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CMS-B2G-24-007 ; CERN-EP-2025-217
Search for heavy H$\gamma $ and Z$\gamma $ resonances with a bottom quark-antiquark pair in the final state in proton-proton collisions at $ \sqrt{s}= $ 13 TeV
Submitted to Science Bulletin
Abstract: A search for heavy resonances decaying into a Higgs boson (H) or a Z boson and a photon ($ \gamma $), with the H or Z bosons decaying to a bottom quark-antiquark pair ($ \mathrm{b}\overline{\mathrm{b}} $) is presented. The analysis is performed using proton-proton collision data at $ \sqrt{s} = $ 13 TeV collected by the CMS experiment at the CERN Large Hadron Collider, corresponding to an integrated luminosity of 138 fb$ ^{-1} $. The analyzed events contain a photon and a massive large-radius jet originating from a Lorentz-boosted $ \mathrm{b}\overline{\mathrm{b}} $ system. An advanced transformer-based algorithm classifies jets according to their substructure and quark flavors, forming a tagger that identifies jets as candidates from $\mathrm{H} / \mathrm{Z}\to\mathrm{b}\overline{\mathrm{b}} $ decays. A set of parametric functions is used to fit the photon-jet invariant mass spectrum and to extract potential signals. No significant excess is observed above the standard model expectations. The results set upper limits at 95% confidence level on the product of the cross section and the branching fraction for spin-1 H$\gamma $ resonances and spin-0 Z$\gamma $ resonances, below 0.1 and 0.3 fb, respectively, representing the most stringent limits to date.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Schematic illustration indicating the topology of the signal processes under consideration in this search. The spin-1 $\mathrm{Z}^{'}\to\mathrm{H}\gamma\to\mathrm{b}\overline{\mathrm{b}}\gamma $ signal scenario is shown on the left, and the spin-0 $ \mathrm{S}\to\mathrm{Z}\gamma\to\mathrm{b}\overline{\mathrm{b}}\gamma $ signal scenario is shown on the right.

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Figure 2:
The ROC curves of background efficiency ($ \epsilon_\text{B} $) vs. signal efficiency ($ \epsilon_\text{S} $) for the Xbb tagger and other taggers from previous analyses, evaluated using a $ m_{\mathrm{Z}^{'}} = $ 1 TeV signal sample and SM background, are shown on the left. The taggers are listed in chronological order in the legend, based on their first use in similar searches (Refs. [10,69,70,71]). The right plot shows the Xbb score distributions for data and simulated signal samples, along with the significance metric, $ S/\sqrt{D} $, as defined in the text. Both plots use the preselection, with the Z' (S) signals normalized by setting $ \sigma\mathcal{B} $ to the benchmark values (10 fb).

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Figure 2-a:
The ROC curves of background efficiency ($ \epsilon_\text{B} $) vs. signal efficiency ($ \epsilon_\text{S} $) for the Xbb tagger and other taggers from previous analyses, evaluated using a $ m_{\mathrm{Z}^{'}} = $ 1 TeV signal sample and SM background, are shown on the left. The taggers are listed in chronological order in the legend, based on their first use in similar searches (Refs. [10,69,70,71]). The right plot shows the Xbb score distributions for data and simulated signal samples, along with the significance metric, $ S/\sqrt{D} $, as defined in the text. Both plots use the preselection, with the Z' (S) signals normalized by setting $ \sigma\mathcal{B} $ to the benchmark values (10 fb).

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Figure 2-b:
The ROC curves of background efficiency ($ \epsilon_\text{B} $) vs. signal efficiency ($ \epsilon_\text{S} $) for the Xbb tagger and other taggers from previous analyses, evaluated using a $ m_{\mathrm{Z}^{'}} = $ 1 TeV signal sample and SM background, are shown on the left. The taggers are listed in chronological order in the legend, based on their first use in similar searches (Refs. [10,69,70,71]). The right plot shows the Xbb score distributions for data and simulated signal samples, along with the significance metric, $ S/\sqrt{D} $, as defined in the text. Both plots use the preselection, with the Z' (S) signals normalized by setting $ \sigma\mathcal{B} $ to the benchmark values (10 fb).

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Figure 3:
The left and right plots present the distributions of $ m_{\text{j}} $ and $ m_{\text{j}\gamma} $, respectively, in data, MC background, and signal samples, with preselection criteria applied. Both plots use the preselection, with the Z' (S) signals normalized by setting $ \sigma\mathcal{B} $ to the benchmark (10 fb) values.

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Figure 3-a:
The left and right plots present the distributions of $ m_{\text{j}} $ and $ m_{\text{j}\gamma} $, respectively, in data, MC background, and signal samples, with preselection criteria applied. Both plots use the preselection, with the Z' (S) signals normalized by setting $ \sigma\mathcal{B} $ to the benchmark (10 fb) values.

