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| CMS-PAS-HIG-20-010 | ||
| Search for nonresonant Higgs boson pair production in final states with two bottom quarks and two tau leptons in proton-proton collisions at $\sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| March 2022 | ||
| Abstract: A search for the nonresonant production of Higgs boson pairs (HH) via gluon-gluon and vector boson fusion processes in final states with two bottom quarks and two tau leptons is presented. The search uses data from proton-proton collisions at a center-of-mass energy of $\sqrt{s}= $ 13 TeV recorded with the CMS detector at the LHC, corresponding to an integrated luminosity of 138 fb$^{-1}$. Events in which at least one tau lepton decays hadronically are considered and multiple machine learning techniques are used to identify and extract the signal. The data are found to be consistent, within uncertainties, with the standard model background predictions. Upper limits on the HH production cross section are set to constrain the parameter space for anomalous Higgs boson couplings. The observed (expected) upper limit at 95% confidence level corresponds to 3.3 (5.2) times the standard model prediction for the inclusive HH cross section and to 124 (154) times the standard model prediction for the vector boson fusion HH cross section. At a 95% confidence level, the Higgs field self-coupling is constrained to be within $-$1.8 and 8.8 times the standard model expectation, and the coupling of two Higgs bosons to two vector bosons is constrained to be within $-$0.4 and 2.6. | ||
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Links:
CDS record (PDF) ;
CADI line (restricted) ;
These preliminary results are superseded in this paper, Submitted to PLB. The superseded preliminary plots can be found here. |
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| Figures & Tables | Summary | Additional Figures | References | CMS Publications |
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| Figures | |
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Figure 1:
Feynman diagrams contributing to Higgs boson pair production via gluon-gluon fusion in the SM at leading order. |
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Figure 2:
Feynman diagrams contributing to Higgs boson pair production via vector boson fusion in the SM at leading order. |
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Figure 3:
DNN prediction distributions in the ${\tau _{{\text h}}\tau _{{\text h}}}$ channel in 2018 for the most sensitive category in the ggF (left) and VBF (right) searches. The shaded band in the plots represents the statistical plus systematic uncertainty. |
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Figure 3-a:
DNN prediction distributions in the ${\tau _{{\text h}}\tau _{{\text h}}}$ channel in 2018 for the most sensitive category in the ggF search. The shaded band in the plots represents the statistical plus systematic uncertainty. |
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Figure 3-b:
DNN prediction distributions in the ${\tau _{{\text h}}\tau _{{\text h}}}$ channel in 2018 for the most sensitive category in the VBF search. The shaded band in the plots represents the statistical plus systematic uncertainty. |
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Figure 4:
Combination of bins of all postfit distributions, ordered and merged according to their prefit signal-to-background ratio, separately for the ${\tau _{\mathrm{e}} \tau _{{\text h}}}$ channel (top left), the ${\tau _{\mu} \tau _{{\text h}}}$ channel (top right), and ${\tau _{{\text h}}\tau _{{\text h}}}$ channel (bottom). The ratio also shows the signal scaled to the observed exclusion limit (see Table 2). |
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Figure 4-a:
Combination of bins of all postfit distributions, ordered and merged according to their prefit signal-to-background ratio, separately for the ${\tau _{\mathrm{e}} \tau _{{\text h}}}$ channel. The ratio also shows the signal scaled to the observed exclusion limit (see Table 2). |
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Figure 4-b:
Combination of bins of all postfit distributions, ordered and merged according to their prefit signal-to-background ratio, separately for the ${\tau _{\mu} \tau _{{\text h}}}$ channel. The ratio also shows the signal scaled to the observed exclusion limit (see Table 2). |
