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CMS-HIG-21-003 ; CERN-EP-2022-095
Search for the exotic decay of the Higgs boson into two light pseudoscalars with four photons in the final state in proton-proton collisions at $\sqrt{s} = $ 13 TeV
JHEP 07 (2023) 148
Abstract: A search for the exotic decay of the Higgs boson to a pair of light pseudoscalars, each of which subsequently decays into a pair of photons, is presented. The search uses data from proton-proton collisions at $\sqrt{s} = $ 13 TeV recorded with the CMS detector at the LHC that corresponds to an integrated luminosity of 132 fb$^{-1}$. The analysis probes pseudoscalar bosons with masses in the range 15-62 GeV, coming from the Higgs boson decay, which leads to four well-isolated photons in the final state. No significant deviation from the background-only hypothesis is observed. Upper limits are set on the product of the Higgs boson production cross section and branching fraction into four photons. The observed (expected) limits range from 0.80 (1.00) fb for a pseudoscalar boson mass of 15 GeV to 0.26 (0.24) fb for a mass of 62 GeV at 95% confidence level.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Feynman diagram for a BSM decay of the Higgs boson into a pair of light pseudoscalar bosons that subsequently decay into photons.

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Figure 2:
Distributions of the four most highly ranked discriminating variables: the difference between the invariant masses of the pseudoscalar bosons and the ${m_{a,\text {hyp}}}$ parameter, divided by the invariant mass of the four-photon system (upper left), with off-zero signal peaks from photon pairing mismatches; the difference between the invariant masses of the pseudoscalar bosons (upper right); the photon identification BDT score of the third leading, $\gamma _{3}$ (lower left) and the fourth leading, $\gamma _{4}$ (lower right) photons. The events shown are selected from the ${m_{\gamma \gamma \gamma \gamma}}$ sidebands (110 $< {m_{\gamma \gamma \gamma \gamma}} < $ 115 GeV or 135 $ < {m_{\gamma \gamma \gamma \gamma}} < $ 180 GeV) for event mixing and data after fulfilling the selection criteria described in Section 4, while the signals are scaled with a cross-section of 1 pb.

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Figure 2-a:
Distribution of the difference between the invariant masses of the pseudoscalar bosons. The events shown are selected from the ${m_{\gamma \gamma \gamma \gamma}}$ sidebands (110 $< {m_{\gamma \gamma \gamma \gamma}} < $ 115 GeV or 135 $ < {m_{\gamma \gamma \gamma \gamma}} < $ 180 GeV) for event mixing and data after fulfilling the selection criteria described in Section 4, while the signals are scaled with a cross-section of 1 pb.

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Figure 2-b:
Distributions of the four most highly ranked discriminating variables: the difference between the invariant masses of the pseudoscalar bosons and the ${m_{a,\text {hyp}}}$ parameter, divided by the invariant mass of the four-photon system (upper left), with off-zero signal peaks from photon pairing mismatches; the difference between the invariant masses of the pseudoscalar bosons (upper right); the photon identification BDT score of the third leading, $\gamma _{3}$ (lower left) and the fourth leading, $\gamma _{4}$ (lower right) photons. The events shown are selected from the ${m_{\gamma \gamma \gamma \gamma}}$ sidebands (110 $< {m_{\gamma \gamma \gamma \gamma}} < $ 115 GeV or 135 $ < {m_{\gamma \gamma \gamma \gamma}} < $ 180 GeV) for event mixing and data after fulfilling the selection criteria described in Section 4, while the signals are scaled with a cross-section of 1 pb.

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Figure 2-c:
Distribution of the photon identification BDT score of the third leading photon, $\gamma _{3}$. The events shown are selected from the ${m_{\gamma \gamma \gamma \gamma}}$ sidebands (110 $< {m_{\gamma \gamma \gamma \gamma}} < $ 115 GeV or 135 $ < {m_{\gamma \gamma \gamma \gamma}} < $ 180 GeV) for event mixing and data after fulfilling the selection criteria described in Section 4, while the signals are scaled with a cross-section of 1 pb.

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Figure 2-d:
Distribution of the photon identification BDT score of the fourth leading photon, $\gamma _{4}$. The events shown are selected from the ${m_{\gamma \gamma \gamma \gamma}}$ sidebands (110 $< {m_{\gamma \gamma \gamma \gamma}} < $ 115 GeV or 135 $ < {m_{\gamma \gamma \gamma \gamma}} < $ 180 GeV) for event mixing and data after fulfilling the selection criteria described in Section 4, while the signals are scaled with a cross-section of 1 pb.

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Figure 3:
Distribution of the BDT output for ${m_{a}} = $ 15 GeV (left) and 50 GeV (right) in data and simulated signal and event mixing (after smoothing) events. Events shown are selected after fulfilling the selection criteria described in Section 4 in the mass window 110 $ < {m_{\gamma \gamma \gamma \gamma}} < $ 180 GeV, while the signal is scaled with a cross-section of 1 pb.

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Figure 3-a:
Distribution of the BDT output for ${m_{a}} = $ 15 GeV in data and simulated signal and event mixing (after smoothing) events. Events shown are selected after fulfilling the selection criteria described in Section 4 in the mass window 110 $ < {m_{\gamma \gamma \gamma \gamma}} < $ 180 GeV, while the signal is scaled with a cross-section of 1 pb.

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Figure 3-b:
Distribution of the BDT output for ${m_{a}} = $ 50 GeV in data and simulated signal and event mixing (after smoothing) events. Events shown are selected after fulfilling the selection criteria described in Section 4 in the mass window 110 $ < {m_{\gamma \gamma \gamma \gamma}} < $ 180 GeV, while the signal is scaled with a cross-section of 1 pb.

