Measurements of the Higgs boson production and decay rates and coupling strengths using pp collision data at √s = 7 and 8 TeV in the ATLAS experiment (original) (raw)
Combined analyses of the Higgs boson production and decay rates as well as of its coupling strengths to vector bosons and fermions are presented. Included in the combinations are the results of the decay modes H → γγ, ZZ∗, WW∗, Zγ, bb ̄, ττ and μμ, 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 fb−1 at √s = 7 TeV and 20.3 fb−1 at √s = 8 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 1.18 ± 0.10 ± 0.07±0.08, where the first error reflects the statistical uncertainty and 0.07 the second and third errors reflect respectively the experimental and theoretical systematic uncertainties. Strong evidence is found for the vector boson fusion process with a signific- ance of 4.3σ. 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 assumption on the SM particle content in loop processes. Within the assumption of unified couplings to up-type fermions, down-type fermions and the W/Z boson respectively, strong evidence for Higgs boson couplings to down-type fermions is found with a significance of 4.5σ. Generic Higgs boson coupling models that allow to measure coupling strengths to μ, τ leptons, b, t quarks and W , Z bosons, or ratios of these coupling strengths, are presented. The observed data are found to be compatible with the SM expectations for a Higgs boson at a mass of 125.36 GeV for all models considered.
16 March 2015
These preliminary results are superseded by the following paper:
HIGG-2014-06
ATLAS recommends to use the results from the paper.
Figure 01
Summary of the signal-strength measurements, as published, from individual analyses that are inputs to the combinations. The Higgs boson mass column indicates the mH 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). The error bars represent ± 1σ total uncertainties, combining statistical and systematic contributions. The green shaded bands indicate the uncertainty of the overall signal strength of its respective analysis. The combined signal strength of the Hyy analysis also includes the ttH contribution which is listed separately under the ttH production.
Figure 02
The observed signal strengths and uncertainties for different Higgs boson decay channels and their combination for mH=125.36 GeV. Higgs boson signals corresponding to the same decay channel are combined together for all analyses. The best-fit values are shown by the solid vertical lines. The total ±1σ 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 theory systematic uncertainty (bottom) on the signal strength shown as horizontal error bars.
Figure 03
Likelihood contours in the (μfggF+ttH, μfVBF+VH) plane for a Higgs boson mass mH=125.36 GeV measured separately for H→ WW*, ZZ*, bb, γγ and ττ decays. The sharp lower edges of the Hyy and Hllll 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 (+) and the 68% (full) and 95% (dashed) CL contours are indicated, as well as the SM expectation (star).
Figure 04
The cross-section ratios between vector boson and fermion-mediated processes relative to their SM values at mH=125.36 GeV, measured in the individual Higgs boson decay final states and their combination, R Combined (see text). The inner and outer error bars represent 68% CL and 95% CL intervals, combining statistical and systematic uncertainties. These measurements are independent on the assumptions of Higgs boson decays.
Figure 05
The best-fit signal-strength values of different production modes determined from the combined fit to the √s=7 and 8 TeV data. The inner and outer error bars correspond to 68% CL and 95% CL intervals. Total uncertainties combining statistical, experimental and theoretical systematic uncertainties are shown. The fit assumes the SM values of the Higgs boson decay branching ratios for mH=125.36 GeV.
Figure 06
The gg→ H→ WW* signal strength, ratios of cross sections and of branching ratios from the combined analyses of the √s=7 and 8 TeV data. All ratios are normalised to their SM values at mH=125.36 GeV. The inner and outer error bars represent 68% CL and 95% CL intervals.
