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| CMS-EXO-24-025 ; CERN-EP-2025-251 | ||
| Search for exotic Higgs boson decays $ \mathrm{H}\to \mathcal{A}\mathcal{A} $ with $ \mathcal{A}\to\gamma\gamma $ in events with a semi-merged topology in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 30 December 2025 | ||
| Submitted to J. High Energy Phys. | ||
| Abstract: A search for exotic Higgs boson decays $ \mathrm{H}\to \mathcal{A}\mathcal{A} $, with $ \mathcal{A}\to\gamma\gamma $ is presented, using events with a semi-merged topology. One of the hypothetical particles, $ \mathcal{A} $, is assumed to decay promptly into a semi-merged diphoton system reconstructed as a single photon-like object, while the other $ \mathcal{A} $ decays into two resolved photons. The search is performed using proton-proton collision data collected by the CMS experiment at $ \sqrt{s} = $ 13 TeV, corresponding to an integrated luminosity of 138 fb$ ^{-1} $. The data agree with the standard model background expectation. Upper limits are set on the product of the Higgs boson production cross section and the branching fraction, $ \sigma(\mathrm{p}\mathrm{p} \to \mathrm{H}) \mathcal{B}(\mathrm{H}\to \mathcal{A}\mathcal{A} \to 4\gamma) $, which range from 0.264 to 0.005$ $ pb at 95% confidence level, for $ \mathcal{A} $ masses in the range 1 $ < m_{\mathcal{A}} < $ 15 GeV. These limits are the most stringent to date in the 1-5 GeV $ m_{\mathcal{A}} $ range. | ||
| Links: e-print arXiv:2601.00183 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Energy deposit maps in the ECAL from simulated $ \mathrm{H}\to \mathcal{A}\mathcal{A} \to 4\gamma $ events corresponding to the 2017 data-taking conditions for the masses $ m_{\mathcal{A}} = $ 3 (left), 5 (middle), and 15 (right) GeV, shown in the relative ECAL crystal index coordinates ($ i\eta^{'}, i\phi^{'} $). Each image displays the ECAL deposits from a single $ \mathcal{A}\to\gamma\gamma $ decay of the merged leg. A close-up of the merged-photon candidate in the center of each image is shown, and the generator-level photon separation $ \Delta R_{\text{gen}}(\gamma\gamma) $ is indicated above each panel for the corresponding mass point. |
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Figure 1-a:
Energy deposit maps in the ECAL from simulated $ \mathrm{H}\to \mathcal{A}\mathcal{A} \to 4\gamma $ events corresponding to the 2017 data-taking conditions for the masses $ m_{\mathcal{A}} = $ 3 (left), 5 (middle), and 15 (right) GeV, shown in the relative ECAL crystal index coordinates ($ i\eta^{'}, i\phi^{'} $). Each image displays the ECAL deposits from a single $ \mathcal{A}\to\gamma\gamma $ decay of the merged leg. A close-up of the merged-photon candidate in the center of each image is shown, and the generator-level photon separation $ \Delta R_{\text{gen}}(\gamma\gamma) $ is indicated above each panel for the corresponding mass point. |
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Figure 1-b:
Energy deposit maps in the ECAL from simulated $ \mathrm{H}\to \mathcal{A}\mathcal{A} \to 4\gamma $ events corresponding to the 2017 data-taking conditions for the masses $ m_{\mathcal{A}} = $ 3 (left), 5 (middle), and 15 (right) GeV, shown in the relative ECAL crystal index coordinates ($ i\eta^{'}, i\phi^{'} $). Each image displays the ECAL deposits from a single $ \mathcal{A}\to\gamma\gamma $ decay of the merged leg. A close-up of the merged-photon candidate in the center of each image is shown, and the generator-level photon separation $ \Delta R_{\text{gen}}(\gamma\gamma) $ is indicated above each panel for the corresponding mass point. |
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Figure 1-c:
Energy deposit maps in the ECAL from simulated $ \mathrm{H}\to \mathcal{A}\mathcal{A} \to 4\gamma $ events corresponding to the 2017 data-taking conditions for the masses $ m_{\mathcal{A}} = $ 3 (left), 5 (middle), and 15 (right) GeV, shown in the relative ECAL crystal index coordinates ($ i\eta^{'}, i\phi^{'} $). Each image displays the ECAL deposits from a single $ \mathcal{A}\to\gamma\gamma $ decay of the merged leg. A close-up of the merged-photon candidate in the center of each image is shown, and the generator-level photon separation $ \Delta R_{\text{gen}}(\gamma\gamma) $ is indicated above each panel for the corresponding mass point. |
