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CMS-EXO-21-007 ; TOTEM-2023-003 ; CERN-EP-2023-143
Search for high-mass exclusive diphoton production with tagged protons in proton-proton collisions at $ \sqrt{s} = $ 13 TeV
Accepted for publication in Phys. Rev. D
Abstract: A search is presented for high-mass exclusive diphoton production via photon-photon fusion in proton-proton collisions at $ \sqrt{s} = $ 13 TeV in events where both protons survive the interaction. The analysis utilizes data corresponding to an integrated luminosity of 103 fb$ ^{-1} $ collected in 2016--2018 with the central CMS detector and the CMS and TOTEM precision proton spectrometer (PPS). Events that have two photons with high transverse momenta ($ p_{\mathrm{T}}^{\gamma} > $ 100 GeV), back-to-back in azimuth, and with a large diphoton invariant mass ($ m_{\gamma\gamma} > $ 350 GeV) are selected. To remove the dominant inclusive diphoton backgrounds, the kinematic properties of the protons detected in PPS are required to match those of the central diphoton system. Only events having opposite-side forward protons detected with a fractional momentum loss between 0.035 and 0.15 (0.18) for the detectors on the negative (positive) side of CMS are considered. One exclusive diphoton candidate is observed for an expected background of 1.1 events. Limits at 95% confidence level are derived for the four-photon anomalous coupling parameters $ |\zeta_1| < $ 0.073 TeV$^{-4} $ and $ |\zeta_2| < $ 0.15 TeV$^{-4} $, using an effective field theory. Additionally, upper limits are placed on the production of axion-like particles with coupling strength to photons $ f^{-1} $ that varies from 0.03 TeV$^{-1} $ to 1 TeV$^{-1} $ over the mass range from 500 to 2000 GeV.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Diagram of diphoton production via photon fusion with intact protons in the final state. The four-photon vertex includes virtual contributions from SM or BSM charged fermions or bosons. In other BSM scenarios, a new heavy particle can be produced in the $ s $-channel, such as an axion-like particle that decays into two photons.

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Figure 2:
A schematic view of one side of the PPS detector with respect to the central CMS detector. The stations labeled as (or located at) 210 and 220\unitm house the Roman Pot detectors. Timing detector stations are also shown, although they are not used in this analysis. A symmetric set of detectors exists on the opposite side of CMS as well.

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Figure 3:
Kinematic distributions of simulated aQGC $ \gamma\gamma \to \gamma\gamma $ events: Single-photon $ \eta $ (upper left) and $ p_{\mathrm{T}} $ (upper right), and diphoton acoplanarity (lower left) and mass (lower right). The events are generated with FPMC, reconstructed accounting for the full CMS detector response, for aQGC parameters $ \zeta_1 = $ 0.5 TeV$^{-4} $ and $ \zeta_2 = $ 0 TeV$^{-4} $. A preselection is applied to these events as described in Section 5.

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Figure 3-a:
Distribution of the diphoton mass in simulated aQGC $ \gamma\gamma \to \gamma\gamma $ events. The events are generated with FPMC, reconstructed accounting for the full CMS detector response, for aQGC parameters $ \zeta_1 = $ 0.5 TeV$^{-4} $ and $ \zeta_2 = $ 0 TeV$^{-4} $. A preselection is applied to these events as described in Section 5.

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Figure 3-b:
Distribution of the single-photon $ p_{\mathrm{T}} $ in simulated aQGC $ \gamma\gamma \to \gamma\gamma $ events.The events are generated with FPMC, reconstructed accounting for the full CMS detector response, for aQGC parameters $ \zeta_1 = $ 0.5 TeV$^{-4} $ and $ \zeta_2 = $ 0 TeV$^{-4} $. A preselection is applied to these events as described in Section 5.

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Figure 3-c:
Distribution of the diphoton acoplanarity in simulated aQGC $ \gamma\gamma \to \gamma\gamma $ events. The events are generated with FPMC, reconstructed accounting for the full CMS detector response, for aQGC parameters $ \zeta_1 = $ 0.5 TeV$^{-4} $ and $ \zeta_2 = $ 0 TeV$^{-4} $. A preselection is applied to these events as described in Section 5.