Figure 07a
Results of fits for the two-parameter benchmark model defined in Section 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 κF and κV, including 68% and 95% CL contours; overlaying the 68% CL contours derived from the individual channels and their combination; profile likelihood ratios as functions of the coupling strength scale factors (b) the same measurement, without the overlays of the individual channels, (c) κF (κV is profiled) and (d) κV (κF is profiled). The dashed curves in (c) and (d) show the SM expectations. In (d) the sign of the chosen profiled solution for κF changes at κV ≈ 0.8 , causing a kink in the likelihood. The profile likelihood curves restricting κF 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 lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 07b
Results of fits for the two-parameter benchmark model defined in Section 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 κF and κV, including 68% and 95% CL contours; overlaying the 68% CL contours derived from the individual channels and their combination; profile likelihood ratios as functions of the coupling strength scale factors (b) the same measurement, without the overlays of the individual channels, (c) κF (κV is profiled) and (d) κV (κF is profiled). The dashed curves in (c) and (d) show the SM expectations. In (d) the sign of the chosen profiled solution for κF changes at κV ≈ 0.8 , causing a kink in the likelihood. The profile likelihood curves restricting κF 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 lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 07c
Results of fits for the two-parameter benchmark model defined in Section 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 κF and κV, including 68% and 95% CL contours; overlaying the 68% CL contours derived from the individual channels and their combination; profile likelihood ratios as functions of the coupling strength scale factors (b) the same measurement, without the overlays of the individual channels, (c) κF (κV is profiled) and (d) κV (κF is profiled). The dashed curves in (c) and (d) show the SM expectations. In (d) the sign of the chosen profiled solution for κF changes at κV ≈ 0.8 , causing a kink in the likelihood. The profile likelihood curves restricting κF 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 lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 07d
Results of fits for the two-parameter benchmark model defined in Section 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 κF and κV, including 68% and 95% CL contours; overlaying the 68% CL contours derived from the individual channels and their combination; profile likelihood ratios as functions of the coupling strength scale factors (b) the same measurement, without the overlays of the individual channels, (c) κF (κV is profiled) and (d) κV (κF is profiled). The dashed curves in (c) and (d) show the SM expectations. In (d) the sign of the chosen profiled solution for κF changes at κV ≈ 0.8 , causing a kink in the likelihood. The profile likelihood curves restricting κF 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 lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 08a
Results of fits for the two-parameter benchmark model defined in Section 5.2.2 that probes different coupling strength scale factors for fermions and vector bosons without assumptions on the total width: (a) profile likelihood ratio as function of the coupling strength scale factor ratio λFV (κVV is profiled). The dashed curve shows the SM expectation. (b) Results of the two-dimensional fit to κVV and λFV, including 68% and 95% CL contours. The red(green) horizontal lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 08b
Results of fits for the two-parameter benchmark model defined in Section 5.2.2 that probes different coupling strength scale factors for fermions and vector bosons without assumptions on the total width: (a) profile likelihood ratio as function of the coupling strength scale factor ratio λFV (κVV is profiled). The dashed curve shows the SM expectation. (b) Results of the two-dimensional fit to κVV and λFV, including 68% and 95% CL contours. The red(green) horizontal lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 09a
Results of fits for the benchmark model that probes for contributions from non-SM particles in the H→γγ, hzg and gg→H loops, assuming no extra contributions to the total width: (a) overview of fitted parameters, where the inner and outer bars correspond to 68% CL and 95% CL intervals, and (b) results of the two-dimensional fit to κγ and κg, including 68% and 95% CL contours (κZγ is profiled).
Figure 09b
Results of fits for the benchmark model that probes for contributions from non-SM particles in the H→γγ, hzg and gg→H loops, assuming no extra contributions to the total width: (a) overview of fitted parameters, where the inner and outer bars correspond to 68% CL and 95% CL intervals, and (b) results of the two-dimensional fit to κγ and κg, including 68% and 95% CL contours (κZγ is profiled).