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Figure 3-b:
The left and right plots present the distributions of $ m_{\text{j}} $ and $ m_{\text{j}\gamma} $, respectively, in data, MC background, and signal samples, with preselection criteria applied. Both plots use the preselection, with the Z' (S) signals normalized by setting $ \sigma\mathcal{B} $ to the benchmark (10 fb) values.

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Figure 4:
A schematic illustration of the SR and CR definitions in the $ m_{\text{j}} $-Xbb plane is shown on the left. On the right, the product of signal efficiency and acceptance is plotted as a function of the resonance mass for the simulated signal samples in the relevant SRs. The percentages in the legend refer to the corresponding $ \Gamma/m $ values. Here, SRZ(H) denotes SRZ(H)1+SRZ(H)2.

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Figure 4-a:
A schematic illustration of the SR and CR definitions in the $ m_{\text{j}} $-Xbb plane is shown on the left. On the right, the product of signal efficiency and acceptance is plotted as a function of the resonance mass for the simulated signal samples in the relevant SRs. The percentages in the legend refer to the corresponding $ \Gamma/m $ values. Here, SRZ(H) denotes SRZ(H)1+SRZ(H)2.

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Figure 4-b:
A schematic illustration of the SR and CR definitions in the $ m_{\text{j}} $-Xbb plane is shown on the left. On the right, the product of signal efficiency and acceptance is plotted as a function of the resonance mass for the simulated signal samples in the relevant SRs. The percentages in the legend refer to the corresponding $ \Gamma/m $ values. Here, SRZ(H) denotes SRZ(H)1+SRZ(H)2.

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Figure 5:
The $ m_{\text{j}\gamma} $ distributions of the data in CR1 (left) and CR2 (right) fitted with the six parametric functions. The legends specify the $ \chi^2/\text{ndf} $ for each fit. The lower panels show the pull distributions as defined in the text, with respect to the best fit function specified in the legend.

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Figure 5-a:
The $ m_{\text{j}\gamma} $ distributions of the data in CR1 (left) and CR2 (right) fitted with the six parametric functions. The legends specify the $ \chi^2/\text{ndf} $ for each fit. The lower panels show the pull distributions as defined in the text, with respect to the best fit function specified in the legend.

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Figure 5-b:
The $ m_{\text{j}\gamma} $ distributions of the data in CR1 (left) and CR2 (right) fitted with the six parametric functions. The legends specify the $ \chi^2/\text{ndf} $ for each fit. The lower panels show the pull distributions as defined in the text, with respect to the best fit function specified in the legend.

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Figure 6:
Post-fit $ m_{\text{j}\gamma} $ spectra in the four SRs: SRH1 (upper left), SRZ1 (upper right), SRH2 (lower left), and SRZ2 (lower right). The legends specify the $ \chi^2/\text{ndf} $ for each fit. The lower panels show the pull distributions with respect to the best fit function specified in the legend. The signals with the largest local significances are shown with continuous lines in each SR and are normalized to the observed $ \sigma\mathcal{B} $ upper limits.

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Figure 6-a:
Post-fit $ m_{\text{j}\gamma} $ spectra in the four SRs: SRH1 (upper left), SRZ1 (upper right), SRH2 (lower left), and SRZ2 (lower right). The legends specify the $ \chi^2/\text{ndf} $ for each fit. The lower panels show the pull distributions with respect to the best fit function specified in the legend. The signals with the largest local significances are shown with continuous lines in each SR and are normalized to the observed $ \sigma\mathcal{B} $ upper limits.

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Figure 6-b:
Post-fit $ m_{\text{j}\gamma} $ spectra in the four SRs: SRH1 (upper left), SRZ1 (upper right), SRH2 (lower left), and SRZ2 (lower right). The legends specify the $ \chi^2/\text{ndf} $ for each fit. The lower panels show the pull distributions with respect to the best fit function specified in the legend. The signals with the largest local significances are shown with continuous lines in each SR and are normalized to the observed $ \sigma\mathcal{B} $ upper limits.

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Figure 6-c:
Post-fit $ m_{\text{j}\gamma} $ spectra in the four SRs: SRH1 (upper left), SRZ1 (upper right), SRH2 (lower left), and SRZ2 (lower right). The legends specify the $ \chi^2/\text{ndf} $ for each fit. The lower panels show the pull distributions with respect to the best fit function specified in the legend. The signals with the largest local significances are shown with continuous lines in each SR and are normalized to the observed $ \sigma\mathcal{B} $ upper limits.