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Figure 3-d:
Kinematic distributions of simulated aQGC $ \gamma\gamma \to \gamma\gamma $ events: Single-photon $ \eta $ (upper left) and $ p_{\mathrm{T}} $ (upper right), and diphoton acoplanarity (lower left) and mass (lower right). The events are generated with FPMC, reconstructed accounting for the full CMS detector response, for aQGC parameters $ \zeta_1 = $ 0.5 TeV$^{-4} $ and $ \zeta_2 = $ 0 TeV$^{-4} $. A preselection is applied to these events as described in Section 5.

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Figure 4:
Kinematic distributions of simulated ALP $ \gamma\gamma \to a \to \gamma\gamma $ events: Single-photon $ \eta $ (upper left) and $ p_{\mathrm{T}} $ (upper right), and diphoton acoplanarity (lower left) and mass (lower right). The events are generated with FPMC, reconstructed accounting for the full CMS detector response, for a value $ f^{-1} =$ 0.1 TeV$^{-1} $ of the ALP-photon coupling. A preselection is applied to these events as described in Section 5.

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Figure 4-a:
Distribution of single-photon $ \eta $ in simulated ALP $ \gamma\gamma \to a \to \gamma\gamma $ events. The events are generated with FPMC, reconstructed accounting for the full CMS detector response, for a value $ f^{-1} =$ 0.1 TeV$^{-1} $ of the ALP-photon coupling. A preselection is applied to these events as described in Section 5.

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Figure 4-b:
Distribution of single-photon $ p_{\mathrm{T}} $ in simulated ALP $ \gamma\gamma \to a \to \gamma\gamma $ events. The events are generated with FPMC, reconstructed accounting for the full CMS detector response, for a value $ f^{-1} =$ 0.1 TeV$^{-1} $ of the ALP-photon coupling. A preselection is applied to these events as described in Section 5.

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Figure 4-c:
Distribution of diphoton acoplanarity in simulated ALP $ \gamma\gamma \to a \to \gamma\gamma $ events. The events are generated with FPMC, reconstructed accounting for the full CMS detector response, for a value $ f^{-1} =$ 0.1 TeV$^{-1} $ of the ALP-photon coupling. A preselection is applied to these events as described in Section 5.

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Figure 4-d:
Distribution of diphoton mass in simulated ALP $ \gamma\gamma \to a \to \gamma\gamma $ events. The events are generated with FPMC, reconstructed accounting for the full CMS detector response, for a value $ f^{-1} =$ 0.1 TeV$^{-1} $ of the ALP-photon coupling. A preselection is applied to these events as described in Section 5.

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Figure 5:
Number of events in data (black symbols) and simulated backgrounds (histograms) after each of the three consecutive selection criteria applied (upper plot), and ratio of data to sum of all backgrounds (lower plot). The first bin corresponds to the preselection region, the second bin to the acoplanarity criterion, and the third bin to the diphoton $ \xi $ selection defined in the text. The lined red histogram represents an aQGC signal with $ \zeta_1 = $ 0.5 TeV$^{-4} $ and $ \zeta_2 = $ 0.1 TeV$^{-4} $ for reference. Hatched bands indicate systematic uncertainties (statistical uncertainties are smaller than the symbols size).

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Figure 6:
Kinematic distributions for events passing all selection criteria. From upper to lower and left to right are the single-photon $ \eta $, and $ p_{\mathrm{T}} $, diphoton acoplanarity, mass, $ \xi^{-}_{\gamma\gamma} $, and $ \xi^{+}_{\gamma\gamma} $ distributions. The black dots represent the data, filled histograms represent the simulated SM backgrounds, and the lined red histogram represents an aQGC signal with $ \zeta_1 = $ 50 TeV$^{-4} $ and $ \zeta_2 = $ 100 TeV$^{-4} $ for reference. The lower panels in each plot show the ratio of the number of data events to the total SM background expectation. The dashed box indicates the systematic uncertainties.