Figure 10a
Results of fits for benchmark models that probe for contributions from non-SM particles in the H→γγ, hzg and gg→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% CL and 95% CL intervals The confidence intervals for BRinv.,undet. are estimated with respect to the physical boundary as described in the text. (b) Profile likelihood ratio as function of the branching fraction BRinv.,undet. to invisible or undetected decay modes (κγ, κg and κZγ are profiled). The red(green) horizontal lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 10b
Results of fits for benchmark models that probe for contributions from non-SM particles in the H→γγ, hzg and gg→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% CL and 95% CL intervals The confidence intervals for BRinv.,undet. are estimated with respect to the physical boundary as described in the text. (b) Profile likelihood ratio as function of the branching fraction BRinv.,undet. to invisible or undetected decay modes (κγ, κg and κZγ are profiled). The red(green) horizontal lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 11
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→γγ, gg→H and hzg loops, with free gauge and fermion coupling strengths κV,κF. The result for each parameter marked by a full box corresponds to the model with a constraint on the total width from μ off. The result for each parameter marked by a full circle corresponds to the model with the constraint κV<1 imposed. The the inner and outer bars correspond to 68% CL and 95% CL intervals. The confidence intervals of BRinv.,undet. and, in the benchmark model with the constraint κV<1, also κV, are estimated with respect to their physical boundaries as described in the text.
Figure 12
Results of fits for benchmark models that probe for contributions from non-SM particles in the H→γγ, gg→H and hzg loops, with free gauge and fermion coupling strengths κV,κF, while allowing for potential extra contributions to the total width. The result for each parameter marked by a full box corresponds to the model with a constraint on the total width from μ off. The result for each parameter marked by a full circle corresponds to the model with the constraint κV<1 imposed. The the inner and outer bars correspond to 68% CL and 95% CL intervals. The confidence intervals of BRinv.,undet. and, in the benchmark model with the constraint κV<1, also κV, are estimated with respect to their physical boundaries as described in the text.
Figure 13a
Results of fits for the benchmark model described in Section 5.5.1 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) λdu (λVu and κuu are profiled), (b) λVu (λdu and κuu are profiled), and (c) the overall scale factor κuu (λdu and λVu are profiled). The dashed curves show the SM expectations. The red(green) horizontal lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 13b
Results of fits for the benchmark model described in Section 5.5.1 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) λdu (λVu and κuu are profiled), (b) λVu (λdu and κuu are profiled), and (c) the overall scale factor κuu (λdu and λVu are profiled). The dashed curves show the SM expectations. The red(green) horizontal lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 13c
Results of fits for the benchmark model described in Section 5.5.1 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) λdu (λVu and κuu are profiled), (b) λVu (λdu and κuu are profiled), and (c) the overall scale factor κuu (λdu and λVu are profiled). The dashed curves show the SM expectations. The red(green) horizontal lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 14a
Results of fits for the benchmark model described in Section 5.5.2 that probes the symmetry between quarks and leptons: profile likelihood ratios as functions of the coupling strength scale factor ratios (a) λlq (λVq and κqq are profiled), (b) λVq (λlq and κqq are profiled), and (c) the overall scale factor κqq (λlq and λVq are profiled). The dashed curves show the SM expectations. The red(green) horizontal lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 14b
Results of fits for the benchmark model described in Section 5.5.2 that probes the symmetry between quarks and leptons: profile likelihood ratios as functions of the coupling strength scale factor ratios (a) λlq (λVq and κqq are profiled), (b) λVq (λlq and κqq are profiled), and (c) the overall scale factor κqq (λlq and λVq are profiled). The dashed curves show the SM expectations. The red(green) horizontal lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 14c
Results of fits for the benchmark model described in Section 5.5.2 that probes the symmetry between quarks and leptons: profile likelihood ratios as functions of the coupling strength scale factor ratios (a) λlq (λVq and κqq are profiled), (b) λVq (λlq and κqq are profiled), and (c) the overall scale factor κqq (λlq and λVq are profiled). The dashed curves show the SM expectations. The red(green) horizontal lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 15
Overview of best-fit values of parameters with 68% and 95% CL intervals for the generic model 1 (see text). In this model only SM particles are considered in loops and no invisible or undetected Higgs boson decay are allowed. The sign of κW is assumed to be positive, as indicated by the hatched area, without loss of generality. The inner and outer bars correspond to 68% CL and 95% CL intervals.
