CMSEXO22022 ; CERNEP2024101  
Search for new resonances decaying to pairs of merged diphotons in protonproton collisions at $ \sqrt{s} = $ 13 TeV  
CMS Collaboration  
1 May 2024  
Submitted to Phys. Rev. Lett.  
Abstract: A search is presented for an extended Higgs sector with two new particles, $ \mathrm{X} $ and $ \phi $, in the process $ \mathrm{X} \to \phi\phi \to (\gamma\gamma)(\gamma\gamma) $. Novel neural networks classify events with diphotons that are merged and determine the diphoton masses. The search uses LHC protonproton collision data at $ \sqrt{s} = $ 13 TeV collected with the CMS detector, corresponding to an integrated luminosity of 138 fb$ ^{1} $. No evidence of such resonances is seen. Upper limits are set on the production cross section versus the resonance masses, representing the most sensitive search in this channel.  
Links: eprint arXiv:2405.00834 [hepex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; 
Figures  Summary  Additional Figures  References  CMS Publications 

Figures  
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Figure 1:
Cluster mass ($ m_{\Gamma} $) distribution in data for both the passing (left) and failing (right) regions, in the energy range for which the $ \eta $ meson is expected to form a single $ \Gamma $ candidate. The signal (background) is modeled by a Gaussian (exponential) function. Blue and red dashed lines depict Gaussian fits to the data and Monte Carlo (MC) simulation, respectively. The solid blue line shows the background component of the fit. Ratios of the Gaussian fit means ($ \mu $) and widths ($ \sigma $) are displayed, where $ m_{\eta}^{\text{true}} $ is the true mass of the $ \eta $ meson. 
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Figure 1a:
Cluster mass ($ m_{\Gamma} $) distribution in data for both the passing (left) and failing (right) regions, in the energy range for which the $ \eta $ meson is expected to form a single $ \Gamma $ candidate. The signal (background) is modeled by a Gaussian (exponential) function. Blue and red dashed lines depict Gaussian fits to the data and Monte Carlo (MC) simulation, respectively. The solid blue line shows the background component of the fit. Ratios of the Gaussian fit means ($ \mu $) and widths ($ \sigma $) are displayed, where $ m_{\eta}^{\text{true}} $ is the true mass of the $ \eta $ meson. 
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Figure 1b:
Cluster mass ($ m_{\Gamma} $) distribution in data for both the passing (left) and failing (right) regions, in the energy range for which the $ \eta $ meson is expected to form a single $ \Gamma $ candidate. The signal (background) is modeled by a Gaussian (exponential) function. Blue and red dashed lines depict Gaussian fits to the data and Monte Carlo (MC) simulation, respectively. The solid blue line shows the background component of the fit. Ratios of the Gaussian fit means ($ \mu $) and widths ($ \sigma $) are displayed, where $ m_{\eta}^{\text{true}} $ is the true mass of the $ \eta $ meson. 
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Figure 2:
Dicluster mass ($ m_{\Gamma\Gamma} $) distribution for the data (points) for one of the $ \alpha^{\text{reco}} $ bins of the search (0.44 $ < \alpha^{\text{reco}} < $ 0.49%), fitted with the diphoton function (red), one of the considered five background parametrizations. Examples of two representative predicted signals are shown (blue and pink). The lower panel shows the difference between the observed data and the background prediction divided by the statistical uncertainty of the data ($ \sigma_{\text{data}} $), the aforementioned signals divided by $ \sigma_{\text{data}} $, and the goodness of fit measure $ \chi^2/\text{NDF} $ (where NDF is the number of degrees of freedom). 
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Figure 3:
Exclusion limits at 95% CL on $ \sigma(\mathrm{X} \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)) $ displayed in the ($ m_{\phi}/m_{\mathrm{X}} $)$ m_{\mathrm{X}} $ plane. Branching fractions ($ \mathcal{B} $) of both $ \mathrm{X} \to \phi\phi $ and $ \phi \to \gamma\gamma $ are assumed to be 100%. The black (red) lines represent the observed (expected) mass exclusions corresponding to different assumptions of $ (m_{\mathrm{X}} N)/f $. The observed upper limits on the cross section are shown on the color $ z $ axis. 
