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| CMS-PAS-HIG-21-002 | ||
| Search for Higgs boson pairs decaying to WWWW, WW$\tau\tau$, and $\tau\tau\tau\tau$ in proton-proton collisions at $\sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| January 2022 | ||
| Abstract: The results of a search for Higgs boson pair (HH) production in the WWWW, WW$ \tau \tau $, and $ \tau\tau\tau\tau $ decay modes are presented. The search uses proton-proton collision data recorded by the CMS experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. The analyzed events contain two, three, or four reconstructed leptons, including electrons, muons, and hadronically decaying tau leptons. No evidence for a signal is found in the data, and upper limits are set on the cross section for nonresonant HH production, as well as resonant production in which a new heavy particle decays to a pair of Higgs bosons. For nonresonant HH production, the observed (expected) upper limit on the cross section at 95% confidence level (CL) is 21.8 (19.6) times the standard model (SM) prediction. The ratio of the trilinear Higgs boson self-coupling to its value in the SM is constrained to be between -7.0 and 11.2 at 95% CL, and limits are set on a variety of new-physics models using an effective field theory approach. The observed (expected) limits on the cross section for resonant HH production range from 0.18 to 0.90 (0.08 to 1.07) pb at 95% CL for new heavy-particle masses from 250 to 1000 GeV. | ||
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These preliminary results are superseded in this paper, JHEP 07 (2023) 095. The superseded preliminary plots can be found here. |
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| Figures | |
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Figure 1:
LO Feynman diagrams for SM nonresonant HH production via gluon fusion (a, b) and via vector boson fusion (c, d, e). |
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Figure 1-a:
LO Feynman diagrams for SM nonresonant HH production via gluon fusion (a, b) and via vector boson fusion (c, d, e). |
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Figure 1-b:
LO Feynman diagrams for SM nonresonant HH production via gluon fusion (a, b) and via vector boson fusion (c, d, e). |
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Figure 1-c:
LO Feynman diagrams for SM nonresonant HH production via gluon fusion (a, b) and via vector boson fusion (c, d, e). |
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Figure 1-d:
LO Feynman diagrams for SM nonresonant HH production via gluon fusion (a, b) and via vector boson fusion (c, d, e). |
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Figure 1-e:
LO Feynman diagrams for SM nonresonant HH production via gluon fusion (a, b) and via vector boson fusion (c, d, e). |
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Figure 2:
LO Feynman diagrams for nonresonant HH production via gluon fusion in an effective field theory approach where loop-mediated contact interactions between (a) two gluons and one Higgs boson, (b) two gluons and two Higgs bosons, and (c) two top quarks and two Higgs bosons are parametrized by three effective couplings: $ {\text {c}_{{\mathrm{g}}}} $, $ {\text {c}_{2 {\mathrm{g}}}} $, and $ {\text {c}_{2}} $. |
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Figure 2-a:
LO Feynman diagrams for nonresonant HH production via gluon fusion in an effective field theory approach where loop-mediated contact interactions between (a) two gluons and one Higgs boson, (b) two gluons and two Higgs bosons, and (c) two top quarks and two Higgs bosons are parametrized by three effective couplings: $ {\text {c}_{{\mathrm{g}}}} $, $ {\text {c}_{2 {\mathrm{g}}}} $, and $ {\text {c}_{2}} $. |
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Figure 2-b:
LO Feynman diagrams for nonresonant HH production via gluon fusion in an effective field theory approach where loop-mediated contact interactions between (a) two gluons and one Higgs boson, (b) two gluons and two Higgs bosons, and (c) two top quarks and two Higgs bosons are parametrized by three effective couplings: $ {\text {c}_{{\mathrm{g}}}} $, $ {\text {c}_{2 {\mathrm{g}}}} $, and $ {\text {c}_{2}} $. |
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Figure 2-c:
LO Feynman diagrams for nonresonant HH production via gluon fusion in an effective field theory approach where loop-mediated contact interactions between (a) two gluons and one Higgs boson, (b) two gluons and two Higgs bosons, and (c) two top quarks and two Higgs bosons are parametrized by three effective couplings: $ {\text {c}_{{\mathrm{g}}}} $, $ {\text {c}_{2 {\mathrm{g}}}} $, and $ {\text {c}_{2}} $. |
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Figure 3:
LO Feynman diagram for resonant HH production. |
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Figure 4:
Distribution in the observable $ {m_\text {T}} $ in the 3$ {\ell} $WZ CR (left) and in the observable $m_{4 {\ell}}$ in the 4$ {\ell} $ZZ CR (right). The distributions expected for the WZ and ZZ as well as for other background processes are shown for the values of nuisance parameters obtained from the ML fit described in Section 9. |
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Figure 4-a:
Distribution in the observable $ {m_\text {T}} $ in the 3$ {\ell} $WZ CR (left) and in the observable $m_{4 {\ell}}$ in the 4$ {\ell} $ZZ CR (right). The distributions expected for the WZ and ZZ as well as for other background processes are shown for the values of nuisance parameters obtained from the ML fit described in Section 9. |
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Figure 4-b:
Distribution in the observable $ {m_\text {T}} $ in the 3$ {\ell} $WZ CR (left) and in the observable $m_{4 {\ell}}$ in the 4$ {\ell} $ZZ CR (right). The distributions expected for the WZ and ZZ as well as for other background processes are shown for the values of nuisance parameters obtained from the ML fit described in Section 9. |
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Figure 5:
Distribution in the output of the BDT for nonresonant HH production used in the $\kappa $ scans (BM7 from Ref. [24]) for the 2$ {\ell} $ ss (top left), 3${\ell}$ (top right), and 4${\ell}$ (bottom) categories. The SM HH signal is shown for a cross section amounting to $30$ times the value predicted in the SM. The distributions expected for the background processes are shown for the values of the signal strength parameter $\mu $ and of the nuisance parameters obtained from the ML fit. The best-fit value of the HH production rate amounts to $\hat{\mu} = $ 1.96$^{+10.57}_{-9.98}$ times the rate expected in the SM. |
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Figure 5-a:
Distribution in the output of the BDT for nonresonant HH production used in the $\kappa $ scans (BM7 from Ref. [24]) for the 2$ {\ell} $ ss (top left), 3${\ell}$ (top right), and 4${\ell}$ (bottom) categories. The SM HH signal is shown for a cross section amounting to $30$ times the value predicted in the SM. The distributions expected for the background processes are shown for the values of the signal strength parameter $\mu $ and of the nuisance parameters obtained from the ML fit. The best-fit value of the HH production rate amounts to $\hat{\mu} = $ 1.96$^{+10.57}_{-9.98}$ times the rate expected in the SM. |
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Figure 5-b:
Distribution in the output of the BDT for nonresonant HH production used in the $\kappa $ scans (BM7 from Ref. [24]) for the 2$ {\ell} $ ss (top left), 3${\ell}$ (top right), and 4${\ell}$ (bottom) categories. The SM HH signal is shown for a cross section amounting to $30$ times the value predicted in the SM. The distributions expected for the background processes are shown for the values of the signal strength parameter $\mu $ and of the nuisance parameters obtained from the ML fit. The best-fit value of the HH production rate amounts to $\hat{\mu} = $ 1.96$^{+10.57}_{-9.98}$ times the rate expected in the SM. |
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Figure 5-c:
Distribution in the output of the BDT for nonresonant HH production used in the $\kappa $ scans (BM7 from Ref. [24]) for the 2$ {\ell} $ ss (top left), 3${\ell}$ (top right), and 4${\ell}$ (bottom) categories. The SM HH signal is shown for a cross section amounting to $30$ times the value predicted in the SM. The distributions expected for the background processes are shown for the values of the signal strength parameter $\mu $ and of the nuisance parameters obtained from the ML fit. The best-fit value of the HH production rate amounts to $\hat{\mu} = $ 1.96$^{+10.57}_{-9.98}$ times the rate expected in the SM. |
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Figure 6:
Distribution in the output of the BDT for nonresonant HH production used in the $\kappa $ scans (BM7 from Ref. [24]) for the 3$ {\ell}$ + 1${\tau _{\text {h}}}$ (top left), 2$ {\ell}$ + 2${\tau _{\text {h}}}$ (top right), 1$ {\ell}$ + 3${\tau _{\text {h}}}$ (bottom left), and 4${\tau _{\text {h}}}$ (bottom right) categories. The SM HH signal is shown for a cross section amounting to $30$ times the value predicted in the SM. The distributions expected for the background processes are shown for the values of the signal strength parameter $\mu $ and of the nuisance parameters obtained from the ML fit. The best-fit value of the HH production rate amounts to $\hat{\mu} = $ 1.96$^{+10.57}_{-9.98}$ times the rate expected in the SM. |
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Figure 6-a:
Distribution in the output of the BDT for nonresonant HH production used in the $\kappa $ scans (BM7 from Ref. [24]) for the 3$ {\ell}$ + 1${\tau _{\text {h}}}$ (top left), 2$ {\ell}$ + 2${\tau _{\text {h}}}$ (top right), 1$ {\ell}$ + 3${\tau _{\text {h}}}$ (bottom left), and 4${\tau _{\text {h}}}$ (bottom right) categories. The SM HH signal is shown for a cross section amounting to $30$ times the value predicted in the SM. The distributions expected for the background processes are shown for the values of the signal strength parameter $\mu $ and of the nuisance parameters obtained from the ML fit. The best-fit value of the HH production rate amounts to $\hat{\mu} = $ 1.96$^{+10.57}_{-9.98}$ times the rate expected in the SM. |
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Figure 6-b:
Distribution in the output of the BDT for nonresonant HH production used in the $\kappa $ scans (BM7 from Ref. [24]) for the 3$ {\ell}$ + 1${\tau _{\text {h}}}$ (top left), 2$ {\ell}$ + 2${\tau _{\text {h}}}$ (top right), 1$ {\ell}$ + 3${\tau _{\text {h}}}$ (bottom left), and 4${\tau _{\text {h}}}$ (bottom right) categories. The SM HH signal is shown for a cross section amounting to $30$ times the value predicted in the SM. The distributions expected for the background processes are shown for the values of the signal strength parameter $\mu $ and of the nuisance parameters obtained from the ML fit. The best-fit value of the HH production rate amounts to $\hat{\mu} = $ 1.96$^{+10.57}_{-9.98}$ times the rate expected in the SM. |
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Figure 6-c:
Distribution in the output of the BDT for nonresonant HH production used in the $\kappa $ scans (BM7 from Ref. [24]) for the 3$ {\ell}$ + 1${\tau _{\text {h}}}$ (top left), 2$ {\ell}$ + 2${\tau _{\text {h}}}$ (top right), 1$ {\ell}$ + 3${\tau _{\text {h}}}$ (bottom left), and 4${\tau _{\text {h}}}$ (bottom right) categories. The SM HH signal is shown for a cross section amounting to $30$ times the value predicted in the SM. The distributions expected for the background processes are shown for the values of the signal strength parameter $\mu $ and of the nuisance parameters obtained from the ML fit. The best-fit value of the HH production rate amounts to $\hat{\mu} = $ 1.96$^{+10.57}_{-9.98}$ times the rate expected in the SM. |
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Figure 6-d:
Distribution in the output of the BDT for nonresonant HH production used in the $\kappa $ scans (BM7 from Ref. [24]) for the 3$ {\ell}$ + 1${\tau _{\text {h}}}$ (top left), 2$ {\ell}$ + 2${\tau _{\text {h}}}$ (top right), 1$ {\ell}$ + 3${\tau _{\text {h}}}$ (bottom left), and 4${\tau _{\text {h}}}$ (bottom right) categories. The SM HH signal is shown for a cross section amounting to $30$ times the value predicted in the SM. The distributions expected for the background processes are shown for the values of the signal strength parameter $\mu $ and of the nuisance parameters obtained from the ML fit. The best-fit value of the HH production rate amounts to $\hat{\mu} = $ 1.96$^{+10.57}_{-9.98}$ times the rate expected in the SM. |
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Figure 7:
Observed and expected 95% CL upper limits on the SM HH production cross section, obtained for both individual search categories and from a simultaneous fit of all seven search categories combined. |
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Figure 8:
Observed and expected 95% CL upper limits on the HH production cross section as a function of the Higgs boson self-coupling strength modifier $ {\kappa _{\lambda}} $. All Higgs boson couplings other than $\lambda $ are assumed to have the values predicted in the SM. The plot on the left shows the result obtained by combining all seven search categories, while the plot on the right shows the limits obtained for each search category separately. Overlaid on the left is a curve in red representing the predicted HH production cross section. |