Figure 16a
Results of fits for the generic model 1 (see text): only SM particles in loops, no invisible or undetected Higgs boson decays. Profile likelihood ratio as a function of the coupling strength scale factors (a) κt (other coupling strengths are profiled), (b) κb, (c) κW, and (d) κZ. 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 lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 16b
Results of fits for the generic model 1 (see text): only SM particles in loops, no invisible or undetected Higgs boson decays. Profile likelihood ratio as a function of the coupling strength scale factors (a) κt (other coupling strengths are profiled), (b) κb, (c) κW, and (d) κZ. 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 lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 16c
Results of fits for the generic model 1 (see text): only SM particles in loops, no invisible or undetected Higgs boson decays. Profile likelihood ratio as a function of the coupling strength scale factors (a) κt (other coupling strengths are profiled), (b) κb, (c) κW, and (d) κZ. 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 lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 16d
Results of fits for the generic model 1 (see text): only SM particles in loops, no invisible or undetected Higgs boson decays. Profile likelihood ratio as a function of the coupling strength scale factors (a) κt (other coupling strengths are profiled), (b) κb, (c) κW, and (d) κZ. 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 lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 17
Fit results for the reduced coupling strength scale factors yV,i = √ κV,i gV,i/2v = √κV,icmV,i/v for weak bosons and yF,i = κF,igF,i/√2 = κF,icmF,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.
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Figure 18a
Results of fits for the generic model 2 (see text): effective coupling strengths for loop processes allowing non-SM contributions, but assuming that the total Higgs boson decay width is not modified with respect to the SM (BRinv.,undet.=0). Profile likelihood ratios as functions of the coupling strength scale factors (a) κt, (b) κb, (c) κW, and (d) κZ. For each measurement, the other coupling strength scale factors are profiled. The red(green) horizontal lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 18b
Results of fits for the generic model 2 (see text): effective coupling strengths for loop processes allowing non-SM contributions, but assuming that the total Higgs boson decay width is not modified with respect to the SM (BRinv.,undet.=0). Profile likelihood ratios as functions of the coupling strength scale factors (a) κt, (b) κb, (c) κW, and (d) κZ. For each measurement, the other coupling strength scale factors are profiled. The red(green) horizontal lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 18c
Results of fits for the generic model 2 (see text): effective coupling strengths for loop processes allowing non-SM contributions, but assuming that the total Higgs boson decay width is not modified with respect to the SM (BRinv.,undet.=0). Profile likelihood ratios as functions of the coupling strength scale factors (a) κt, (b) κb, (c) κW, and (d) κZ. For each measurement, the other coupling strength scale factors are profiled. The red(green) horizontal lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 18d
Results of fits for the generic model 2 (see text): effective coupling strengths for loop processes allowing non-SM contributions, but assuming that the total Higgs boson decay width is not modified with respect to the SM (BRinv.,undet.=0). Profile likelihood ratios as functions of the coupling strength scale factors (a) κt, (b) κb, (c) κW, and (d) κZ. For each measurement, the other coupling strength scale factors are profiled. The red(green) horizontal lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 19
Results of fits for the generic model 2 (see text): the results indicated by a full box are obtained for a benchmark model with effective coupling strengths for loop processes allowing non-SM contributions, and a floating BRinv.,undet. allowing non-SM contributions to the total decay width. The fit results indicated by a full circle represent a benchmark model where the total Higgs boson decay width is not modified with respect to the SM. The hatched area indicates regions that are outside the defined parameter boundaries. The inner and outer bars correspond to 68% CL and 95% CL intervals. The confidence intervals of BRinv.,undet. and, in the benchmark model with the constraints κW<1 and |κZ|<1, also κW and κZ, are estimated with respect to their physical boundaries as described in the text. Numerical results are shown in Table 8.