Summary 
In summary, a search for an extended Higgs sector with two new particles, $ \mathrm{X} $ and $ \phi $, with unknown masses $ m_{\mathrm{X}} $ and $ m_{\phi} $, has been presented for the decay sequence $ \mathrm{X} \to \phi\phi \to (\gamma\gamma)(\gamma\gamma) $. The search uses protonproton collision data at $ \sqrt{s}= $ 13 TeV, collected with the CMS detector at the LHC in 20162018, corresponding to an integrated luminosity of 138 fb$ ^{1} $. The analysis considers $ m_{\mathrm{X}} $ between 0.3 and 3 TeV, and is restricted to values of $ m_{\phi} $ for which the ratio $ m_{\phi} / m_{\mathrm{X}} $ is between 0.5 and 2.5%. As a result, the two photons from each $ \phi $ boson overlap significantly in the electromagnetic calorimeter. Convolutional neural networks trained on clusters of calorimeter energy deposits are used to classify events containing merged diphotons and to regress the mass of the diphoton system. The dicluster mass spectra, in bins of the ratio of the average cluster mass divided by the dicluster mass, are analyzed for the presence of new resonances, and are found to be consistent with the standard model expectations. Upper limits are set at 95% confidence level (CL) on the production cross section for $ \mathrm{X} \to \phi\phi \to (\gamma\gamma)(\gamma\gamma) $, as a function of the resonance masses, where both the $ \mathrm{X} \to \phi\phi $ and $ \phi \to \gamma\gamma $ branching fractions are assumed to be 100%. Observed (expected) limits range within 0.031.06 (0.030.79) fb at 95% CL for the masses considered. These results represent the most sensitive search of an extended Higgs sector with this final state. 
Additional Figures  
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Additional Figure 1:
Feynman diagram of the production and decay of $ \mathrm{X} \to \phi\phi \to (\gamma \gamma)(\gamma \gamma) $. The dominant production mechanism occurs via a fermion loop as shown in the diagram. Additional partons produced by initialstate radiation may be present. 
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Additional Figure 2:
Architecture of the convolutional neural network used for classification. The network takes in a pixelated image of a candidate cluster made from ECAL energy deposits, where each pixel is exactly one ECAL crystal. The output is fed through a fully connected linear network which gives three output scores corresponding to the likelihood of the cluster being a single photon, diphoton, or hadron. 
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Additional Figure 3:
Architecture of the convolutional neural network used for diphoton $ m/E $ regression. The network takes in a pixelated image of a diphoton cluster as selected by the classification neural network. The output is fed through three fully connected linear networks which give the final $ m/E $ of the diphoton. 
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Additional Figure 4:
Ternary diagram showing showing the classification scores for true diphoton validation events. In this diagram each edge of the triangle is an axis depicting the associated classifier score from 0 to 1. The highconcentration of events near $ P_{\gamma\gamma} $ demonstrates the effectiveness of the classification NN. 
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Additional Figure 5:
Ternary diagram showing showing the classification scores for true monophoton validation events. In this diagram each edge of the triangle is an axis depicting the associated classifier score from 0 to 1. The highconcentration of events near $ P_{\gamma} $ demonstrates the effectiveness of the classification NN. 
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Additional Figure 6:
Ternary diagram showing showing the classification scores for true hadron validation events. In this diagram each edge of the triangle is an axis depicting the associated classifier score from 0 to 1. The highconcentration of events near $ P_{\text{had}} $ demonstrates the effectiveness of the classification NN. 
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Additional Figure 7:
Predicted $ m/E $ from the regression NN vs. the generated $ \phi$ $m/E $ for $ \mathrm{X} \to \phi \phi \to (\gamma \gamma)(\gamma \gamma) $ signal MC. The tight clustering of events near the line $ y = x $ (black, dashed) shows the effectiveness of the regression NN. 
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Additional Figure 8:
Cluster mass ($ m_{\Gamma} $) distribution in data for both the passing and failing (inset) regions, in the energy range for which the $ \eta $ meson is expected to form a single $ \Gamma $ candidate. The signal (background) is modeled by a Gaussian (exponential) function. Blue and red dashed lines depict Gaussian fits to the data and Monte Carlo (MC) simulation, respectively. The solid blue line shows the background component of the fit. Ratios of the Gaussian fit means ($ \mu $) and widths ($ \sigma $) are displayed, where $ m_{\eta}^{\text{true}} $ is the true mass of the $ \eta $ meson. 
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Additional Figure 9:
Signal efficiencies in the $ {m_\phi}/{m_{\mathrm{X}}}  m_{\mathrm{X}} $ plane after applying all analysis event selection criteria to $ \mathrm{X} \to \phi \phi \to (\gamma \gamma)(\gamma \gamma) $ signal MC. Efficiencies ranges from about 1045%. 