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Figure 4-c:
Combination of bins of all postfit distributions, ordered and merged according to their prefit signal-to-background ratio, separately for the ${\tau _{{\text h}}\tau _{{\text h}}}$ channel. The ratio also shows the signal scaled to the observed exclusion limit (see Table 2). |
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Figure 5:
Combination of bins of all postfit distributions, ordered and merged according to their prefit signal-to-background ratio, separately for the background contribution split into physics processes (left), and split into the three considered final state channels (right). The ratio also shows the signal scaled to the observed exclusion limit (see Table 2). |
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Figure 5-a:
Combination of bins of all postfit distributions, ordered and merged according to their prefit signal-to-background ratio, separately for the background contribution split into physics processes. The ratio also shows the signal scaled to the observed exclusion limit (see Table 2). |
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Figure 5-b:
Combination of bins of all postfit distributions, ordered and merged according to their prefit signal-to-background ratio, separately for the background contribution split into the three considered final state channels. The ratio also shows the signal scaled to the observed exclusion limit (see Table 2). |
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Figure 6:
Upper limit on the HH ggF + VBF signal strength at 95% CL for $\kappa _{\lambda} = $ 1, separated into different years and combined for the full Run 2 data set. |
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Figure 7:
Observed and expected upper limits at 95% CL as a function of $\kappa _{\lambda}$ on the HH ggF + VBF signal strength (left) and on the HH ggF + VBF cross section times the bb$ \tau \tau $ branching ratio (right). In both cases all other couplings are set to their SM expectation. |
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Figure 7-a:
Observed and expected upper limits at 95% CL as a function of $\kappa _{\lambda}$ on the HH ggF + VBF signal strength. All other couplings are set to their SM expectation. |
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Figure 7-b:
Observed and expected upper limits at 95% CL as a function of $\kappa _{\lambda}$ on the HH ggF + VBF cross section times the bb$ \tau \tau $ branching ratio. All other couplings are set to their SM expectation. |
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Figure 8:
Upper limit on the HH VBF signal strength at 95% CL for $\kappa _{2{\mathrm{V}}} = $ 1, separated into different years and combined for the full Run 2 data set. |
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Figure 9:
Observed and expected upper limits at 95% CL as a function of $\kappa _{2{\mathrm{V}}}$ on the HH VBF signal strength (left) and on the HH VBF cross section times the bb$ \tau \tau $ branching ratio (right). In both cases all other couplings are set to their SM expectation. |
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Figure 9-a:
Observed and expected upper limits at 95% CL as a function of $\kappa _{2{\mathrm{V}}}$ on the HH VBF signal strength. All other couplings are set to their SM expectation. |
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Figure 9-b:
Observed and expected upper limits at 95% CL as a function of $\kappa _{2{\mathrm{V}}}$ on the HH VBF cross section times the bb$ \tau \tau $ branching ratio. All other couplings are set to their SM expectation. |
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Figure 10:
Two-dimensional exclusion regions as a function of the $\kappa _{\lambda}$ and $\kappa _{\mathrm{t}}$ couplings for the full Run2 combination (left), both $\kappa _{2{\mathrm{V}}}$ and $\kappa _{{\mathrm{V}}}$ are fixed to unity. Two-dimensional exclusion regions as a function of the $\kappa _{2{\mathrm{V}}}$ and $\kappa _{{\mathrm{V}}}$ couplings (right), both $\kappa _{\lambda}$ and $\kappa _{\mathrm{t}}$ are set to unity. Expected uncertainties on exclusion boundaries are inferred from uncertainty bands of the limit calculation, and are denoted by dark and light grey areas. The blue area marks parameter combinations that are observed to be excluded. For visual guidance, theoretical cross section values are illustrated by thin, labeled contour lines with the SM configuration denoted by a red diamond. |
