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| CMS-PAS-FTR-18-020 | ||
| Constraints on the Higgs boson self-coupling from ttH+tH, $\mathrm{H}\rightarrow\gamma\gamma$ differential measurements at the HL-LHC | ||
| CMS Collaboration | ||
| November 2018 | ||
| Abstract: This note details a study of prospects for ttH+tH, $\mathrm{H}\rightarrow\gamma\gamma$ differential cross section measurements at the HL-LHC with the CMS Phase-2 detector. The study is performed using simulated proton-proton collisions at a centre-of-mass energy of $\sqrt{s}=$ 14 TeV, corresponding to 3 ab$^{-1}$ of data. The expected performance of the upgraded CMS detector is used to model the object reconstruction efficiencies under HL-LHC conditions. The results are interpreted in terms of the expected sensitivity to deviations of the Higgs boson self-coupling, $\kappa_\lambda$, from beyond standard model effects. Using the HL-LHC data, the precision expected in ttH+tH, $\mathrm{H}\rightarrow\gamma\gamma$ differential cross section measurements will constrain $\kappa_\lambda$ within the range $-4.1 < \kappa_\lambda < 14.1$, at the 95% confidence level, assuming all other Higgs boson couplings are fixed to standard model predictions. Moreover, it is possible to disentangle the effects of a modified Higgs boson self coupling from the presence of other anomalous couplings by using the differences in the shape of the measured spectrum. This separation is unique to differential cross section measurements. The ultimate sensitivity to the Higgs boson self coupling, achievable using differential cross section measurements, will result from a combination across Higgs boson production modes and decay channels. | ||
| Links: CDS record (PDF) ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures & Tables | Summary | Additional Figures | References | CMS Publications |
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| Figures | |
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Figure 1:
Example of a NLO Feynman diagram for $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $ production which includes the Higgs boson self-coupling. |
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Figure 2:
The BDT output distributions for the hadronic (left) and leptonic (right) channels, after pre-selection has been applied. Events with a BDT output value greater than 0.28 (0.13) are selected for the hadronic (leptonic) categories. This selection boundary is indicated by the leftmost (single) dashed line in the hadronic (leptonic) BDT output distribution. The second dashed line in the hadronic BDT output distribution shows the additional boundary at 0.61, which is used to further split the hadronic categories according to high and low ttH purity. |
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Figure 2-a:
The BDT output distributions for the hadronic (left) and leptonic (right) channels, after pre-selection has been applied. Events with a BDT output value greater than 0.28 (0.13) are selected for the hadronic (leptonic) categories. This selection boundary is indicated by the leftmost (single) dashed line in the hadronic (leptonic) BDT output distribution. The second dashed line in the hadronic BDT output distribution shows the additional boundary at 0.61, which is used to further split the hadronic categories according to high and low ttH purity. |
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Figure 2-b:
The BDT output distributions for the hadronic (left) and leptonic (right) channels, after pre-selection has been applied. Events with a BDT output value greater than 0.28 (0.13) are selected for the hadronic (leptonic) categories. This selection boundary is indicated by the leftmost (single) dashed line in the hadronic (leptonic) BDT output distribution. The second dashed line in the hadronic BDT output distribution shows the additional boundary at 0.61, which is used to further split the hadronic categories according to high and low ttH purity. |
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Figure 3:
Best-fit signal (S) + background (B) models for the reconstruction-level categories in the $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $+$ {{\mathrm {t}} {\mathrm {H}}} $ hadronic channel, in the three lowest $ {{p_{\mathrm {T}}} ^{\gamma \gamma}} $ bins: [0,45] GeV, [45,80] GeV and [80,120] GeV. A pseudo-data set is thrown from the best-fit functions, represented by the black points. The one (green) and two (yellow) standard deviation bands show the uncertainties in the background component of the fit. The residual plots, pseudo-data minus the background component, are shown in the lower panels. |
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Figure 3-a:
Best-fit signal (S) + background (B) models for the reconstruction-level categories in the $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $+$ {{\mathrm {t}} {\mathrm {H}}} $ hadronic channel, in the three lowest $ {{p_{\mathrm {T}}} ^{\gamma \gamma}} $ bins: [0,45] GeV, [45,80] GeV and [80,120] GeV. A pseudo-data set is thrown from the best-fit functions, represented by the black points. The one (green) and two (yellow) standard deviation bands show the uncertainties in the background component of the fit. The residual plots, pseudo-data minus the background component, are shown in the lower panels. |
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Figure 3-b:
Best-fit signal (S) + background (B) models for the reconstruction-level categories in the $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $+$ {{\mathrm {t}} {\mathrm {H}}} $ hadronic channel, in the three lowest $ {{p_{\mathrm {T}}} ^{\gamma \gamma}} $ bins: [0,45] GeV, [45,80] GeV and [80,120] GeV. A pseudo-data set is thrown from the best-fit functions, represented by the black points. The one (green) and two (yellow) standard deviation bands show the uncertainties in the background component of the fit. The residual plots, pseudo-data minus the background component, are shown in the lower panels. |
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Figure 3-c:
Best-fit signal (S) + background (B) models for the reconstruction-level categories in the $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $+$ {{\mathrm {t}} {\mathrm {H}}} $ hadronic channel, in the three lowest $ {{p_{\mathrm {T}}} ^{\gamma \gamma}} $ bins: [0,45] GeV, [45,80] GeV and [80,120] GeV. A pseudo-data set is thrown from the best-fit functions, represented by the black points. The one (green) and two (yellow) standard deviation bands show the uncertainties in the background component of the fit. The residual plots, pseudo-data minus the background component, are shown in the lower panels. |
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Figure 3-d:
Best-fit signal (S) + background (B) models for the reconstruction-level categories in the $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $+$ {{\mathrm {t}} {\mathrm {H}}} $ hadronic channel, in the three lowest $ {{p_{\mathrm {T}}} ^{\gamma \gamma}} $ bins: [0,45] GeV, [45,80] GeV and [80,120] GeV. A pseudo-data set is thrown from the best-fit functions, represented by the black points. The one (green) and two (yellow) standard deviation bands show the uncertainties in the background component of the fit. The residual plots, pseudo-data minus the background component, are shown in the lower panels. |
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Figure 3-e:
Best-fit signal (S) + background (B) models for the reconstruction-level categories in the $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $+$ {{\mathrm {t}} {\mathrm {H}}} $ hadronic channel, in the three lowest $ {{p_{\mathrm {T}}} ^{\gamma \gamma}} $ bins: [0,45] GeV, [45,80] GeV and [80,120] GeV. A pseudo-data set is thrown from the best-fit functions, represented by the black points. The one (green) and two (yellow) standard deviation bands show the uncertainties in the background component of the fit. The residual plots, pseudo-data minus the background component, are shown in the lower panels. |
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Figure 3-f:
Best-fit signal (S) + background (B) models for the reconstruction-level categories in the $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $+$ {{\mathrm {t}} {\mathrm {H}}} $ hadronic channel, in the three lowest $ {{p_{\mathrm {T}}} ^{\gamma \gamma}} $ bins: [0,45] GeV, [45,80] GeV and [80,120] GeV. A pseudo-data set is thrown from the best-fit functions, represented by the black points. The one (green) and two (yellow) standard deviation bands show the uncertainties in the background component of the fit. The residual plots, pseudo-data minus the background component, are shown in the lower panels. |
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Figure 4:
Best-fit signal (S) + background (B) models for the reconstruction-level categories in the $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $+$ {{\mathrm {t}} {\mathrm {H}}} $ hadronic channel, in the three highest $ {{p_{\mathrm {T}}} ^{\gamma \gamma}} $ bins: [120,200] GeV, [200,350] GeV and [350,$\infty $] GeV. A pseudo-data set is thrown from the best-fit functions, represented by the black points. The one (green) and two (yellow) standard deviation bands show the uncertainties in the background component of the fit. The residual plots, pseudo-data minus the background component, are shown in the lower panels. |
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Figure 4-a:
Best-fit signal (S) + background (B) models for the reconstruction-level categories in the $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $+$ {{\mathrm {t}} {\mathrm {H}}} $ hadronic channel, in the three highest $ {{p_{\mathrm {T}}} ^{\gamma \gamma}} $ bins: [120,200] GeV, [200,350] GeV and [350,$\infty $] GeV. A pseudo-data set is thrown from the best-fit functions, represented by the black points. The one (green) and two (yellow) standard deviation bands show the uncertainties in the background component of the fit. The residual plots, pseudo-data minus the background component, are shown in the lower panels. |