Figure 20
Comparison of measurements of κt with and without resolved loop processes: shown are models with no loop processes resolved (blue), only ggZH resolved (red, generic model 2), gg→H additionally resolved (green), and H→γγ and hzg 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. The red(green) horizontal lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 21
Results of fits for the generic model 3 (see text): allowing deviations in vertex loop coupling strengths and in the total width. Overview of best-fit values of parameters, where the inner and outer bars correspond to 68% CL and 95% CL intervals. The hatched area indicates regions that are outside the defined parameter boundaries.
Figure 22a
Results of fits for the generic model 3 (see text): allowing deviations in vertex loop coupling strengths and in the total width. (a) Profile likelihood ratio as a function of the coupling strength scale factor ratio λWZ (other parameters are profiled). (b) Profile likelihood ratio as a function of the coupling strength scale factor ratio λtg (other parameters are profiled). (c) Profile likelihood ratio as a function of the coupling strength scale factor ratio λγZ (other parameters are profiled). The dashed curves show the SM expectations. The red(green) horizontal lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 22b
Results of fits for the generic model 3 (see text): allowing deviations in vertex loop coupling strengths and in the total width. (a) Profile likelihood ratio as a function of the coupling strength scale factor ratio λWZ (other parameters are profiled). (b) Profile likelihood ratio as a function of the coupling strength scale factor ratio λtg (other parameters are profiled). (c) Profile likelihood ratio as a function of the coupling strength scale factor ratio λγZ (other parameters are profiled). The dashed curves show the SM expectations. The red(green) horizontal lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 22c
Results of fits for the generic model 3 (see text): allowing deviations in vertex loop coupling strengths and in the total width. (a) Profile likelihood ratio as a function of the coupling strength scale factor ratio λWZ (other parameters are profiled). (b) Profile likelihood ratio as a function of the coupling strength scale factor ratio λtg (other parameters are profiled). (c) Profile likelihood ratio as a function of the coupling strength scale factor ratio λγZ (other parameters are profiled). The dashed curves show the SM expectations. The red(green) horizontal lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 23
Results of fits for the benchmark model that probe the custodial symmetry through the ratio λWZ = κW / κZ (λFZ and κZZ are profiled); The dashed curves show the SM expectations. The red(green) horizontal lines indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 24a
Likelihood scans of VBF (left), VH (middle) and ttH (right) cross sections relative to that of ggF. See Section 4.4 for details. The dashed horizontal lines at 1(4) indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 24b
Likelihood scans of VBF (left), VH (middle) and ttH (right) cross sections relative to that of ggF. See Section 4.4 for details. The dashed horizontal lines at 1(4) indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 24c
Likelihood scans of VBF (left), VH (middle) and ttH (right) cross sections relative to that of ggF. See Section 4.4 for details. The dashed horizontal lines at 1(4) indicates the cutoff values on the profile likelihood ratio corresponding to a 68%(95%) confidence interval on the parameter of interest, assuming the asymptotic χ2 distribution for the test statistic.
Figure 25
The observed and expected signal strengths and uncertainties for different Higgs boson decay channels and their combination for mH=125.36 GeV. Higgs boson signals of the same decay in all analyses are combined together. The best-fit values are shown by the solid vertical lines. The observed total ±1σ uncertainties are indicated by green shaded bands and blue error bars, whereas the expected ±1σ total uncertainties are indicated by red error bars, centered at the expected signal strength of 1.
Figure 26
Correlation matrix of the coupling strength ratio parameter of Generic Model 3, detailed in Section 5.6.3.
Table 01
SM predictions of the Higgs boson production cross sections and decay branching ratios and their uncertainties for mH=125.36 GeV, obtained by linear interpolations from those at 125.3 and 125.4 GeV from Ref. [11] except for the tH production cross section which is obtained from Ref. [26]. The uncertainties on the cross sections are the quadratic sum of the uncertainties on the QCD scales, parton distribution functions and αs. The uncertainty on the tH cross section is calculated following the procedure of Ref. [11].
