95 %) confidence interval for the parameter of interest, assuming the asymptotic ${\mathit{\chi }}^2$ distribution for the test statistic

Fig. 17

Results of fits for the benchmark model that probes for contributions from non-SM particles in the $H\to \mathit{\gamma }\mathit{\gamma }$, $H\to Z\mathit{\gamma }$ and $gg\to H$ loops, assuming no extra contributions to the total width: a overview of fitted parameters, where the inner and outer bars correspond to 68 and 95 % CL intervals, and b results of the two-dimensional fit to ${\mathit{\kappa }}_{\mathit{\gamma }}$ and ${\mathit{\kappa }}_g$, including 68 and $95\%$ CL contours (${\mathit{\kappa }}_{Z\mathit{\gamma }}$ is profiled)

Fig. 18

Results of fits for benchmark models that probe for contributions from non-SM particles in the $H\to \mathit{\gamma }\mathit{\gamma }$, $H\to Z\mathit{\gamma }$ and $gg\to H$ loops, while allowing for potential extra contributions to the total width: a overview of fitted parameters. The inner and outer bars correspond to 68 and 95 % CL intervals. The confidence intervals for ${\mathrm{BR}}_{\mathrm{i}.,\mathrm{u}.}$ are estimated with respect to the physical bounds as described in the text. b Profile likelihood ratio as a function of the branching fraction ${\mathrm{BR}}_{\mathrm{i}.,\mathrm{u}.}$ to invisible or undetected decay modes (${\mathit{\kappa }}_{\mathit{\gamma }}$, ${\mathit{\kappa }}_g$ and ${\mathit{\kappa }}_{Z\mathit{\gamma }}$ are profiled). The red (green) horizontal line indicates the value of the profile likelihood ratio corresponding to a 68 % (95 %) confidence interval for the parameter of interest, assuming the asymptotic ${\mathit{\chi }}^2$ distribution for the test statistic

Fig. 19

Results of fits for benchmark models that probe for contributions from non-SM particles in the $H\to \mathit{\gamma }\mathit{\gamma }$, $gg\to H$ and $H\to Z\mathit{\gamma }$ loops, with free gauge and fermion coupling-strength scale factors ${\mathit{\kappa }}_V,{\mathit{\kappa }}_F$, while allowing for potential extra contributions to the total width. The estimated values of each parameter under the constraint ${\mathit{\kappa }}_V<1$ or ${\mathit{\kappa }}_{\mathrm{on}}={\mathit{\kappa }}_{\mathrm{off}}$ are shown with markers in the shape of a box or a circle, respectively. The inner and outer bars correspond to 68 and 95 % CL intervals. The confidence intervals of ${\mathrm{BR}}_{\mathrm{i}.,\mathrm{u}.}$ and, in the benchmark model with the constraint ${\mathit{\kappa }}_V<1$, also ${\mathit{\kappa }}_V$, are estimated with respect to their physical constraints as described in the text. The numerical values of the fit under the constraint ${\mathit{\kappa }}_V<1$ are shown on the left. Values for the alternative ${\mathit{\kappa }}_{\mathrm{on}}={\mathit{\kappa }}_{\mathrm{off}}$ constraint are also shown (in a reduced font size due to space constraints)

Fig. 20

Overview of best-fit values of parameters with 68 and 95 % CL intervals for generic model 1 (see text). In this model only SM particles are considered in loops and no invisible or undetected Higgs boson decays are allowed. The sign of ${\mathit{\kappa }}_W$ is assumed to be positive, as indicated by the hatched area, without loss of generality. The inner and outer bars correspond to 68 and 95 % CL intervals

Fig. 21

Results of fits for generic model 1 (see text): profile likelihood ratios as functions of the coupling-strength scale factors a ${\mathit{\kappa }}_t$, b ${\mathit{\kappa }}_b$, c ${\mathit{\kappa }}_W$, and d ${\mathit{\kappa }}_Z$. For each measurement, the other coupling-strength scale factors are profiled. The kinks in the curves of a and c are caused by transitions in solutions chosen by the profile likelihood for the relative sign between profiled couplings. The dashed curves show the SM expectations. The red (green) horizontal line indicates the value of the profile likelihood ratio corresponding to a 68 % (95 %) confidence interval for the parameter of interest, assuming the asymptotic ${\mathit{\chi }}^2$ distribution for the test statistic