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Figure 6-a:
Distribution of the single-photon $ \eta $ for events passing all selection criteria. The black dots represent the data, filled histograms represent the simulated SM backgrounds, and the lined red histogram represents an aQGC signal with $ \zeta_1 = $ 50 TeV$^{-4} $ and $ \zeta_2 = $ 100 TeV$^{-4} $ for reference. The lower panel shows the ratio of the number of data events to the total SM background expectation. The dashed box indicates the systematic uncertainties.

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Figure 6-b:
Distribution of the single-photon $ p_{\mathrm{T}} $ for events passing all selection criteria. The black dots represent the data, filled histograms represent the simulated SM backgrounds, and the lined red histogram represents an aQGC signal with $ \zeta_1 = $ 50 TeV$^{-4} $ and $ \zeta_2 = $ 100 TeV$^{-4} $ for reference. The lower panel shows the ratio of the number of data events to the total SM background expectation. The dashed box indicates the systematic uncertainties.

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Figure 6-c:
Distribution of the diphoton acoplanarity for events passing all selection criteria. The black dots represent the data, filled histograms represent the simulated SM backgrounds, and the lined red histogram represents an aQGC signal with $ \zeta_1 = $ 50 TeV$^{-4} $ and $ \zeta_2 = $ 100 TeV$^{-4} $ for reference. The lower panel shows the ratio of the number of data events to the total SM background expectation. The dashed box indicates the systematic uncertainties.

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Figure 6-d:
Distribution of the diphoton mass for events passing all selection criteria. The black dots represent the data, filled histograms represent the simulated SM backgrounds, and the lined red histogram represents an aQGC signal with $ \zeta_1 = $ 50 TeV$^{-4} $ and $ \zeta_2 = $ 100 TeV$^{-4} $ for reference. The lower panel shows the ratio of the number of data events to the total SM background expectation. The dashed box indicates the systematic uncertainties.

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Figure 6-e:
Distribution of the diphoton $ \xi^{-}_{\gamma\gamma} $ for events passing all selection criteria. The black dots represent the data, filled histograms represent the simulated SM backgrounds, and the lined red histogram represents an aQGC signal with $ \zeta_1 = $ 50 TeV$^{-4} $ and $ \zeta_2 = $ 100 TeV$^{-4} $ for reference. The lower panel shows the ratio of the number of data events to the total SM background expectation. The dashed box indicates the systematic uncertainties.

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Figure 6-f:
Distribution of the diphoton $ \xi^{+}_{\gamma\gamma} $ events passing all selection criteria. The black dots represent the data, filled histograms represent the simulated SM backgrounds, and the lined red histogram represents an aQGC signal with $ \zeta_1 = $ 50 TeV$^{-4} $ and $ \zeta_2 = $ 100 TeV$^{-4} $ for reference. The lower panel shows the ratio of the number of data events to the total SM background expectation. The dashed box indicates the systematic uncertainties.

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Figure 7:
Mass versus rapidity matching distributions for events passing the diphoton and diproton selection criteria described in the text. The matching window is shown by a green rectangle corresponding to two standard deviations.

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Figure 8:
Distributions of combined efficiency-times-acceptance ($ \epsilon A $) for diffractively scattered protons as a function of the proton $ \xi $ for each running year for PPS sectors 45 (left) and 56 (right), respectively. Differences in the overall reconstruction efficiency are explained by varying detector location, configuration, and design across the years.

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Figure 8-a:
Distribution of the combined efficiency-times-acceptance ($ \epsilon A $) for diffractively scattered protons as a function of the proton $ \xi $ for each running year for PPS sector 45. Differences in the overall reconstruction efficiency are explained by varying detector location, configuration, and design across the years.

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Figure 8-b:
Distribution of the combined efficiency-times-acceptance ($ \epsilon A $) for diffractively scattered protons as a function of the proton $ \xi $ for each running year for PPS sector 56. Differences in the overall reconstruction efficiency are explained by varying detector location, configuration, and design across the years.