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Additional Figure 10:
Dicluster mass ($ m_{\Gamma\Gamma} $) distribution (black points) from a signal with $ m_{\mathrm{X}} = $ 600 GeV and $ m_{\phi} = $ 6 GeV ($ \alpha = $ 0.1%). A doublesided Crystal Ball function fit is also shown (red line). 
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Additional Figure 11:
Dicluster mass ($ m_{\Gamma\Gamma} $) distribution for the data (points) for one of the nine $ \alpha^{\text{reco}} $ bins of the search (0.30 $ \leq \alpha^{\text{reco}} < $ 0.35%), fitted with one of the considered five functions, the dijet function (red). Examples of two representative predicted signals are shown (blue and pink). The lower panels show the pulls from the fit of the dijet function to the data calculated using the statistical uncertainty of the data, the aforementioned signals, and the goodness of fit measure $ \chi^2/ $NDF. 
png pdf 
Additional Figure 12:
Dicluster mass ($ m_{\Gamma\Gamma} $) distribution for the data (points) for one of the nine $ \alpha^{\text{reco}} $ bins of the search (0.35 $ \leq \alpha^{\text{reco}} < $ 0.40%), fitted with one of the considered five functions, the dijet function (red). Examples of two representative predicted signals are shown (blue and pink). The lower panels show the pulls from the fit of the dijet function to the data calculated using the statistical uncertainty of the data, the aforementioned signals, and the goodness of fit measure $ \chi^2/ $NDF. 
png pdf 
Additional Figure 13:
Dicluster mass ($ m_{\Gamma\Gamma} $) distribution for the data (points) for one of the nine $ \alpha^{\text{reco}} $ bins of the search (0.40 $ \leq \alpha^{\text{reco}} < $ 0.44%), fitted with one of the considered five functions, the dijet function (red). Examples of two representative predicted signals are shown (blue and pink). The lower panels show the pulls from the fit of the dijet function to the data calculated using the statistical uncertainty of the data, the aforementioned signals, and the goodness of fit measure $ \chi^2/ $NDF. 
png pdf 
Additional Figure 14:
Dicluster mass ($ m_{\Gamma\Gamma} $) distribution for the data (points) for one of the nine $ \alpha^{\text{reco}} $ bins of the search (0.49 $ \leq \alpha^{\text{reco}} < $ 0.55%), fitted with one of the considered five functions, the dijet function (red). Examples of two representative predicted signals are shown (blue and pink). The lower panels show the pulls from the fit of the dijet function to the data calculated using the statistical uncertainty of the data, the aforementioned signals, and the goodness of fit measure $ \chi^2/ $NDF. 
png pdf 
Additional Figure 15:
Dicluster mass ($ m_{\Gamma\Gamma} $) distribution for the data (points) for one of the nine $ \alpha^{\text{reco}} $ bins of the search (0.55 $ \leq \alpha^{\text{reco}} < $ 0.60%), fitted with one of the considered five functions, the dijet function (red). Examples of two representative predicted signals are shown (blue and pink). The lower panels show the pulls from the fit of the dijet function to the data calculated using the statistical uncertainty of the data, the aforementioned signals, and the goodness of fit measure $ \chi^2/ $NDF. 
png pdf 
Additional Figure 16:
Dicluster mass ($ m_{\Gamma\Gamma} $) distribution for the data (points) for one of the nine $ \alpha^{\text{reco}} $ bins of the search (0.60 $ \leq \alpha^{\text{reco}} < $ 0.70%), fitted with one of the considered five functions, the diphoton function (red). Examples of two representative predicted signals are shown (blue and pink). The lower panels show the pulls from the fit of the diphoton function to the data calculated using the statistical uncertainty of the data, the aforementioned signals, and the goodness of fit measure $ \chi^2/ $NDF. 
png pdf 
Additional Figure 17:
Dicluster mass ($ m_{\Gamma\Gamma} $) distribution for the data (points) for one of the nine $ \alpha^{\text{reco}} $ bins of the search (0.70 $ \leq \alpha^{\text{reco}} < $ 0.81%), fitted with one of the considered five functions, the modified dijet function (red). Examples of two representative predicted signals are shown (blue and pink). The lower panels show the pulls from the fit of the modified dijet function to the data calculated using the statistical uncertainty of the data, the aforementioned signals, and the goodness of fit measure $ \chi^2/ $NDF. 