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Figure 2:
Illustration of the network architecture used for the mass regression. Input energy and position of the calorimeter deposits are processed by an MLP, followed by EdgeConv and clustering + pooling layers with residual connections. The final graph representation is passed through an output MLP to predict the object mass. |
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Figure 3:
True vs. predicted mass from the mass regression during training validation using simulated $ \mathcal{A}\to\gamma\gamma $ samples corresponding to the 2017 data-taking conditions generated with a continuous uniform distribution in mass and $ p_{\mathrm{T}} $. As discussed in Section 5.2, the training includes domain continuation, which introduces negative target mass labels to improve linearity near the boundary; regions below and to the left of the solid red lines correspond to these negative mass predictions, which are not considered in the final selection. |
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Figure 4:
Predicted mass distribution from the mass regression on the merged leg of the simulated $ \mathrm{H}\to \mathcal{A}\mathcal{A} \to 4\gamma $ events corresponding to the 2017 data-taking conditions, which pass the event selection criteria, for different simulated mass points. The variable $ f $ denotes the fraction of events per bin. The area of each distribution is normalized to unity. Negative mass predictions shown in the hatched region are not considered for final selections. |
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Figure 5:
Predicted mass distribution from the mass regression on the merged leg of the simulated $ \mathrm{H}\to \mathcal{A}\mathcal{A} \to 4\gamma $ events with $ m_{\mathcal{A}} = $ 5 GeV, reconstructed under detector conditions corresponding to the 2016, 2017, and 2018 data-taking periods. The same regression and event selection are applied in all cases. The variable $ f $ denotes the fraction of events per bin. The area of each distribution is normalized to unity. |
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Figure 6:
Regressed mass for $ \mathrm{Z} \to \mathrm{e}^+\mathrm{e}^- $ electrons in the 2017 data vs. simulation for all events passing the selections (left), showing a peak at zero, and for a subset of those events with a soft photon-like deposit near the electron (right), showing a peak away from zero. The variable $ f $ denotes the fraction of events per bin. The area of each distribution is normalized to unity. In the upper panels of each plot, the coverage of the best fit scale and smearing estimates in simulated events (``MC, stat $ \oplus $ syst''), plus statistical uncertainties added in quadrature, are plotted as the red bands around the original simulated sample, which are shown as the blue lines (``MC''). The data events are shown as black points, with statistical uncertainties indicated by the error bars. In the lower panels of each plot, the ratio of data to simulation is shown with the black points, where the error bars represent the statistical uncertainties in the data. The red-filled area represents the combined statistical and systematic uncertainty in the best fit corrected simulation, shown relative to the nominal prediction as an uncertainty envelope around unity. The gray hatched regions correspond to events that do not enter the selection. |
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Figure 6-a:
Regressed mass for $ \mathrm{Z} \to \mathrm{e}^+\mathrm{e}^- $ electrons in the 2017 data vs. simulation for all events passing the selections (left), showing a peak at zero, and for a subset of those events with a soft photon-like deposit near the electron (right), showing a peak away from zero. The variable $ f $ denotes the fraction of events per bin. The area of each distribution is normalized to unity. In the upper panels of each plot, the coverage of the best fit scale and smearing estimates in simulated events (``MC, stat $ \oplus $ syst''), plus statistical uncertainties added in quadrature, are plotted as the red bands around the original simulated sample, which are shown as the blue lines (``MC''). The data events are shown as black points, with statistical uncertainties indicated by the error bars. In the lower panels of each plot, the ratio of data to simulation is shown with the black points, where the error bars represent the statistical uncertainties in the data. The red-filled area represents the combined statistical and systematic uncertainty in the best fit corrected simulation, shown relative to the nominal prediction as an uncertainty envelope around unity. The gray hatched regions correspond to events that do not enter the selection. |
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Figure 6-b:
Regressed mass for $ \mathrm{Z} \to \mathrm{e}^+\mathrm{e}^- $ electrons in the 2017 data vs. simulation for all events passing the selections (left), showing a peak at zero, and for a subset of those events with a soft photon-like deposit near the electron (right), showing a peak away from zero. The variable $ f $ denotes the fraction of events per bin. The area of each distribution is normalized to unity. In the upper panels of each plot, the coverage of the best fit scale and smearing estimates in simulated events (``MC, stat $ \oplus $ syst''), plus statistical uncertainties added in quadrature, are plotted as the red bands around the original simulated sample, which are shown as the blue lines (``MC''). The data events are shown as black points, with statistical uncertainties indicated by the error bars. In the lower panels of each plot, the ratio of data to simulation is shown with the black points, where the error bars represent the statistical uncertainties in the data. The red-filled area represents the combined statistical and systematic uncertainty in the best fit corrected simulation, shown relative to the nominal prediction as an uncertainty envelope around unity. The gray hatched regions correspond to events that do not enter the selection. |
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Figure 7:
The 2 $ \mathrm{D} m_{\mathcal{A}} $ distribution of the signal model from 2017 simulation for the $ m_{\mathcal{A}}= $ 5 GeV hypothesis, normalized to $ \sigma(\mathrm{p}\mathrm{p} \to \mathrm{H})\mathcal{B} (\mathrm{H}\to \mathcal{A}\mathcal{A} \to 4\gamma) = $ 1 pb. The region enclosed by the jagged lines defines the $ m_{\mathcal{A}}$-SR region, while the area outside corresponds to the $ m_{\mathcal{A}}$-SB region. |
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Figure 8:
The 2 $ \mathrm{D} m_{\mathcal{A}} $ distribution of the background model constructed from data sidebands. The region enclosed by the jagged lines defines the $ m_{\mathcal{A}}$-SR region, while the area outside corresponds to the $ m_{\mathcal{A}}$-SB region. |
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Figure 9:
Expected background versus observed data 2 $ \mathrm{D} m_{\mathcal{A}} $ spectra in the $ m_{\mathrm{H}}$-SR $\cap\ m_{\mathcal{A}}$-SB region. Upper plot: unrolled spectra made by scanning along bins of increasing $ m_{\mathcal{A}2} $ at fixed $ m_{\mathcal{A}1} $ before incrementing in $ m_{\mathcal{A}1} $. Only the bins in the $ m_{\mathcal{A}}$-SB region are included, with the x-axis corresponding to the unrolled bin index of the selected bins, listed sequentially. Lower plot: projected 1D $ m_{\mathcal{A}} $ spectra corresponding to merged (left) and resolved (right) candidates. In the upper panels of each plot, the black points with error bars (``Data'') are the observed data values, with the error bars corresponding to statistical uncertainties. The blue line corresponds to the background model, with the blue band corresponding to its statistical uncertainties and systematic uncertainties added in quadrature (``Bkg, stat $ \oplus $ syst''). In the lower panel of the same plot, the ratio of the observed data over the estimated background value is shown as black points, with error bars corresponding to statistical uncertainties in the former. The ratio of the statistical plus systematic uncertainties in the background over the background prediction is shown as the blue band. |