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Figure 9:
Observed (solid ellipse) and expected (dashed ellipse) exclusion limits at 95% CL on the anomalous coupling parameters $ \zeta_1 $ and $ \zeta_2 $ derived from the analysis of high-mass exclusive diphoton events in pp collisions at 13 TeV.

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Figure 10:
Product of the ALP efficiency and acceptance ($ \epsilon A $) values as a function of mass $ m_a $ for samples generated with $ f^{-1} = $ 0.1 TeV$^{-1} $ ALP-$ \gamma $ coupling, within the fiducial volume of this search. The curves shown correspond to the PPS $ \epsilon A $ values (dashed curves), as well as the latter convolved with the central-CMS $ \epsilon A $ (solid curves), for each data-taking year and for the full Run-2.

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Figure 11:
Upper limits at 95% CL on ALP-photon coupling strength as a function of the ALP mass. The shape of the limit curve is determined by the PPS efficiency-times-acceptance curve. The expected limits almost completely overlap with the observed ones.
Tables

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Table 1:
Selection criteria applied to simulated $ \gamma $+jet(s) samples to train the BDT for signal photon identification.

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Table 2:
Summary of the criteria applied to select exclusive diphoton events.

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Table 3:
Summary of the predicted number of events for each SM background contributing to the $ \xi \in \text{PPS} $ selection region, their sum, and the observed number of events. The uncertainties quoted are statistical only.

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Table 4:
Systematic uncertainties corresponding to each year of data taking used in the analysis.

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Table 5:
Product of efficiency and acceptance values for each year of data taking, for aQGC signal protons (populating mostly the high-$ \xi $ region in Fig. 8). The second column corresponds to the central CMS detectors, the third column to the PPS, and the fourth column is the product of the two previous ones.
Summary
A search has been performed for events with a high-mass exclusive diphoton system and two intact protons produced in the final state, $ \mathrm{p}\mathrm{p}\to\mathrm{p}\gamma\gamma\mathrm{p} $, in proton-proton collisions at $ \sqrt{s} = $ 13 TeV. The data set corresponds to an integrated luminosity of 103 fb$ ^{-1} $ collected with the CMS central detectors and the CMS and TOTEM precision proton spectrometer (PPS) in 2016--2018. Light-by-light (LbL) signal events are selected by requiring the measurement of two high-$ p_{\mathrm{T}} $ photons emitted back-to-back, in coincidence with two opposite-side forward protons, measured in PPS, whose kinematic properties match those of the central diphoton system. The data are found to be in agreement with the predicted standard model (SM) background, with one event observed and 1.10 $ \pm $ 0.00 (stat) $ \pm $ 0.24 (syst) events expected. An upper limit on the LbL cross section of $ \sigma(\mathrm{p}\mathrm{p}\to \mathrm{p}\gamma\gamma \mathrm{p}) < $ 0.61 fb is set within the fiducial range of the analysis defined as $ p_{\mathrm{T}}^{\gamma} > $ 100 GeV, $ |\eta^{\gamma}| < $ 2.5, $ m_{\gamma\gamma} > $ 350 GeV, and fractional proton energy loss of 0.035 $ < \xi_{\mathrm{p}} < $ 0.150 (0.180) for the positive-$ z $ (negative-$ z $) arm of PPS. Limits at 95% confidence level are derived for the four-photon anomalous quartic gauge couplings (aQGC) parameters $ |\zeta_1| < $ 0.073 TeV$^{-4} $ and $ |\zeta_2| < $ 0.15 TeV$^{-4} $ (setting, alternatively, the other to zero), using an effective field theory. Additionally, limits on the production of axion-like particles (ALPs) coupling to photons with strengths $ f^{-1} \approx $ 0.03 to 1 TeV$^{-1} $ are set over the mass range from 500 to 2000 GeV. These are the most restrictive limits to date on 4 $ \gamma $ aQGC and on ALPs coupling to photons, in the very high mass phase space region. \newpage
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LHC, CERN