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Additional Figure 18:
Dicluster mass ($ m_{\Gamma\Gamma} $) distribution for the data (points) for one of the nine $ \alpha^{\text{reco}} $ bins of the search (0.81 $ \leq \alpha^{\text{reco}} < $ 3.00%), fitted with one of the considered five functions, the dijet function (red). Examples of two representative predicted signals are shown (blue and pink). The lower panels show the pulls from the fit of the dijet function to the data calculated using the statistical uncertainty of the data, the aforementioned signals, and the goodness of fit measure $ \chi^2/ $NDF. 
png pdf 
Additional Figure 19:
Upper limits at 95% CL on the production cross section for the process $ \mathrm{X} \to \phi \phi \to (\gamma \gamma)(\gamma \gamma) $ as a function of $ m_{\mathrm{X}} $. Each subpanel shows the limits for a fixed value of $ \alpha $. The branching fractions $ \mathrm{X} \to \phi \phi $ and $ \phi \to \gamma \gamma $ are both assumed to be 100%. The observed limits are shown as solid black lines with markers; the expected limits are shown as dashed lines. The green (inner) and yellow (outer) bands represent one and two standard deviation intervals. In the considered model, the coupling of the $ \mathrm{X} $ to gluons is evaluated by integrating over $ N $ flavors of quarks that receive all their mass from the $ \mathrm{X} $ vacuum expectation value $ f $, such that the cross section depends only on the quantity $ (m_\mathrm{X} N)/f $. Different values of this parameter are shown with the dashed and dashdotted curves. 
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Additional Figure 20:
Expected cross section upper limits at 95% CL for the production of $ \mathrm{X} \to \phi \phi \to (\gamma \gamma)(\gamma \gamma) $ displayed in the $ ({m_\phi}/{m_{\mathrm{X}}})  m_{\mathrm{X}} $ plane. The branching fractions $ \mathrm{X} \to \phi \phi $ and $ \phi \to \gamma \gamma $ are both assumed to be 100%. 
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Additional Figure 21:
Local significance in units of standard deviations ($ \sigma $) in the $ {m_\phi}/{m_{\mathrm{X}}}  m_{\mathrm{X}} $ plane. The largest excess corresponds to about $ m_{\mathrm{X}} = $ 720 GeV and $ m_\phi = $ 5.04 GeV with a local significance of 3.57 $ \sigma $. This significance becomes 1.07 $ \sigma $ when accounting for the lookelsewhere effect. 
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Additional Figure 22:
CMS event display in the $ \rho\phi $ plane for an event with $ m_{\Gamma\Gamma} = $ 349 GeV. Images showing the clusters in the $ \eta\phi $ plane and are matched to the corresponding deposits in the ECAL. The cluster images are designed to include two merged photons in a single image. Each pixel in the images is equal to one crystal in the ECAL and the pixel color value is the energy deposited in the crystal. Images are then normalized to $ E_{\text{total}}= $ 1 and are centered on the most energetic crystal. 
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Additional Figure 23:
CMS event display in the $ \rho\phi $ plane for an event with $ m_{\Gamma\Gamma} = $ 377 GeV. Images showing the clusters in the $ \eta\phi $ plane and are matched to the corresponding deposits in the ECAL. The cluster images are designed to include two merged photons in a single image. Each pixel in the images is equal to one crystal in the ECAL and the pixel color value is the energy deposited in the crystal. Images are then normalized to $ E_{\text{total}}= $ 1 and are centered on the most energetic crystal. 
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Additional Figure 24:
CMS event display in the $ \rho\phi $ plane for an event with $ m_{\Gamma\Gamma} = $ 718 GeV. This event is near the largest excess observed in this analysis. Images showing the clusters in the $ \eta\phi $ plane and are matched to the corresponding deposits in the ECAL. The cluster images are designed to include two merged photons in a single image. Each pixel in the images is equal to one crystal in the ECAL and the pixel color value is the energy deposited in the crystal. Images are then normalized to $ E_{\text{total}}= $ 1 and are centered on the most energetic crystal. 
png pdf 
Additional Figure 25:
CMS event display in the $ \rho\phi $ plane for an event with $ m_{\Gamma\Gamma} = $ 1596 GeV. This event has the highest observed $ m_{\Gamma\Gamma} $ in this analysis. Images showing the clusters in the $ \eta\phi $ plane and are matched to the corresponding deposits in the ECAL. The cluster images are designed to include two merged photons in a single image. Each pixel in the images is equal to one crystal in the ECAL and the pixel color value is the energy deposited in the crystal. Images are then normalized to $ E_{\text{total}}= $ 1 and are centered on the most energetic crystal. 
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