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Figure 10-a:
Two-dimensional exclusion regions as a function of the $\kappa _{\lambda}$ and $\kappa _{\mathrm{t}}$ couplings for the full Run2 combination, both $\kappa _{2{\mathrm{V}}}$ and $\kappa _{{\mathrm{V}}}$ are fixed to unity. Expected uncertainties on exclusion boundaries are inferred from uncertainty bands of the limit calculation, and are denoted by dark and light grey areas. The blue area marks parameter combinations that are observed to be excluded. For visual guidance, theoretical cross section values are illustrated by thin, labeled contour lines with the SM configuration denoted by a red diamond. |
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Figure 10-b:
Two-dimensional exclusion regions as a function of the $\kappa _{2{\mathrm{V}}}$ and $\kappa _{{\mathrm{V}}}$ couplings, both $\kappa _{\lambda}$ and $\kappa _{\mathrm{t}}$ are set to unity. Expected uncertainties on exclusion boundaries are inferred from uncertainty bands of the limit calculation, and are denoted by dark and light grey areas. The blue area marks parameter combinations that are observed to be excluded. For visual guidance, theoretical cross section values are illustrated by thin, labeled contour lines with the SM configuration denoted by a red diamond. |
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Figure 11:
Observed likelihood scan as a function of $\kappa _{\lambda}$ (left) and $\kappa _{2{\mathrm{V}}}$ (right) for the full Run 2 combination. The dashed lines show the intersection with threshold values one and four, corresponding to 68% and 95% confidence intervals, respectively. |
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Figure 11-a:
Observed likelihood scan as a function of $\kappa _{\lambda}$ for the full Run 2 combination. The dashed lines show the intersection with threshold values one and four, corresponding to 68% and 95% confidence intervals, respectively. |
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Figure 11-b:
Observed likelihood scan as a function of $\kappa _{2{\mathrm{V}}}$ for the full Run 2 combination. The dashed lines show the intersection with threshold values one and four, corresponding to 68% and 95% confidence intervals, respectively. |
| Tables | |
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Table 1:
Summary of selections applied to the $\tau \tau $ pair. Trigger thresholds in parentheses refer to the 2017-2018 data-taking period. |
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Table 2:
Expected and observed upper limits at 95% CL for the SM point ($\kappa _{\lambda} = $ 1), where $\sigma _{ggF + \text {VBF}}^{SM}=$ 2.39 fb represents the product of the ggF plus VBF HH cross section (32.776 fb) and the branching fraction $\mathcal {B}({\mathrm{H} \mathrm{H}} \to \mathrm{b} \mathrm{b} \tau \tau)=$ 0.073. |
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Table 3:
Expected and observed upper limits at 95% CL for the SM point ($\kappa _{2{\mathrm{V}}} = $ 1), where $\sigma _{\text {VBF}}^{SM}=$ 0.126 fb represents the product of the VBF HH cross section (1.726 fb) and the branching fraction $\mathcal {B}({\mathrm{H} \mathrm{H}} \to \mathrm{b} \mathrm{b} \tau \tau)=$ 0.073. |
| Summary |
|
A search for nonresonant Higgs boson pair (HH) production via gluon-gluon fusion and vector boson fusion (VBF) processes in final states with two bottom quarks and two $\tau$ leptons was presented. The search uses the full Run 2 data set of proton-proton collisions at a center-of-mass energy of $\sqrt{s} = $ 13 TeV recorded with the CMS detector at the LHC, corresponding to an integrated luminosity of 138 fb$^{-1}$. The three decay modes of the $\tau\tau$ pair with the largest branching fraction have been selected, requiring one $\tau$ to be always decaying hadronically and the other one either leptonically or hadronically. Upper limits at the 95% confidence level (CL) on the inclusive HH production cross sections are set, as well as on the VBF HH production cross sections. This analysis benefits from an improved trigger strategy as well as from a series of techniques developed especially for this search: among others, several neural networks to identify the b jets from the H decay, categorize the events, and perform signal extraction. At the same