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Figure 9-a:
Expected background versus observed data 2 $ \mathrm{D} m_{\mathcal{A}} $ spectra in the $ m_{\mathrm{H}}$-SR $\cap\ m_{\mathcal{A}}$-SB region. Upper plot: unrolled spectra made by scanning along bins of increasing $ m_{\mathcal{A}2} $ at fixed $ m_{\mathcal{A}1} $ before incrementing in $ m_{\mathcal{A}1} $. Only the bins in the $ m_{\mathcal{A}}$-SB region are included, with the x-axis corresponding to the unrolled bin index of the selected bins, listed sequentially. Lower plot: projected 1D $ m_{\mathcal{A}} $ spectra corresponding to merged (left) and resolved (right) candidates. In the upper panels of each plot, the black points with error bars (``Data'') are the observed data values, with the error bars corresponding to statistical uncertainties. The blue line corresponds to the background model, with the blue band corresponding to its statistical uncertainties and systematic uncertainties added in quadrature (``Bkg, stat $ \oplus $ syst''). In the lower panel of the same plot, the ratio of the observed data over the estimated background value is shown as black points, with error bars corresponding to statistical uncertainties in the former. The ratio of the statistical plus systematic uncertainties in the background over the background prediction is shown as the blue band. |
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Figure 9-b:
Expected background versus observed data 2 $ \mathrm{D} m_{\mathcal{A}} $ spectra in the $ m_{\mathrm{H}}$-SR $\cap\ m_{\mathcal{A}}$-SB region. Upper plot: unrolled spectra made by scanning along bins of increasing $ m_{\mathcal{A}2} $ at fixed $ m_{\mathcal{A}1} $ before incrementing in $ m_{\mathcal{A}1} $. Only the bins in the $ m_{\mathcal{A}}$-SB region are included, with the x-axis corresponding to the unrolled bin index of the selected bins, listed sequentially. Lower plot: projected 1D $ m_{\mathcal{A}} $ spectra corresponding to merged (left) and resolved (right) candidates. In the upper panels of each plot, the black points with error bars (``Data'') are the observed data values, with the error bars corresponding to statistical uncertainties. The blue line corresponds to the background model, with the blue band corresponding to its statistical uncertainties and systematic uncertainties added in quadrature (``Bkg, stat $ \oplus $ syst''). In the lower panel of the same plot, the ratio of the observed data over the estimated background value is shown as black points, with error bars corresponding to statistical uncertainties in the former. The ratio of the statistical plus systematic uncertainties in the background over the background prediction is shown as the blue band. |
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Figure 9-c:
Expected background versus observed data 2 $ \mathrm{D} m_{\mathcal{A}} $ spectra in the $ m_{\mathrm{H}}$-SR $\cap\ m_{\mathcal{A}}$-SB region. Upper plot: unrolled spectra made by scanning along bins of increasing $ m_{\mathcal{A}2} $ at fixed $ m_{\mathcal{A}1} $ before incrementing in $ m_{\mathcal{A}1} $. Only the bins in the $ m_{\mathcal{A}}$-SB region are included, with the x-axis corresponding to the unrolled bin index of the selected bins, listed sequentially. Lower plot: projected 1D $ m_{\mathcal{A}} $ spectra corresponding to merged (left) and resolved (right) candidates. In the upper panels of each plot, the black points with error bars (``Data'') are the observed data values, with the error bars corresponding to statistical uncertainties. The blue line corresponds to the background model, with the blue band corresponding to its statistical uncertainties and systematic uncertainties added in quadrature (``Bkg, stat $ \oplus $ syst''). In the lower panel of the same plot, the ratio of the observed data over the estimated background value is shown as black points, with error bars corresponding to statistical uncertainties in the former. The ratio of the statistical plus systematic uncertainties in the background over the background prediction is shown as the blue band. |
