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CMS-PAS-HIG-17-028
Combined measurement and interpretation of differential Higgs boson production cross sections at $\sqrt{s}= $ 13 TeV
Abstract: The differential Higgs boson production cross sections are sensitive probes for new physics beyond the standard model. In particular, new physics may contribute in the gluon-gluon fusion loop, the dominant Higgs boson production mechanism at the LHC, and manifest itself as deviations from the expected standard model distributions. Combined spectra from the $\mathrm{H}\to\gamma\gamma$, $\mathrm{H}\to \mathrm{ZZ}$ and $\mathrm{H}\to \mathrm{b\bar{b}}$ decay channels are presented, together with limits on the Higgs couplings using 35.9 fb$^{-1}$ of proton-proton collision data recorded with the CMS detector at $\sqrt{s}= $ 13 TeV.
Figures & Tables Summary Additional Figures References CMS Publications
Figures

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Figure 1:
(left) Scan of the total cross section $\sigma _\text {tot}$, based on a combination of the total cross sections from $\mathrm{H} \to \gamma \gamma $ (64.0 $\pm$ 9.6 pb) and $\mathrm{H} \to \mathrm{ZZ}$ (58.2 $\pm$ 9.8 pb. (right) Scan of the ratio of branching fractions $R$ based on a combination of $\mathrm{H} \to \gamma \gamma $ and $\mathrm{H} \to \mathrm{ZZ}$, while profiling all other parameters. The filled markers indicate the one standard deviation interval.

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Figure 1-a:
Scan of the total cross section $\sigma _\text {tot}$, based on a combination of the total cross sections from $\mathrm{H} \to \gamma \gamma $ (64.0 $\pm$ 9.6 pb) and $\mathrm{H} \to \mathrm{ZZ}$ (58.2 $\pm$ 9.8 pb. The filled markers indicate the one standard deviation interval.

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Figure 1-b:
Scan of the ratio of branching fractions $R$ based on a combination of $\mathrm{H} \to \gamma \gamma $ and $\mathrm{H} \to \mathrm{ZZ}$, while profiling all other parameters. The filled markers indicate the one standard deviation interval.

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Figure 2:
Best fit values and uncertainties of the cross sections and signal strengths. (left) $ {p_{\mathrm {T}}} ^{\text {H}}$. (right) $ {p_{\mathrm {T}}} ^{\text {H}}$ while fixing non-gluon-fusion contributions to their SM expectation.

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Figure 2-a:
Best fit values and uncertainties of the cross sections and signal strengths: $ {p_{\mathrm {T}}} ^{\text {H}}$.

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Figure 2-b:
Best fit values and uncertainties of the cross sections and signal strengths: $ {p_{\mathrm {T}}} ^{\text {H}}$ while fixing non-gluon-fusion contributions to their SM expectation.

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Figure 3:
Best fit values and uncertainties of the cross sections and signal strengths for the $N_\text {jets}$-spectrum.

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Figure 4:
Expected best fit values and uncertainties of the cross sections and signal strengths for the $ |y_{\text {H}} |$-spectrum.

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Figure 5:
Expected best fit values and uncertainties of the cross sections and signal strengths for the $ {p_{\mathrm {T}}} ^\text {jet}$-spectrum.

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Figure 6:
Simultaneous fit results for $\kappa _b$ and $\kappa _c$. (left) One and two standard deviation contours are shown for the combined ($\mathrm{H} \to \gamma \gamma $ and $\mathrm{H} \to \mathrm{ZZ}$) fit to data and for $\mathrm{H} \to \gamma \gamma $ and $\mathrm{H} \to \mathrm{ZZ}$ separately, assuming a coupling dependency of the branching fractions. (right) One and two standard deviation contours are shown for the combined ($\mathrm{H} \to \gamma \gamma $ and $\mathrm{H} \to \mathrm{ZZ}$) fit to data and for $\mathrm{H} \to \gamma \gamma $ and $\mathrm{H} \to \mathrm{ZZ}$ separately, assuming freely floating branching fractions.

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Figure 6-a:
Simultaneous fit results for $\kappa _b$ and $\kappa _c$. One and two standard deviation contours are shown for the combined ($\mathrm{H} \to \gamma \gamma $ and $\mathrm{H} \to \mathrm{ZZ}$) fit to data and for $\mathrm{H} \to \gamma \gamma $ and $\mathrm{H} \to \mathrm{ZZ}$ separately, assuming a coupling dependency of the branching fractions.

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Figure 6-b:
Simultaneous fit results for $\kappa _b$ and $\kappa _c$. One and two standard deviation contours are shown for the combined ($\mathrm{H} \to \gamma \gamma $ and $\mathrm{H} \to \mathrm{ZZ}$) fit to data and for $\mathrm{H} \to \gamma \gamma $ and $\mathrm{H} \to \mathrm{ZZ}$ separately, assuming freely floating branching fractions.