time, this analysis builds up on the improvements made by the CMS Collaboration in the jet and $\tau$ lepton identification and reconstruction algorithms. All these techniques enable the achievement of particularly stringent results on the HH production cross sections. The observed 95% CL upper limit on HH total production cross section corresponds to 3.3 times the theoretical SM prediction, and the expected limit is 5.2 times the SM prediction. The observed 95% CL upper limit for the VBF HH SM cross section corresponds to 124 times the theoretical SM prediction and the expected limits is about 154 times the SM prediction. The observed (expected) 95% CL constraints on $\kappa_{\lambda}$ and $\kappa_{2\mathrm{V}}$, derived from limits on the HH production cross section times the bb$\tau\tau$ branching ratio, are found to be $-$1.8 $< \kappa_{\lambda} < $ 8.8 ($-$3 $ < \kappa_{\lambda} < $ 9.9) and $-$0.4 $ < \kappa_{2\mathrm{V}} < $ 2.6 ($-$0.6 $ < \kappa_{2\mathrm{V}} < $ 2.8), respectively. |
| Additional Figures | |
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Additional Figure 1:
Distributions of the reconstructed mass of the bb pair in the most sensitive category of the analysis (res2b). Events are shown in the $\mathrm{e} {{\tau} _\mathrm {h}} $ (left), $\mu {{\tau} _\mathrm {h}} $ (center), and ${{\tau} _{{\text h}} {\tau} _{{\text h}}}$ (right) channels for the full Run 2 combination, after the selection on the reconstructed masses of the $ {\tau} {\tau} $ and bb pairs, as described in the paper, has been applied. |
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Additional Figure 2:
Distributions of the mass of the $ {\tau} {\tau} $ pair, reconstructed using the SVfit algorithm [47], in the most sensitive category of the analysis (res2b). Events are shown in the $\mathrm{e} {{\tau} _\mathrm {h}} $ (left), $\mu {{\tau} _\mathrm {h}} $ (center), and ${{\tau} _{{\text h}} {\tau} _{{\text h}}}$ (right) channels for the full Run 2 combination, after the selection on the reconstructed masses of the $ {\tau} {\tau} $ and bb pairs, as described in the paper, has been applied. |
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Additional Figure 3:
Distributions of the reconstructed mass of the HH pair in the most sensitive category of the analysis (res2b). Events are shown in the $\mathrm{e} {{\tau} _\mathrm {h}} $ (left), $\mu {{\tau} _\mathrm {h}} $ (center), and ${{\tau} _{{\text h}} {\tau} _{{\text h}}}$ (right) channels for the full Run 2 combination, after the selection on the reconstructed masses of the $ {\tau} {\tau} $ and bb pairs, as described in the paper, has been applied. |
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Additional Figure 4:
Normalized distribution of reconstructed $m_{{{\mathrm {H}} {\mathrm {H}}}}$ for the gluon fusion simulated signal events (ggHH) in a common baseline selection for the combination in the three channels, with and without trigger selection applied. Two b jet and two ${\tau}$ lepton candidates are required in the event. The efficiency of the trigger selection is shown in the bottom frame. |
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Additional Figure 5:
Normalized distribution of reconstructed $m_{{{\mathrm {H}} {\mathrm {H}}}}$ for the vector boson fusion simulated signal events (qqHH) in a common baseline selection for the combination in the three channels, with and without trigger selection applied. Two b jet and two ${\tau}$ lepton candidates are required in the event. The efficiency of the trigger selection is shown in the bottom frame. |
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Additional Figure 6:
DNN prediction distributions in the $\mathrm{e} {{\tau} _\mathrm {h}} $ channel in 2016 for the eight analysis categories. The shaded band in the plots represents the statistical plus systematic uncertainty. |
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Additional Figure 7:
DNN prediction distributions in the $\mathrm{e} {{\tau} _\mathrm {h}} $ channel in 2017 for the eight analysis categories. The shaded band in the plots represents the statistical plus systematic uncertainty. |
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Additional Figure 8:
DNN prediction distributions in the $\mathrm{e} {{\tau} _\mathrm {h}} $ channel in 2017 for the eight analysis categories. The shaded band in the plots represents the statistical plus systematic uncertainty. |