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Figure 4-b:
Best-fit signal (S) + background (B) models for the reconstruction-level categories in the $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $+$ {{\mathrm {t}} {\mathrm {H}}} $ hadronic channel, in the three highest $ {{p_{\mathrm {T}}} ^{\gamma \gamma}} $ bins: [120,200] GeV, [200,350] GeV and [350,$\infty $] GeV. A pseudo-data set is thrown from the best-fit functions, represented by the black points. The one (green) and two (yellow) standard deviation bands show the uncertainties in the background component of the fit. The residual plots, pseudo-data minus the background component, are shown in the lower panels. |
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Figure 4-c:
Best-fit signal (S) + background (B) models for the reconstruction-level categories in the $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $+$ {{\mathrm {t}} {\mathrm {H}}} $ hadronic channel, in the three highest $ {{p_{\mathrm {T}}} ^{\gamma \gamma}} $ bins: [120,200] GeV, [200,350] GeV and [350,$\infty $] GeV. A pseudo-data set is thrown from the best-fit functions, represented by the black points. The one (green) and two (yellow) standard deviation bands show the uncertainties in the background component of the fit. The residual plots, pseudo-data minus the background component, are shown in the lower panels. |
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Figure 4-d:
Best-fit signal (S) + background (B) models for the reconstruction-level categories in the $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $+$ {{\mathrm {t}} {\mathrm {H}}} $ hadronic channel, in the three highest $ {{p_{\mathrm {T}}} ^{\gamma \gamma}} $ bins: [120,200] GeV, [200,350] GeV and [350,$\infty $] GeV. A pseudo-data set is thrown from the best-fit functions, represented by the black points. The one (green) and two (yellow) standard deviation bands show the uncertainties in the background component of the fit. The residual plots, pseudo-data minus the background component, are shown in the lower panels. |
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Figure 4-e:
Best-fit signal (S) + background (B) models for the reconstruction-level categories in the $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $+$ {{\mathrm {t}} {\mathrm {H}}} $ hadronic channel, in the three highest $ {{p_{\mathrm {T}}} ^{\gamma \gamma}} $ bins: [120,200] GeV, [200,350] GeV and [350,$\infty $] GeV. A pseudo-data set is thrown from the best-fit functions, represented by the black points. The one (green) and two (yellow) standard deviation bands show the uncertainties in the background component of the fit. The residual plots, pseudo-data minus the background component, are shown in the lower panels. |
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Figure 5:
Best-fit signal (S) + background (B) models for each reconstruction-level category in the $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $+$ {{\mathrm {t}} {\mathrm {H}}} $ leptonic channel. A pseudo-data set is thrown from the best-fit functions, represented by the black points. The one (green) and two (yellow) standard deviation bands show the uncertainties in the background component of the fit. The residual plots, pseudo-data minus the background component, are shown in the lower panels. |
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Figure 5-a:
Best-fit signal (S) + background (B) models for each reconstruction-level category in the $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $+$ {{\mathrm {t}} {\mathrm {H}}} $ leptonic channel. A pseudo-data set is thrown from the best-fit functions, represented by the black points. The one (green) and two (yellow) standard deviation bands show the uncertainties in the background component of the fit. The residual plots, pseudo-data minus the background component, are shown in the lower panels. |
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Figure 5-b:
Best-fit signal (S) + background (B) models for each reconstruction-level category in the $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $+$ {{\mathrm {t}} {\mathrm {H}}} $ leptonic channel. A pseudo-data set is thrown from the best-fit functions, represented by the black points. The one (green) and two (yellow) standard deviation bands show the uncertainties in the background component of the fit. The residual plots, pseudo-data minus the background component, are shown in the lower panels. |
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Figure 5-c:
Best-fit signal (S) + background (B) models for each reconstruction-level category in the $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $+$ {{\mathrm {t}} {\mathrm {H}}} $ leptonic channel. A pseudo-data set is thrown from the best-fit functions, represented by the black points. The one (green) and two (yellow) standard deviation bands show the uncertainties in the background component of the fit. The residual plots, pseudo-data minus the background component, are shown in the lower panels. |
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Figure 5-d:
Best-fit signal (S) + background (B) models for each reconstruction-level category in the $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $+$ {{\mathrm {t}} {\mathrm {H}}} $ leptonic channel. A pseudo-data set is thrown from the best-fit functions, represented by the black points. The one (green) and two (yellow) standard deviation bands show the uncertainties in the background component of the fit. The residual plots, pseudo-data minus the background component, are shown in the lower panels. |
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Figure 5-e:
Best-fit signal (S) + background (B) models for each reconstruction-level category in the $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $+$ {{\mathrm {t}} {\mathrm {H}}} $ leptonic channel. A pseudo-data set is thrown from the best-fit functions, represented by the black points. The one (green) and two (yellow) standard deviation bands show the uncertainties in the background component of the fit. The residual plots, pseudo-data minus the background component, are shown in the lower panels. |
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Figure 5-f:
Best-fit signal (S) + background (B) models for each reconstruction-level category in the $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $+$ {{\mathrm {t}} {\mathrm {H}}} $ leptonic channel. A pseudo-data set is thrown from the best-fit functions, represented by the black points. The one (green) and two (yellow) standard deviation bands show the uncertainties in the background component of the fit. The residual plots, pseudo-data minus the background component, are shown in the lower panels. |
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Figure 6:
The expected differential $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $+$ {{\mathrm {t}} {\mathrm {H}}} $ cross sections times branching ratio, along with their respective uncertainties, in bins of $ {p_{\mathrm {T}}} ^{{\mathrm {H}}}$. These are for the fiducial region of phase space defined in the bottom left of the plot. The error bars on the black points include the statistical uncertainty, the experimental systematic uncertainties and the theoretical uncertainties related to the $ {{\mathrm {g}} {\mathrm {g}} {\mathrm {H}}} $ and V$ {\mathrm {H}} $ yields. The theoretical uncertainties in the inclusive $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}}+{{\mathrm {t}} {\mathrm {H}}} $ cross section and those effecting the shape of the $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} + {{\mathrm {t}} {\mathrm {H}}} $ $p_{\mathrm{T}}^{\mathrm{H}}$ spectrum, originating from the uncertainty in the QCD scales, are shown by the shaded yellow regions. Contributions from the individual hadronic and leptonic channels are shown in red and purple respectively. The cross section for the $ {p_{\mathrm {T}}} ^{{\mathrm {H}}}$ = [350,$\infty $] GeV bin is scaled by the width of the previous bin. Additionally, the expected differential $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $ + $ {{\mathrm {t}} {\mathrm {H}}} $ cross sections for anomalous values of the Higgs boson self-coupling ($\kappa _\lambda = $ 10 and $\kappa _\lambda = -5$) are shown by the horizontal dashed lines. |
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Figure 7:
Results of the likelihood scan in $\kappa _\lambda $. The individual contributions of the statistical and systematic uncertainties are separated by performing a likelihood scan with all systematics removed. The observed deviation from the statistical uncertainty only curve is driven by the theoretical systematic uncertainties in the Higgs boson production yields. Additionally, the contributions from the hadronic and leptonic channels have been separated, shown in red and purple, respectively. |
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Figure 8:
Results of the two-dimensional likelihood scan in $\kappa _\lambda $-vs-$\mu _{{\mathrm {H}}}$, where $\mu _{{\mathrm {H}}}$ allows all Higgs boson production modes to scale relative to the SM prediction. The 68% and 95% confidence level contours are shown by the solid and dashed lines respectively. The SM expectation is shown by the black cross. |
| Tables | |
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Table 1:
Summary of the input variables for both the hadronic and leptonic BDT classifiers. |
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Table 2:
Number of events remaining at the subsequent stages of the $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $ + $ {{\mathrm {t}} {\mathrm {H}}} $ hadronic selection. Also shown are the respective efficiencies of selection at each stage. The BDT efficiency, $\epsilon _{\textrm {BDT}}$, is defined as the ratio of the number of events remaining after the cut on the BDT output, to the number of events remaining after pre-selection. All event yields are normalised to 3 ab$^{-1}$. |
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Table 3:
Number of events remaining at the subsequent stages of the $ {{\mathrm {t}} {\mathrm {t}} {\mathrm {H}}} $ + $ {{\mathrm {t}} {\mathrm {H}}} $ leptonic selection. Also shown are the respective efficiencies of selection at each stage. The BDT efficiency, $\epsilon _{\textrm {BDT}}$, is defined as the ratio of the number of events remaining after the cut on the BDT output, to the number of events remaining after pre-selection. All event yields are normalised to 3 ab$^{-1}$. |
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Table 4:
The kinematic bins in which the differential cross sections are measured. |
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Table 5:
The 68% and 95% confidence level intervals for $\kappa _\lambda $ for different integrated luminosities recorded by the CMS Phase-2 detector at the HL-LHC, assuming constant detector performance. The 95% upper limit for $\mathcal {L}_{\textrm {int}}$ = 1 ab$^{-1}$ goes outside of the valid region, and is specified as 20+ in the table. |
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Table 6:
The 1$\sigma $ uncertainties in $\mu _H$ and the 95% confidence level intervals for $\kappa _\lambda $, when the other parameter is profiled or fixed to the SM prediction. |
| Summary |
|
The precision of ${\mathrm{t}\mathrm{t}\mathrm{H}} +{\mathrm{t}\mathrm{H}} $, ${\mathrm{H}\to\gamma\gamma} $ differential cross section measurements, at the HL-LHC with the CMS Phase-2 detector, have been determined as a function of $p_T^H$. The analysis has been conducted using a simulated event sample corresponding to 3 ab$^{-1}$ of pp collision data under HL-LHC conditions. A combination of the hadronic and leptonic top decay channels is performed to maximise the sensitivity of the cross section measurements to the Higgs boson self-coupling. With the data expected by the end of the HL-LHC, the cross section in bins of ${p_{\mathrm{T}}}^{\mathrm{H}}$ can be measured within uncertainties of 20-40%, depending on the ${p_{\mathrm{T}}}$ range. When deviations from the standard model prediction for the ${\mathrm{t}\mathrm{t}\mathrm{H}} $+${\mathrm{t}\mathrm{H}} $ ${p_{\mathrm{T}}}^{\mathrm{H}}$ differential cross section are interpreted as modifications of the Higgs boson self-coupling, $\kappa_\lambda$, these measurements exclude values outside of the range -4.1 $ < \kappa_\lambda < $ 14.1, at the 95% confidence level. Furthermore, it has been shown such measurements still provide sensitivity to $\kappa_\lambda$, without exploiting the overall normalisation of the ${p_{\mathrm{T}}}^{\mathrm{H}}$ spectrum, thus allowing for other effects, such as the presence of anomalous top-Higgs couplings. This property is unique to differential cross section measurements. This analysis indicates that additional sensitivity to the Higgs boson self-coupling is available through studies of the differential cross section of single Higgs boson production in association with top quarks. It should be noted that the ultimate sensitivity to the Higgs boson self-coupling, achievable at the HL-LHC, will result from a combination of analyses such as that described in this note with other Higgs decay channels and production modes, and with direct searches for double Higgs boson production. |
| Additional Figures | |
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Additional Figure 1:
Results of the likelihood scan in $\kappa _\lambda $ for different uncertainty scenarios. The nominal result, with all systematic uncertainties included, is shown by the solid black curve. The result when only including experimental systematic uncertainties is shown by the red curve. The statistical uncertainty only curve is shown by the dashed black line. |
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Additional Figure 2:
Results of the likelihood scan in $\kappa _\lambda $ for different integrated luminosities recorded by the CMS Phase-2 detector. |
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Additional Figure 3:
Results of the likelihood scan in $\kappa _\lambda $, when profiling $\mu_{\mathrm{H}}$ (blue) and fixing $\mu_{\mathrm{H}}$ to the standard model prediction (black). |
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Additional Figure 4:
Results of the likelihood scan in $\mu_{\mathrm{H}}$, when profiling $\kappa _\lambda $ (blue) and fixing $\kappa _\lambda $ to the standard model prediction (black). |
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