Table 02
Overview of the individual analyses that are included in the combinations described in this paper. The signal strengths, the statistical significances of a Higgs boson signal, or the 95% CL upper limits on the Higgs boson production rates or properties are also shown wherever appropriate. A range is quoted for the upper limit on the off-shell signal strength, depending on the assumption of the continuum gg→ WW/ZZ cross section. These results are taken directly from individual publications. Results of the on-shell analyses are quoted for mH=125.36 GeV except that mH=125.5 GeV is assumed for the Hzg and Hmm analyses and that mH=125 GeV is used for the ttH searches with Hbb and ttH→ multileptons. The luminosity used for the √s=7 TeV VH→ Vbb analysis differs slightly from the other analyses because a previous version of the luminosity calibration was applied. The significance is given in units of standard deviations (σ). The numbers in parentheses are the expected values from the SM Higgs boson. The ttH analysis in the H→γγ decay is part of the H→γγ analysis and is also included separately under the ttH production for completeness. The checkmark indicates whether the analysis is performed for the respective √s=7 and 8 TeV dataset.
Table 03
Measured signal strengths μ at mH=125.36 GeV and their total ± 1σ uncertainties for different production modes for the √s=8 TeV data and the combination with the √s=7 TeV data. The √s=7 TeV data do not have sufficient statistical power to yield meaningful measurements for individual production modes, but are included in the combination. Shown in the square brackets are uncertainty components: statistical (first), experimental (second) and theoretical (third) systematic uncertainties. These results are derived using the SM values of the Higgs boson decay branching ratios.
Table 04
Measured cross sections of different Higgs boson production modes at √s=8 TeV for mH=125.36 GeV obtained from the signal-strength values of Table 3. Uncertainty breakdowns are shown in the square brackets. These results are derived using the SM values of the Higgs boson decay branching ratios.
Table 05
Best-fit values of gg→ H→ WW* signal strength μ ggFWW*, ratios of cross sections Ri/ ggF and of branching ratios ρf/WW*. All Ri/ ggF and ρf/WW*are measured relative to their SM values for mH=125.36 GeV from the combined analysis of the √s=7 and 8 TeV data. The observed and expected significances of the VBF, VH and ttH production with respect to the background-only hypothesis are also shown.
Table 06
Overview of Higgs boson production cross sections σi and Higgs boson partial decay widths Γf. For each production or decay mode the scaling of the corresponding rate in terms of Higgs boson coupling strength scale factors is given. For processes where multiple amplitudes contribute, the rate may depend on multiple Higgs boson coupling strength scale factors, and interference terms may give rise to scalar product terms κiκj that allow to determine the relative sign of the coupling strengths κi and κj. Expressions originate from Ref. [11], except for σ(gg→ ZH) (from Ref. [40]) and σ(gb → WtH) and σ(qb → tHqprime) (calculated using Ref. [26]). The expressions are given for rts = 8TeV and mH = 125.36GeV and are similar for rts = 7TeV. Interference contributions with negligible magnitudes have been been omitted in this table.
Table 07
Summary of coupling benchmark models considered in this paper, where λij≡κi/κj, κii≡κiκi/κH, and the functional dependence assumptions are: κV=κW= κZ, κF = κPQt = κPQb = κPGt = κPGm (and similarly for the other fermions), κg = κg(κPQb, κPQt), κγ=κγ(κPQb, κPQt, κPGt, κW), and κH=κH(κi). The tick marks indicate which assumptions are made in each case. The last column shows, as an example, the relative coupling strengths involved in the gg→H→γγ process.
Table 08
Numerical results of the fits to generic model 2 : effective coupling strengths for loop processes allowing non-SM contributions with various assumptions on the total Higgs boson width. The inner and outer bars correspond to 68% CL and 95% CL intervals. The confidence interval of BRinv.,undet. in the benchmark model with the constraints κW<1 and |κZ|<1, and the confidence intervals κW and κZ, are estimated with respect to their physical boundaries as described in the text. These results are also shown in Fig. 19.
Table 09
Numerical results of the fits for generic model 3. These results are also shown in Fig. 21.