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Additional Figure 9:
DNN prediction distributions in the $\mu {{\tau} _\mathrm {h}} $ channel in 2016 for the eight analysis categories. The shaded band in the plots represents the statistical plus systematic uncertainty. |
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Additional Figure 10:
DNN prediction distributions in the $\mu {{\tau} _\mathrm {h}} $ channel in 2017 for the eight analysis categories. The shaded band in the plots represents the statistical plus systematic uncertainty. |
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Additional Figure 11:
DNN prediction distributions in the $\mu {{\tau} _\mathrm {h}} $ channel in 2018 for the eight analysis categories. The shaded band in the plots represents the statistical plus systematic uncertainty. |
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Additional Figure 12:
DNN prediction distributions in the ${{\tau} _{{\text h}} {\tau} _{{\text h}}}$ channel in 2016 for the eight analysis categories. The shaded band in the plots represents the statistical plus systematic uncertainty. |
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Additional Figure 13:
DNN prediction distributions in the ${{\tau} _{{\text h}} {\tau} _{{\text h}}}$ channel in 2017 for the eight analysis categories. The shaded band in the plots represents the statistical plus systematic uncertainty. |
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Additional Figure 14:
DNN prediction distributions in the ${{\tau} _{{\text h}} {\tau} _{{\text h}}}$ channel in 2018 for the eight analysis categories. The shaded band in the plots represents the statistical plus systematic uncertainty. |
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Additional Figure 15:
Upper limit on the HH ggF + VBF signal strength at 95% CL, separated into different years and channels, and combined in different channels. All Higgs couplings are set to their SM expectation. |
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Additional Figure 16:
Upper limit on the HH VBF signal strength at 95% CL, separated into different years and channels, and combined in different channels. All Higgs couplings are set to their SM expectation. |
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Additional Figure 17:
Observed and expected upper limits, separated into categories, on the HH ggF + VBF signal strength at 95% CL as a function of $\kappa _{\lambda}$, with all other couplings set to their SM expectation. |
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Additional Figure 18:
Observed and expected upper limits, separated into categories, on the HH VBF signal strength at 95% CL as a function of $\kappa _{2}$, with all other couplings set to their SM expectation. |
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Additional Figure 19:
Two-dimensional exclusion regions as a function of the $\kappa _{\lambda}$ and $\kappa _{2}$ coupling modifiers for the full Run2 combination, both $\kappa _{}$ and $\kappa _{\mathrm{t}}$ are fixed to unity. Expected uncertainties on exclusion boundaries are inferred from uncertainty bands of the limit calculation, and are denoted by dark and light grey areas. The blue area marks parameter combinations that are observed to be excluded. For visual guidance, theoretical cross section values are illustrated by thin, labeled contour lines with the SM configuration denoted by a red diamond. |
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Additional Figure 20:
Observed likelihood scan as a function of $\kappa _{\mathrm{t}}$ for the full Run 2 combination. The dashed lines show the intersection with threshold values one and four, corresponding to 68% and 95% confidence intervals, respectively. |
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Additional Figure 21:
Observed likelihood scan as a function of $\kappa _{}$ for the full Run 2 combination. The dashed lines show the intersection with threshold values one and four, corresponding to 68% and 95% confidence intervals, respectively. |
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Additional Figure 22:
2D likelihood scan as function of $\kappa _{2}$ and $\kappa _{}$, assuming $r=\kappa _{\mathrm{t}}=\kappa _{\lambda}=1$. The best fit value and its uncertainty are denoted by the black marker and lines, whereas the full uncertainty contours referring to one and two standard deviations are visualized by the green and yellow lines, respectively. The enclosing box refers to the uncertainty construction as described in [62], Figure 40.5. The red diamond represents the SM prediction. |