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Figure 10:
The 2 $ \mathrm{D} m_{\mathcal{A}} $ spectra in the final signal region. Upper plot: The unrolled 2 $ \mathrm{D} m_{\mathcal{A}} $ distribution made by scanning along bins of increasing $ m_{\mathcal{A}2} $ at fixed $ m_{\mathcal{A}1} $ before incrementing in $ m_{\mathcal{A}1} $. Only the bins in the $ m_{\mathcal{A}}$-SR region are included, with the x-axis corresponding to the unrolled bin index of the selected bins, listed sequentially. Lower plot: 1D projections on the $ m_{\mathcal{A}1} $ (left) and $ m_{\mathcal{A}2} $ (right) axes of the 2 $ \mathrm{D} m_{\mathcal{A}} $ distribution. The data distributions (black points) are plotted against the total predicted background distributions (blue curves) after fitting to the data. The statistical plus systematic uncertainties in the background distribution are plotted as the blue band. The corresponding distributions of simulated $ \mathrm{H}\to \mathcal{A}\mathcal{A} \to 4\gamma $ events for $ m_{\mathcal{A}} = $ 3 (purple curve), 10 (gray curve), and 15 GeV (orange curve) are also overlaid on top. They are each normalized to the value of the expected upper limit to the signal cross section times 50. The lower panels of each plot show the ratio of the observed data over the predicted background as the black points, with the error bars representing the statistical uncertainties in the former. The ratio of the statistical plus systematic uncertainties in the background over the background prediction is shown as the blue band. |
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Figure 10-a:
The 2 $ \mathrm{D} m_{\mathcal{A}} $ spectra in the final signal region. Upper plot: The unrolled 2 $ \mathrm{D} m_{\mathcal{A}} $ distribution made by scanning along bins of increasing $ m_{\mathcal{A}2} $ at fixed $ m_{\mathcal{A}1} $ before incrementing in $ m_{\mathcal{A}1} $. Only the bins in the $ m_{\mathcal{A}}$-SR region are included, with the x-axis corresponding to the unrolled bin index of the selected bins, listed sequentially. Lower plot: 1D projections on the $ m_{\mathcal{A}1} $ (left) and $ m_{\mathcal{A}2} $ (right) axes of the 2 $ \mathrm{D} m_{\mathcal{A}} $ distribution. The data distributions (black points) are plotted against the total predicted background distributions (blue curves) after fitting to the data. The statistical plus systematic uncertainties in the background distribution are plotted as the blue band. The corresponding distributions of simulated $ \mathrm{H}\to \mathcal{A}\mathcal{A} \to 4\gamma $ events for $ m_{\mathcal{A}} = $ 3 (purple curve), 10 (gray curve), and 15 GeV (orange curve) are also overlaid on top. They are each normalized to the value of the expected upper limit to the signal cross section times 50. The lower panels of each plot show the ratio of the observed data over the predicted background as the black points, with the error bars representing the statistical uncertainties in the former. The ratio of the statistical plus systematic uncertainties in the background over the background prediction is shown as the blue band. |
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Figure 10-b:
The 2 $ \mathrm{D} m_{\mathcal{A}} $ spectra in the final signal region. Upper plot: The unrolled 2 $ \mathrm{D} m_{\mathcal{A}} $ distribution made by scanning along bins of increasing $ m_{\mathcal{A}2} $ at fixed $ m_{\mathcal{A}1} $ before incrementing in $ m_{\mathcal{A}1} $. Only the bins in the $ m_{\mathcal{A}}$-SR region are included, with the x-axis corresponding to the unrolled bin index of the selected bins, listed sequentially. Lower plot: 1D projections on the $ m_{\mathcal{A}1} $ (left) and $ m_{\mathcal{A}2} $ (right) axes of the 2 $ \mathrm{D} m_{\mathcal{A}} $ distribution. The data distributions (black points) are plotted against the total predicted background distributions (blue curves) after fitting to the data. The statistical plus systematic uncertainties in the background distribution are plotted as the blue band. The corresponding distributions of simulated $ \mathrm{H}\to \mathcal{A}\mathcal{A} \to 4\gamma $ events for $ m_{\mathcal{A}} = $ 3 (purple curve), 10 (gray curve), and 15 GeV (orange curve) are also overlaid on top. They are each normalized to the value of the expected upper limit to the signal cross section times 50. The lower panels of each plot show the ratio of the observed data over the predicted background as the black points, with the error bars representing the statistical uncertainties in the former. The ratio of the statistical plus systematic uncertainties in the background over the background prediction is shown as the blue band. |