Fig. 22

Fit results for the reduced coupling-strength scale factors $y_{V,i}=\sqrt{{\mathit{\kappa }}_{V,i}\frac{g_{V,i}}{2v}}=\sqrt{{\mathit{\kappa }}_{V,i}}\frac{m_{V,i}}{v}$ for weak bosons and $y_{F,i}={\mathit{\kappa }}_{F,i}\frac{g_{F,i}}{\sqrt{2}}={\mathit{\kappa }}_{F,i}\frac{m_{F,i}}{v}$ for fermions as a function of the particle mass, assuming a SM Higgs boson with a mass of 125.36 GeV. The dashed line indicates the predicted mass dependence for the SM Higgs boson

Fig. 23

Results of fits for generic model 2 (see text): the estimated values of each parameter under the constraint ${\mathit{\kappa }}_V<1$, ${\mathit{\kappa }}_{\mathrm{on}}={\mathit{\kappa }}_{\mathrm{off}}$ or ${\mathrm{BR}}_{\mathrm{i}.,\mathrm{u}.}=0$ are shown with markers in the shape of a box, a circle, or a diamond, respectively. The hatched area indicates regions that are outside the defined parameter boundaries. The inner and outer bars correspond to 68 and 95 % CL intervals. The confidence intervals of ${\mathrm{BR}}_{\mathrm{i}.,\mathrm{u}.}$ and, in the benchmark model with the constraints ${\mathit{\kappa }}_W<1$ and $|{\mathit{\kappa }}_Z|<1$, also ${\mathit{\kappa }}_W$ and ${\mathit{\kappa }}_Z$, are estimated with respect to their physical bounds as described in the text. Numerical results are shown in Table 11

Fig. 24

Results of fits for generic model 2 (see text): profile likelihood ratios as functions of the coupling-strength scale factors a ${\mathit{\kappa }}_t$, b ${\mathit{\kappa }}_b$, c ${\mathit{\kappa }}_W$, and d ${\mathit{\kappa }}_Z$. For each measurement, the other coupling-strength scale factors are profiled. The red (green) horizontal line indicates the value of the profile likelihood ratio corresponding to a 68 % (95 %) confidence interval for the parameter of interest, assuming the asymptotic ${\mathit{\chi }}^2$ distribution for the test statistic

Fig. 25

Profile likelihood ratio as a function of ${\mathit{\kappa }}_t$ for models with and without resolved loop processes: shown are measurements of ${\mathit{\kappa }}_t$ with no loop processes resolved (blue), only $gg\to ZH$ resolved (red, generic model 2), $gg\to H$ additionally resolved (green), and $H\to \mathit{\gamma }\mathit{\gamma }$ and $H\to Z\mathit{\gamma }$ additionally resolved (orange, generic model 1). The dashed blue and orange curves correspond to the expected sensitivity for the no-loop and all-loop models. All profile likelihood curves are drawn for the full range of ${\mathit{\kappa }}_t$, however some curves are partially obscured when overlapping with another nearly identical curve. The red (green) horizontal line indicates the value of the profile likelihood ratio corresponding to a 68 % (95 %) confidence interval for the parameter of interest, assuming the asymptotic ${\mathit{\chi }}^2$ distribution for the test statistic

Fig. 26

Results of fits for generic model 3 (see text): allowing deviations in vertex loop-coupling scale factors and in the total width. Overview of best-fit values of parameters, where the inner and outer bars correspond to 68 and 95 % CL intervals. The hatched areas indicate regions that are outside the defined parameter boundaries

Fig. 27

Results of fits for generic model 3 (see text): profile likelihood ratios as functions of the coupling-strength scale factor ratios a ${\mathit{\lambda }}_{WZ}$, b ${\mathit{\lambda }}_{tg}$ and c ${\mathit{\lambda }}_{\mathit{\gamma }Z}$. In all cases, the other parameters are profiled. The dashed curves show the SM expectations. The red (green) horizontal line indicates the cutoff value of the profile likelihood ratio corresponding to a 68 % (95 %) confidence interval for the parameter of interest, assuming the asymptotic ${\mathit{\chi }}^2$ distribution for the test statistic