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Figure 8-a:
Observed and expected 95% CL upper limits on the HH production cross section as a function of the Higgs boson self-coupling strength modifier $ {\kappa _{\lambda}} $. All Higgs boson couplings other than $\lambda $ are assumed to have the values predicted in the SM. The plot on the left shows the result obtained by combining all seven search categories, while the plot on the right shows the limits obtained for each search category separately. Overlaid on the left is a curve in red representing the predicted HH production cross section. |
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Figure 8-b:
Observed and expected 95% CL upper limits on the HH production cross section as a function of the Higgs boson self-coupling strength modifier $ {\kappa _{\lambda}} $. All Higgs boson couplings other than $\lambda $ are assumed to have the values predicted in the SM. The plot on the left shows the result obtained by combining all seven search categories, while the plot on the right shows the limits obtained for each search category separately. Overlaid on the left is a curve in red representing the predicted HH production cross section. |
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Figure 9:
Observed and expected 95% CL upper limits on the HH production cross section for twelve benchmark scenarios from Ref. [24], the additional benchmark scenario 8a from Ref. [62], and for the SM. The plot on the left shows the result obtained by combining all seven search categories, while the plot on the right shows the limits obtained for each search category separately. |
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Figure 9-a:
Observed and expected 95% CL upper limits on the HH production cross section for twelve benchmark scenarios from Ref. [24], the additional benchmark scenario 8a from Ref. [62], and for the SM. The plot on the left shows the result obtained by combining all seven search categories, while the plot on the right shows the limits obtained for each search category separately. |
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Figure 9-b:
Observed and expected 95% CL upper limits on the HH production cross section for twelve benchmark scenarios from Ref. [24], the additional benchmark scenario 8a from Ref. [62], and for the SM. The plot on the left shows the result obtained by combining all seven search categories, while the plot on the right shows the limits obtained for each search category separately. |
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Figure 10:
Observed and expected 95% CL upper limits on the HH production cross section for seven benchmark scenarios from Ref. [61]. The plot on the left shows the result obtained by combining all seven search categories, while the plot on the right shows the limits obtained for each search category separately. |
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Figure 10-a:
Observed and expected 95% CL upper limits on the HH production cross section for seven benchmark scenarios from Ref. [61]. The plot on the left shows the result obtained by combining all seven search categories, while the plot on the right shows the limits obtained for each search category separately. |
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Figure 10-b:
Observed and expected 95% CL upper limits on the HH production cross section for seven benchmark scenarios from Ref. [61]. The plot on the left shows the result obtained by combining all seven search categories, while the plot on the right shows the limits obtained for each search category separately. |
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Figure 11:
Observed and expected limits on the HH production cross section as function of the effective coupling $ {\text {c}_{2}} $ (left) and region excluded in the $ {\kappa _{{\mathrm{t}}}} $-$ {\text {c}_{2}} $ plane (right). All limits are computed at 95% CL. Higgs boson couplings other than the ones shown in the plots ($ {\text {c}_{2}} $ in the left plot and $ {\text {c}_{2}} $ and $ {\kappa _{{\mathrm{t}}}} $ in the right plot) are assumed to have the values predicted by the SM. |
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Figure 11-a:
Observed and expected limits on the HH production cross section as function of the effective coupling $ {\text {c}_{2}} $ (left) and region excluded in the $ {\kappa _{{\mathrm{t}}}} $-$ {\text {c}_{2}} $ plane (right). All limits are computed at 95% CL. Higgs boson couplings other than the ones shown in the plots ($ {\text {c}_{2}} $ in the left plot and $ {\text {c}_{2}} $ and $ {\kappa _{{\mathrm{t}}}} $ in the right plot) are assumed to have the values predicted by the SM. |
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Figure 11-b:
Observed and expected limits on the HH production cross section as function of the effective coupling $ {\text {c}_{2}} $ (left) and region excluded in the $ {\kappa _{{\mathrm{t}}}} $-$ {\text {c}_{2}} $ plane (right). All limits are computed at 95% CL. Higgs boson couplings other than the ones shown in the plots ($ {\text {c}_{2}} $ in the left plot and $ {\text {c}_{2}} $ and $ {\kappa _{{\mathrm{t}}}} $ in the right plot) are assumed to have the values predicted by the SM. |
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Figure 12:
Observed and expected 95% CL upper limits on the production of new particles X of spin $0$ (top) and spin $2$ (bottom) and mass $m_{{\textrm {X}}}$ in the range 250 $\leq m_{{\textrm {X}}} \leq $ 1000 GeV, which decay to Higgs boson pairs, for the combination of all seven search categories (left) and for each search category separately (right). |
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Figure 12-a:
Observed and expected 95% CL upper limits on the production of new particles X of spin $0$ (top) and spin $2$ (bottom) and mass $m_{{\textrm {X}}}$ in the range 250 $\leq m_{{\textrm {X}}} \leq $ 1000 GeV, which decay to Higgs boson pairs, for the combination of all seven search categories (left) and for each search category separately (right). |
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Figure 12-b:
Observed and expected 95% CL upper limits on the production of new particles X of spin $0$ (top) and spin $2$ (bottom) and mass $m_{{\textrm {X}}}$ in the range 250 $\leq m_{{\textrm {X}}} \leq $ 1000 GeV, which decay to Higgs boson pairs, for the combination of all seven search categories (left) and for each search category separately (right). |
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Figure 12-c:
Observed and expected 95% CL upper limits on the production of new particles X of spin $0$ (top) and spin $2$ (bottom) and mass $m_{{\textrm {X}}}$ in the range 250 $\leq m_{{\textrm {X}}} \leq $ 1000 GeV, which decay to Higgs boson pairs, for the combination of all seven search categories (left) and for each search category separately (right). |
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Figure 12-d:
Observed and expected 95% CL upper limits on the production of new particles X of spin $0$ (top) and spin $2$ (bottom) and mass $m_{{\textrm {X}}}$ in the range 250 $\leq m_{{\textrm {X}}} \leq $ 1000 GeV, which decay to Higgs boson pairs, for the combination of all seven search categories (left) and for each search category separately (right). |
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Figure 13:
Distribution in BDT classifier output for resonances of spin 2 and mass 750 GeV in the 2$ {\ell} $ ss (left) and 3${\ell}$ (right) categories. The resonant HH signal is shown for a cross section amounting to 1 pb. The distributions expected for the background processes are shown for the values of the signal strength parameter $\mu $ and of the nuisance parameters obtained from the ML fit. The best-fit value for the HH production cross section amounts to $\hat{\sigma} = $ 0.15$^{+0.09}_{-0.07}$ pb. |
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Figure 13-a:
Distribution in BDT classifier output for resonances of spin 2 and mass 750 GeV in the 2$ {\ell} $ ss (left) and 3${\ell}$ (right) categories. The resonant HH signal is shown for a cross section amounting to 1 pb. The distributions expected for the background processes are shown for the values of the signal strength parameter $\mu $ and of the nuisance parameters obtained from the ML fit. The best-fit value for the HH production cross section amounts to $\hat{\sigma} = $ 0.15$^{+0.09}_{-0.07}$ pb. |
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Figure 13-b:
Distribution in BDT classifier output for resonances of spin 2 and mass 750 GeV in the 2$ {\ell} $ ss (left) and 3${\ell}$ (right) categories. The resonant HH signal is shown for a cross section amounting to 1 pb. The distributions expected for the background processes are shown for the values of the signal strength parameter $\mu $ and of the nuisance parameters obtained from the ML fit. The best-fit value for the HH production cross section amounts to $\hat{\sigma} = $ 0.15$^{+0.09}_{-0.07}$ pb. |
| Tables | |
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Table 1:
Selection requirements on ${p_{\mathrm {T}}}$ and $\eta $ of reconstructed electrons (e), muons ($\mu $), and hadronically decaying tau leptons ($ {\tau _{\text {h}}} $) applied by the triggers used in this analysis. The trigger $ {p_{\mathrm {T}}} $ thresholds for leading, subleading, and third e, $\mu $, or $ {\tau _{\text {h}}} $ are separated by commas, while a backslash indicates a threshold that depends on the year of data taking. For trigger thresholds that vary within the same year, the range of variation is indicated using an en dash. |
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Table 2:
Parameter values for $ {\kappa _{\lambda}} $, $ {\kappa _{{\mathrm{t}}}} $, $ {\text {c}_{2}} $, $ {\text {c}_{{\mathrm{g}}}} $, and $ {\text {c}_{2 {\mathrm{g}}}} $ in MC samples modeling $20$ benchmark scenarios in the EFT approach, plus SM and "box-only'' ($\lambda = $ 0) HH production. |
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Table 3:
Number of events selected in each of the seven search categories, plus two control regions (CR) for the irreducible WZ and ZZ backgrounds, described in Section 7. The HH signal represents the sum of the ggHH and qqHH production processes and is normalized to 30 times the event yield expected in the SM, corresponding to a cross section of about 1 pb. The nomenclature HHVVVV refers to the sum of HH $ \rightarrow $ WWWW, WWZZ and ZZZZ decays and HHVV$\tau \tau $ refers to HH $ \rightarrow $ WW$\tau \tau $ and ZZ$ \tau \tau $ decays. The expected event yields are computed for the values of nuisance parameters obtained from the ML fit described in Section 9. Quoted uncertainties represent the sum of statistical and systematic components. |
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Table 4:
Observed (expected) 95% CL upper limits on the ggHH production cross section for the twelve benchmark scenarios from Ref. [24], the additional benchmark scenario 8a from Ref. [62] and the seven benchmark scenarios from Ref. [61]. The limits correspond to the combination of all seven search categories. |
| Summary |
| The results of a search for nonresonant as well as resonant Higgs boson pair (HH) production in final states with multiple reconstructed leptons including electrons and muons (${\ell} $) as well as hadronically decaying tau leptons (${\tau_\mathrm{h}}$) has been presented. The search targets the HH decay modes WWWW, WW$ \tau \tau $, and $\tau\tau\tau\tau$, using proton-proton collision data recorded by the CMS experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$, Seven search categories, distinguished by ${\ell} $ and ${\tau_\mathrm{h}}$ multiplicity, are included in the analysis: 2${{\ell}}$ ss, 3${{\ell} } $, 4${{\ell} } $, 3${\ell} $ + 1${\tau_\mathrm{h}} $, 2${\ell}$ + 2${\tau_\mathrm{h}} $, 1${\ell}$ + 3${\tau_\mathrm{h}} $, and 4${\tau_\mathrm{h}} $, where "ss" indicates two ${\ell} $ with the same charge. No evidence for a signal is found in the data and upper limits on the cross section for nonresonant as well as resonant HH production are set. The observed (expected) limits on nonresonant HH production in 20 effective field theory benchmark scenarios range from 0.21 to 1.1 (0.16 to 1.17) pb at 95% confidence level, depending on the scenario. For nonresonant HH production with event kinematics as predicted by the standard model (SM), the observed (expected) upper limit on the HH production rate is 21.8 (19.6) times the rate expected in the SM. The results of the search for nonresonant HH production are used to exclude regions in the plane of the Higgs boson coupling to the top quark, ${\text{y}_{{\mathrm{t}} }} $, and of the trilinear Higgs boson self-coupling, $\lambda$. Assuming ${\text{y}_{{\mathrm{t}} }} $ has the value expected in the SM, $\lambda$ is constrained to be between $-$7.0 and 11.2 times the value expected in the SM. For resonant HH production, the observed (expected) limits on the production cross section range from 0.18 to 0.90 (0.08 to 1.07) pb, depending on the mass and spin of the resonance. |
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