png pdf |
Figure 10-c:
The 2 $ \mathrm{D} m_{\mathcal{A}} $ spectra in the final signal region. Upper plot: The unrolled 2 $ \mathrm{D} m_{\mathcal{A}} $ distribution made by scanning along bins of increasing $ m_{\mathcal{A}2} $ at fixed $ m_{\mathcal{A}1} $ before incrementing in $ m_{\mathcal{A}1} $. Only the bins in the $ m_{\mathcal{A}}$-SR region are included, with the x-axis corresponding to the unrolled bin index of the selected bins, listed sequentially. Lower plot: 1D projections on the $ m_{\mathcal{A}1} $ (left) and $ m_{\mathcal{A}2} $ (right) axes of the 2 $ \mathrm{D} m_{\mathcal{A}} $ distribution. The data distributions (black points) are plotted against the total predicted background distributions (blue curves) after fitting to the data. The statistical plus systematic uncertainties in the background distribution are plotted as the blue band. The corresponding distributions of simulated $ \mathrm{H}\to \mathcal{A}\mathcal{A} \to 4\gamma $ events for $ m_{\mathcal{A}} = $ 3 (purple curve), 10 (gray curve), and 15 GeV (orange curve) are also overlaid on top. They are each normalized to the value of the expected upper limit to the signal cross section times 50. The lower panels of each plot show the ratio of the observed data over the predicted background as the black points, with the error bars representing the statistical uncertainties in the former. The ratio of the statistical plus systematic uncertainties in the background over the background prediction is shown as the blue band. |
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Figure 11:
Observed (solid black line) and median expected (dashed black line) upper limits at 95% CL on the signal cross section times branching fraction $ \sigma(\mathrm{p}\mathrm{p} \to \mathrm{H}) \mathcal{B}(\mathrm{H}\to \mathcal{A}\mathcal{A} \to 4\gamma) $ at various $ m_{\mathcal{A}} $ mass points. The 68 and 95% confidence intervals around the median expected limit are shown as the green and yellow bands, respectively. |
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Figure 12:
Observed (solid line) and expected (dashed line) upper limits, including the 95% CL interval around the expected limit, from this search (CMS semi-merged) compared to the previous CMS and ATLAS searches [20,19,21], over the full $ m_{\mathcal{A}} $ range of 0.1 to 60 GeV. The limits are shown in terms of $ \sigma(\mathrm{p}\mathrm{p} \to \mathrm{H}) \mathcal{B}(\mathrm{H}\to \mathcal{A}\mathcal{A} \to 4\gamma) $. |
| Summary |
| A search for the exotic decay of the Higgs boson of the form $ \mathrm{H}\to \mathcal{A}\mathcal{A} \to 4\gamma $ in events with three photon-like objects has been performed using proton-proton collision data collected by the CMS experiment at $ \sqrt{s} = $ 13 TeV corresponding to an integrated luminosity of 138 fb$ ^{-1} $. One of the hypothetical particles, $ \mathcal{A} $, is assumed to decay promptly to one semi-merged diphoton candidate reconstructed as a single photon-like object, while the other $ \mathcal{A} $ decays into a pair of resolved photons. No excess above the estimated background is found. Upper limits are set on the product of the Higgs boson production cross section and branching fraction, $ \sigma(\mathrm{p}\mathrm{p} \to \mathrm{H}) \mathcal{B}(\mathrm{H}\to \mathcal{A}\mathcal{A} \to 4\gamma) $, ranging from 0.264 to 0.005$ $ pb at 95% confidence level for masses of $ \mathcal{A} $ in the range 1-15 GeV. These limits are the most stringent to date in the 1-5 GeV mass range. |
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