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Figure 6-d:
Post-fit $ m_{\text{j}\gamma} $ spectra in the four SRs: SRH1 (upper left), SRZ1 (upper right), SRH2 (lower left), and SRZ2 (lower right). The legends specify the $ \chi^2/\text{ndf} $ for each fit. The lower panels show the pull distributions with respect to the best fit function specified in the legend. The signals with the largest local significances are shown with continuous lines in each SR and are normalized to the observed $ \sigma\mathcal{B} $ upper limits.

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Figure 7:
The 95% CL upper limits on the product of production cross section and branching fraction $ \sigma\mathcal{B} $ for $ \mathrm{Z}^{'}\to\mathrm{H}\gamma $ (upper left) and $ \mathrm{S}\to\mathrm{Z}\gamma $ with a narrow width (upper right), 5.6% width (lower left), and 10% width (lower right). Observed (expected) limits are shown with solid (dashed) lines. The colored bands represent the 68 and 95% CL intervals for the expected limits. The red line represents the theory benchmark model used for Z' signal simulation.

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Figure 7-a:
The 95% CL upper limits on the product of production cross section and branching fraction $ \sigma\mathcal{B} $ for $ \mathrm{Z}^{'}\to\mathrm{H}\gamma $ (upper left) and $ \mathrm{S}\to\mathrm{Z}\gamma $ with a narrow width (upper right), 5.6% width (lower left), and 10% width (lower right). Observed (expected) limits are shown with solid (dashed) lines. The colored bands represent the 68 and 95% CL intervals for the expected limits. The red line represents the theory benchmark model used for Z' signal simulation.

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Figure 7-b:
The 95% CL upper limits on the product of production cross section and branching fraction $ \sigma\mathcal{B} $ for $ \mathrm{Z}^{'}\to\mathrm{H}\gamma $ (upper left) and $ \mathrm{S}\to\mathrm{Z}\gamma $ with a narrow width (upper right), 5.6% width (lower left), and 10% width (lower right). Observed (expected) limits are shown with solid (dashed) lines. The colored bands represent the 68 and 95% CL intervals for the expected limits. The red line represents the theory benchmark model used for Z' signal simulation.

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Figure 7-c:
The 95% CL upper limits on the product of production cross section and branching fraction $ \sigma\mathcal{B} $ for $ \mathrm{Z}^{'}\to\mathrm{H}\gamma $ (upper left) and $ \mathrm{S}\to\mathrm{Z}\gamma $ with a narrow width (upper right), 5.6% width (lower left), and 10% width (lower right). Observed (expected) limits are shown with solid (dashed) lines. The colored bands represent the 68 and 95% CL intervals for the expected limits. The red line represents the theory benchmark model used for Z' signal simulation.

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Figure 7-d:
The 95% CL upper limits on the product of production cross section and branching fraction $ \sigma\mathcal{B} $ for $ \mathrm{Z}^{'}\to\mathrm{H}\gamma $ (upper left) and $ \mathrm{S}\to\mathrm{Z}\gamma $ with a narrow width (upper right), 5.6% width (lower left), and 10% width (lower right). Observed (expected) limits are shown with solid (dashed) lines. The colored bands represent the 68 and 95% CL intervals for the expected limits. The red line represents the theory benchmark model used for Z' signal simulation.
Tables

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Table 1:
The sources of systematic uncertainties included in the analysis. The second column indicates whether the uncertainty affects the background or signal shape or its rate. The third column from the left lists the magnitude of the corresponding pre-fit systematic uncertainty. The last column indicates the total number of nuisance parameters (NPs) and whether or not they are treated as correlated across all SRs. An asterisk (*) denotes a value or shape template unique to each signal scenario.
Summary
A search for heavy resonances decaying to a photon and a Z or a Higgs boson (H) in the $ \gamma $+jet final state, using $ \sqrt{s} = $ 13 TeV proton-proton collision data collected with the CMS detector in 2016--2018, corresponding to an integrated luminosity of 138 fb$ ^{-1} $, has been presented. For the H$\gamma $ resonance analysis, a benchmark spin-1 resonance model with a narrow width is considered, while the Z$\gamma $ analysis considers a standard model Higgs-like heavy spin-0 resonance, using several different width hypotheses. The final states of these resonant processes feature a photon and a massive, large-radius jet, containing the decay products of $ \mathrm{H},\,\mathrm{Z}\to\mathrm{b}\overline{\mathrm{b}} $, identified using the particle transformer jet substructure algorithm GLOPART for jet classification and the PARTICLENET algorithm for jet mass regression. These advanced machine-learning techniques greatly improve sensitivity over previous searches. The results are consistent with the predictions of the standard model within the measurement uncertainties. Exclusion limits at 95% confidence level are set on the product of the production cross section and the branching fraction for the resonance decay into H$\gamma $ or Z$\gamma $, with observed values below 0.1 and 0.3 fb for the spin-1 and spin-0 scenarios, respectively. This result establishes the most stringent constraints to date on the production and relevant decay of such heavy resonances.
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