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Figure 7:
Scans of only one coupling, while profiling the other. The filled markers indicate the one standard deviation interval. The branching fractions were considered dependent on the values of the couplings. (left) Scan of $\kappa _b$ while profiling $\kappa _c$. (right) Scan of $\kappa _c$ while profiling $\kappa _b$.

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Figure 7-a:
Scan of $\kappa _b$ while profiling $\kappa _c$. The filled markers indicate the one standard deviation interval. The branching fractions were considered dependent on the values of the couplings.

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Figure 7-b:
Scan of $\kappa _c$ while profiling $\kappa _b$. The filled markers indicate the one standard deviation interval. The branching fractions were considered dependent on the values of the couplings.

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Figure 8:
Scans of only one coupling, while profiling the other. The filled markers indicate the one standard deviation interval. The branching fractions were freely floated in the fit. (left) Scan of $\kappa _b$ while profiling $\kappa _c$. (right) Scan of $\kappa _c$ while profiling $\kappa _b$.

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Figure 8-a:
Scan of $\kappa _b$ while profiling $\kappa _c$. The filled markers indicate the one standard deviation interval. The branching fractions were freely floated in the fit.

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Figure 8-b:
Scan of $\kappa _c$ while profiling $\kappa _b$. The filled markers indicate the one standard deviation interval. The branching fractions were freely floated in the fit.

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Figure 9:
Simultaneous fit results for $\kappa _t$ and $c_g$. (left) One and two standard deviation contours are shown for the combined ($\mathrm{H} \to \gamma \gamma $, $\mathrm{H} \to \mathrm{ZZ}$ and $\mathrm{H} \to \mathrm{ b \bar{b} }$) fit to data and for $\mathrm{H} \to \gamma \gamma $ and $\mathrm{H} \to \mathrm{ZZ}$ separately, assuming a coupling dependency of the branching fractions. (right) One and two standard deviation contours are shown for the combined ($\mathrm{H} \to \gamma \gamma $, $\mathrm{H} \to \mathrm{ZZ}$ and $\mathrm{H} \to \mathrm{ b \bar{b} }$) fit to data and for $\mathrm{H} \to \gamma \gamma $ and $\mathrm{H} \to \mathrm{ZZ}$ separately, assuming freely floating branching fractions.

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Figure 9-a:
One and two standard deviation contours are shown for the combined ($\mathrm{H} \to \gamma \gamma $, $\mathrm{H} \to \mathrm{ZZ}$ and $\mathrm{H} \to \mathrm{ b \bar{b} }$) fit to data and for $\mathrm{H} \to \gamma \gamma $ and $\mathrm{H} \to \mathrm{ZZ}$ separately, assuming a coupling dependency of the branching fractions.

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Figure 9-b:
One and two standard deviation contours are shown for the combined ($\mathrm{H} \to \gamma \gamma $, $\mathrm{H} \to \mathrm{ZZ}$ and $\mathrm{H} \to \mathrm{ b \bar{b} }$) fit to data and for $\mathrm{H} \to \gamma \gamma $ and $\mathrm{H} \to \mathrm{ZZ}$ separately, assuming freely floating branching fractions.

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Figure 10:
Simultaneous combined fit results for $\kappa _t$ and $\kappa _b$. (left) One and two standard deviation contours are shown for the combined ($\mathrm{H} \to \gamma \gamma $, $\mathrm{H} \to \mathrm{ZZ}$ and $\mathrm{H} \to \mathrm{ b \bar{b} }$) fit to data and for $\mathrm{H} \to \gamma \gamma $ and $\mathrm{H} \to \mathrm{ZZ}$ separately, assuming a coupling dependency of the branching fractions. (right) One and two standard deviation contours are shown for the combined ($\mathrm{H} \to \gamma \gamma $, $\mathrm{H} \to \mathrm{ZZ}$ and $\mathrm{H} \to \mathrm{ b \bar{b} }$) fit to data and for $\mathrm{H} \to \gamma \gamma $ and $\mathrm{H} \to \mathrm{ZZ}$ separately, where the branching fractions were freely floated in the fit.

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Figure 10-a:
One and two standard deviation contours are shown for the combined ($\mathrm{H} \to \gamma \gamma $, $\mathrm{H} \to \mathrm{ZZ}$ and $\mathrm{H} \to \mathrm{ b \bar{b} }$) fit to data and for $\mathrm{H} \to \gamma \gamma $ and $\mathrm{H} \to \mathrm{ZZ}$ separately, assuming a coupling dependency of the branching fractions.

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Figure 10-b:
One and two standard deviation contours are shown for the combined ($\mathrm{H} \to \gamma \gamma $, $\mathrm{H} \to \mathrm{ZZ}$ and $\mathrm{H} \to \mathrm{ b \bar{b} }$) fit to data and for $\mathrm{H} \to \gamma \gamma $ and $\mathrm{H} \to \mathrm{ZZ}$ separately, where the branching fractions were freely floated in the fit.