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Figure 4:
The parameterized signal shape for ${m_{a}} = $ 15 GeV is shown for the 2016 (upper left), 2017 (upper right), and 2018 (lower) data-taking years. Separate signal models are built for each of the three data-taking years, which are then scaled by the appropriate luminosity and summed in order to construct the final signal model. The open squares represent simulated events and the blue line is the corresponding model. Also shown is the $\sigma _{\text {eff}}$ value (half the width of the narrowest interval containing 68.3% of the invariant mass distribution), with the corresponding interval as a gray band and the FWHM, with the corresponding interval marked with a double arrow.

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Figure 4-a:
The parameterized signal shape for ${m_{a}} = $ 15 GeV is shown for the 2016 data-taking year. A separate signal model is built, which is then scaled by the appropriate luminosity and summed in order to construct the final signal model. The open squares represent simulated events and the blue line is the corresponding model. Also shown is the $\sigma _{\text {eff}}$ value (half the width of the narrowest interval containing 68.3% of the invariant mass distribution), with the corresponding interval as a gray band and the FWHM, with the corresponding interval marked with a double arrow.

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Figure 4-b:
The parameterized signal shape for ${m_{a}} = $ 15 GeV is shown for the 2017 data-taking year. A separate signal model is built, which is then scaled by the appropriate luminosity and summed in order to construct the final signal model. The open squares represent simulated events and the blue line is the corresponding model. Also shown is the $\sigma _{\text {eff}}$ value (half the width of the narrowest interval containing 68.3% of the invariant mass distribution), with the corresponding interval as a gray band and the FWHM, with the corresponding interval marked with a double arrow.

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Figure 4-c:
The parameterized signal shape for ${m_{a}} = $ 15 GeV is shown for the 2018 data-taking year. A separate signal model is built, which is then scaled by the appropriate luminosity and summed in order to construct the final signal model. The open squares represent simulated events and the blue line is the corresponding model. Also shown is the $\sigma _{\text {eff}}$ value (half the width of the narrowest interval containing 68.3% of the invariant mass distribution), with the corresponding interval as a gray band and the FWHM, with the corresponding interval marked with a double arrow.

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Figure 5:
The invariant mass distribution, ${m_{\gamma \gamma \gamma \gamma}}$, for data (black points) and the signal-plus-background model fit is shown for ${m_{a}} = $ 15 GeV (left) and ${m_{a}} = $ 50 GeV (right). The solid red line shows the total signal-plus-background contribution, whereas the dashed red line shows the background component only. The lower panel in each plot shows the residual signal yield after the background subtraction. The one (green) and two (yellow) standard deviation bands include the uncertainties in the background component of the fit.

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Figure 5-a:
The invariant mass distribution, ${m_{\gamma \gamma \gamma \gamma}}$, for data (black points) and the signal-plus-background model fit is shown for ${m_{a}} = $ 15 GeV. The solid red line shows the total signal-plus-background contribution, whereas the dashed red line shows the background component only. The lower panel in each plot shows the residual signal yield after the background subtraction. The one (green) and two (yellow) standard deviation bands include the uncertainties in the background component of the fit.

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Figure 5-b:
The invariant mass distribution, ${m_{\gamma \gamma \gamma \gamma}}$, for data (black points) and the signal-plus-background model fit is shown for ${m_{a}} = $ 50 GeV. The solid red line shows the total signal-plus-background contribution, whereas the dashed red line shows the background component only. The lower panel in each plot shows the residual signal yield after the background subtraction. The one (green) and two (yellow) standard deviation bands include the uncertainties in the background component of the fit.

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Figure 6:
Expected and observed 95% CL limits on the product of the production cross section of the Higgs boson and the branching fraction into four photons via a pair of pseuodscalars, $ {\sigma _{\mathrm{H}}}\, {\mathcal {B}({\mathrm{H} \to aa \to \gamma \gamma \gamma \gamma})} $, are shown as a function of ${m_{a}}$. The green (yellow) bands represent the 68% (95%) expected limit CL intervals. The fluctuation between individual points is due to the statistical limitation of the data sample and the result of individual BDT training networks utilized for each individual mass point scenario.
Tables

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Table 1:
Summary of the optimized BDT output threshold values and the efficiency with respect to a selection on this output for each of the nominal signal hypothesis.

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Table 2:
Summary of the systematic uncertainties considered in this analysis.
Summary
A search for a pair of light pseudoscalar bosons produced from the decay of the 125 GeV Higgs boson, which subsequently decay into photons, is presented. The analysis is based on proton-proton collision data collected at $\sqrt{s} = $ 13 TeV by the CMS experiment at the LHC in 2016, 2017, and 2018, which corresponds to a total integrated luminosity of 132 fb$^{-1}$. The analysis probes pseudoscalar bosons ranging in mass ($m_{a}$) from 15 to 62 GeV. No significant deviation from the background-only hypothesis is observed. Upper limits are set at 95% confidence level on the product of the production cross section of the Higgs boson and the branching fraction into four photons via a pair of pseuodscalars, ${{\sigma_{\mathrm{H}}}\,{\mathcal{B}({\mathrm{H} \to aa \to \gamma\gamma\gamma\gamma} )} }$. The observed (expected) limits range from 0.80 (1.00) fb for $m_{a} = $ 15 GeV to 0.26 (0.24) fb for $m_{a} = $ 62 GeV.
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