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Additional Figure 23:
2D likelihood scan as function of $\kappa _{\lambda}$ and $\kappa _{2}$, assuming $r=\kappa _{\mathrm{t}}=\kappa _{}=1$. The best fit value and its uncertainty are denoted by the black marker and lines, whereas the full uncertainty contours referring to one and two standard deviations are visualized by the green and yellow lines, respectively. The enclosing box refers to the uncertainty construction as described in [62], Figure 40.5. The red diamond represents the SM prediction. |
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Additional Figure 24:
2D likelihood scan as function of $\kappa _{\lambda}$ and $\kappa _{\mathrm{t}}$, assuming $r=\kappa _{2}=\kappa _{}=1$. The best fit value and its uncertainty are denoted by the black marker and lines, whereas the full uncertainty contours referring to one and two standard deviations are visualized by the green and yellow lines, respectively. The enclosing box refers to the uncertainty construction as described in [62], Figure 40.5. The red diamond represents the SM prediction. |
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Additional Figure 25:
Displays in the transverse (top left) and longitudinal (top right) planes and tridimensional (bottom) view of a candidate $ {{\mathrm {H}} {\mathrm {H}}} \to {\tau} {\tau} {\mathrm {b}} {\mathrm {b}} $ event in the res2b category of the ${{\tau} _{{\text h}} {\tau} _{{\text h}}}$ channel in 2016. |
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Additional Figure 25-a:
Displays in the transverse (top left) and longitudinal (top right) planes and tridimensional (bottom) view of a candidate $ {{\mathrm {H}} {\mathrm {H}}} \to {\tau} {\tau} {\mathrm {b}} {\mathrm {b}} $ event in the res2b category of the ${{\tau} _{{\text h}} {\tau} _{{\text h}}}$ channel in 2016. |
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Additional Figure 25-b:
Displays in the transverse (top left) and longitudinal (top right) planes and tridimensional (bottom) view of a candidate $ {{\mathrm {H}} {\mathrm {H}}} \to {\tau} {\tau} {\mathrm {b}} {\mathrm {b}} $ event in the res2b category of the ${{\tau} _{{\text h}} {\tau} _{{\text h}}}$ channel in 2016. |
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Additional Figure 25-c:
Displays in the transverse (top left) and longitudinal (top right) planes and tridimensional (bottom) view of a candidate $ {{\mathrm {H}} {\mathrm {H}}} \to {\tau} {\tau} {\mathrm {b}} {\mathrm {b}} $ event in the res2b category of the ${{\tau} _{{\text h}} {\tau} _{{\text h}}}$ channel in 2016. |
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Additional Figure 26:
Displays in the transverse (top left) and longitudinal (top right) planes and tridimensional (bottom) view of a candidate $ {{\mathrm {H}} {\mathrm {H}}} \to {\tau} {\tau} {\mathrm {b}} {\mathrm {b}} $ event in the \textit {classVBF} category of the ${{\tau} _{{\text h}} {\tau} _{{\text h}}}$ channel in 2018. |
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Additional Figure 26-a:
Displays in the transverse (top left) and longitudinal (top right) planes and tridimensional (bottom) view of a candidate $ {{\mathrm {H}} {\mathrm {H}}} \to {\tau} {\tau} {\mathrm {b}} {\mathrm {b}} $ event in the \textit {classVBF} category of the ${{\tau} _{{\text h}} {\tau} _{{\text h}}}$ channel in 2018. |
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Additional Figure 26-b:
Displays in the transverse (top left) and longitudinal (top right) planes and tridimensional (bottom) view of a candidate $ {{\mathrm {H}} {\mathrm {H}}} \to {\tau} {\tau} {\mathrm {b}} {\mathrm {b}} $ event in the \textit {classVBF} category of the ${{\tau} _{{\text h}} {\tau} _{{\text h}}}$ channel in 2018. |
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Additional Figure 26-c:
Displays in the transverse (top left) and longitudinal (top right) planes and tridimensional (bottom) view of a candidate $ {{\mathrm {H}} {\mathrm {H}}} \to {\tau} {\tau} {\mathrm {b}} {\mathrm {b}} $ event in the \textit {classVBF} category of the ${{\tau} _{{\text h}} {\tau} _{{\text h}}}$ channel in 2018. |
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