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Figure 11:
(left) Bin-to-bin correlation matrix of the $ {p_{\mathrm {T}}} ^{\text {H}}$-spectrum. (right) Bin-to-bin correlation matrix of the $ {p_{\mathrm {T}}} ^{\text {H}}$-spectrum, while keeping the non-gluon-fusion contributions (xH) fixed to SM expectation.

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Figure 11-a:
Bin-to-bin correlation matrix of the $ {p_{\mathrm {T}}} ^{\text {H}}$-spectrum.

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Figure 11-b:
Bin-to-bin correlation matrix of the $ {p_{\mathrm {T}}} ^{\text {H}}$-spectrum, while keeping the non-gluon-fusion contributions (xH) fixed to SM expectation.

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Figure 12:
Bin-to-bin correlation matrix of the $N_\text {jets}$-spectrum.

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Figure 13:
Bin-to-bin correlation matrix of the $ |y_{\text {H}} |$-spectrum.

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Figure 14:
Bin-to-bin correlation matrix of the $ {p_{\mathrm {T}}} ^\text {jet}$-spectrum.
Tables

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Table 1:
$ {p_{\mathrm {T}}} ^{\text {H}}$ bin boundaries for the $\mathrm{H} \to \gamma \gamma $, $\mathrm{H} \to \mathrm{ZZ}$ and $\mathrm{H} \to \mathrm{ b \bar{b} }$ decay channels.

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Table 2:
$N_\text {jets}$ bins for the $\mathrm{H} \to \gamma \gamma $ and the $\mathrm{H} \to \mathrm{ZZ}$ decay channels.

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Table 3:
$ |y_{\text {H}} |$ bins for the $\mathrm{H} \to \gamma \gamma $ and the $\mathrm{H} \to \mathrm{ZZ}$ decay channels.

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Table 4:
$ {p_{\mathrm {T}}} ^\text {jet}$ bin boundaries for the $\mathrm{H} \to \gamma \gamma $ and the $\mathrm{H} \to \mathrm{ZZ}$ decay channels.

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Table 5:
Theoretical uncertainties for the $\kappa _b$/$\kappa _c$ spectra.

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Table 6:
Theoretical uncertainties for the $\kappa _t$/$c_g$ and $\kappa _t$/$\kappa _b$ spectra.
Summary
A combination of differential cross sections for the differential observables $ {p_{\mathrm{T}}}^{\text{H}}$, $N_\text{jets}$, $ |y_\text{H} |$ and $ {p_{\mathrm{T}}}^{\text{jet}}$ has been presented, using 35.9 fb$^{-1}$ of proton-proton collision data obtained at $\sqrt{s}= $ 13 TeV with the CMS detector. The spectra obtained are based on data from the $\mathrm{H} \to\gamma\gamma$, $\mathrm{H} \to \mathrm{ZZ}$ and $\mathrm{H} \to \mathrm{b\bar{b}}$ decay channels. The overall uncertainty is decreased by 15% relative to that for $\mathrm{H} \to\gamma\gamma$ alone by combining the $ {p_{\mathrm{T}}}^{\text{H}}$ spectra. The decrease is larger in the lower $ {p_{\mathrm{T}}}^{\text{H}}$ region than in the high $ {p_{\mathrm{T}}}^{\text{H}}$ tails. No significant deviations from the SM are observed in any differential distribution.

The spectra obtained were interpreted in the Higgs coupling modifier framework, in which simultaneous variations of $\kappa_b$ and $\kappa_c$, $\kappa_t$ and $\kappa_g$ and $\kappa_t$ and $\kappa_b$ were fitted to the combination of the $ {p_{\mathrm{T}}}^{\text{H}}$-spectrum. The limits obtained on individual couplings were $-0.9 < \kappa_b < 0.9$ and $-4.3 < \kappa_c < 4.3$, assuming the branching fractions scale with the coupling modifiers. For the charm coupling $\kappa_c$ in particular, this measurement is competitive with those obtained from direct searches.
Additional Figures

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Additional Figure 1:
Simultaneous expected fit results for $\kappa _b$ and $\kappa _c$. One and two standard deviation contours are shown for the combined ($\mathrm{H} \rightarrow \gamma \gamma $ and $\mathrm{H} \rightarrow \mathrm{ZZ}$) expectation, fixing the branching fractions to the values expected from the standard model.

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Additional Figure 2:
Expected fit of $\kappa _b$ while profiling $\kappa _c$. The filled markers indicate the one standard deviation interval. The branching fractions were fixed to the values expected from the standard model.

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Additional Figure 3:
Expected fit of $\kappa _c$ while profiling $\kappa _b$. The filled markers indicate the one standard deviation interval. The branching fractions were fixed to the values expected from the standard model.
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