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| CMS-PAS-HIN-21-015 | ||
| Measurements of the light-by-light scattering and the Breit-Wheeler processes, and searches for axion-like particles in ultraperipheral PbPb collisions at $ \sqrt {\smash [b]{s_{_{\mathrm {NN}}}}} = $ 5.02 TeV | ||
| CMS Collaboration | ||
| 10 April 2024 | ||
| Abstract: Measurements of the light-by-light scattering (LbL, $ \gamma\gamma\to\gamma\gamma $) and the Breit-Wheeler (B-W, $ \gamma\gamma\to\mathrm{e}^+\mathrm{e}^- $) processes are reported in ultraperipheral PbPb collisions at a centre-of-mass energy per nucleon pair of 5.02 TeV using a data sample corresponding to an integrated luminosity of 1.65 nb$^{-1}$. Events with a pair of exclusively produced photons or $ \mathrm{e}^+\mathrm{e}^- $ are selected, each with transverse energy $ E_\mathrm{T}^{\gamma,\mathrm{e}} > $ 2 GeV, pseudorapidity $ |\eta^{\gamma,\mathrm{e}}| < $ 2.2, pair invariant mass $ m^{\gamma\gamma,\mathrm{ee}} > $ 5 GeV, pair transverse momentum $ p_\mathrm{T}^{\gamma\gamma,\mathrm{ee}} < $ 1 GeV, and pair azimuthal acoplanarity $ A_\phi < $ 0.01. The measured B-W fiducial cross section, $ \sigma_\text{fid} (\gamma\gamma \to \mathrm{e}^+\mathrm{e}^-)= $ 271.5 $ \pm $ 1.9 (stat) $\pm$ 18.3 (syst) $\mu $b, as well as the differential distributions for various kinematic observables, are in agreement with the standard model (SM) predictions. In the LbL final state, 26 exclusive diphoton candidate events are observed compared with 12.8 $ \pm $ 3.1 events expected for the signal and 12.0 $ \pm $ 2.9 for the background. The observed significance of the LbL signal with respect to the background-only hypothesis is above five standard deviations. The fiducial LbL scattering cross section, $ \sigma_\text{fid} (\gamma\gamma \to \gamma\gamma)= $ 107 $ \pm $ 33 (stat) $\pm$ 20 (syst) nb, is consistent with the SM prediction. Limits on the production of axion-like particles coupling to photons are set over the mass range $ m_\mathrm{a} = $ 5-100 GeV, including the most stringent limits in the 5-10 GeV mass range. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Schematic diagrams of light-by-light scattering ($ \gamma \gamma \to \gamma \gamma $, upper left), the Breit-Wheeler process ($ \gamma \gamma \to \mathrm{e}^+\mathrm{e}^- $, upper right), central exclusive diphoton production ($ \mathrm{g}\mathrm{g} \to \gamma\gamma $, lower left), and axion- or graviton-like particle production ($ \gamma\gamma\to \mathrm{a},\mathrm{G} \to\gamma\gamma $, lower right) in ultraperipheral PbPb collisions. The $ \,^{(*)} $ superindex indicates a potential electromagnetic excitation of the outgoing Pb ions. |
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Figure 2:
Detector-level kinematic distributions for exclusive $ \mathrm{e}^+\mathrm{e}^- $ events passing our analysis requirements (Table 1) in the data (black points) and in SUPERCHIC + PHOTOS++ and STARLIGHT simulations (histograms). The MC simulations are normalised to match $ \sigma_\text{fid,MC}\mathcal{L}_\text{int} $, and corrected with the scale factors listed in Table 2. Ratios of the data to MC expectation are shown in the bottom panels. Error bars (boxes) around the data points indicate statistical (square sum of systematic and MC statistical) uncertainties. |
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Figure 2-a:
Detector-level kinematic distributions for exclusive $ \mathrm{e}^+\mathrm{e}^- $ events passing our analysis requirements (Table 1) in the data (black points) and in SUPERCHIC + PHOTOS++ and STARLIGHT simulations (histograms). The MC simulations are normalised to match $ \sigma_\text{fid,MC}\mathcal{L}_\text{int} $, and corrected with the scale factors listed in Table 2. Ratios of the data to MC expectation are shown in the bottom panels. Error bars (boxes) around the data points indicate statistical (square sum of systematic and MC statistical) uncertainties. |
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Figure 2-b:
Detector-level kinematic distributions for exclusive $ \mathrm{e}^+\mathrm{e}^- $ events passing our analysis requirements (Table 1) in the data (black points) and in SUPERCHIC + PHOTOS++ and STARLIGHT simulations (histograms). The MC simulations are normalised to match $ \sigma_\text{fid,MC}\mathcal{L}_\text{int} $, and corrected with the scale factors listed in Table 2. Ratios of the data to MC expectation are shown in the bottom panels. Error bars (boxes) around the data points indicate statistical (square sum of systematic and MC statistical) uncertainties. |
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Figure 2-c:
Detector-level kinematic distributions for exclusive $ \mathrm{e}^+\mathrm{e}^- $ events passing our analysis requirements (Table 1) in the data (black points) and in SUPERCHIC + PHOTOS++ and STARLIGHT simulations (histograms). The MC simulations are normalised to match $ \sigma_\text{fid,MC}\mathcal{L}_\text{int} $, and corrected with the scale factors listed in Table 2. Ratios of the data to MC expectation are shown in the bottom panels. Error bars (boxes) around the data points indicate statistical (square sum of systematic and MC statistical) uncertainties. |
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Figure 2-d:
Detector-level kinematic distributions for exclusive $ \mathrm{e}^+\mathrm{e}^- $ events passing our analysis requirements (Table 1) in the data (black points) and in SUPERCHIC + PHOTOS++ and STARLIGHT simulations (histograms). The MC simulations are normalised to match $ \sigma_\text{fid,MC}\mathcal{L}_\text{int} $, and corrected with the scale factors listed in Table 2. Ratios of the data to MC expectation are shown in the bottom panels. Error bars (boxes) around the data points indicate statistical (square sum of systematic and MC statistical) uncertainties. |
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Figure 2-e:
Detector-level kinematic distributions for exclusive $ \mathrm{e}^+\mathrm{e}^- $ events passing our analysis requirements (Table 1) in the data (black points) and in SUPERCHIC + PHOTOS++ and STARLIGHT simulations (histograms). The MC simulations are normalised to match $ \sigma_\text{fid,MC}\mathcal{L}_\text{int} $, and corrected with the scale factors listed in Table 2. Ratios of the data to MC expectation are shown in the bottom panels. Error bars (boxes) around the data points indicate statistical (square sum of systematic and MC statistical) uncertainties. |
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Figure 2-f:
Detector-level kinematic distributions for exclusive $ \mathrm{e}^+\mathrm{e}^- $ events passing our analysis requirements (Table 1) in the data (black points) and in SUPERCHIC + PHOTOS++ and STARLIGHT simulations (histograms). The MC simulations are normalised to match $ \sigma_\text{fid,MC}\mathcal{L}_\text{int} $, and corrected with the scale factors listed in Table 2. Ratios of the data to MC expectation are shown in the bottom panels. Error bars (boxes) around the data points indicate statistical (square sum of systematic and MC statistical) uncertainties. |
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Figure 2-g:
Detector-level kinematic distributions for exclusive $ \mathrm{e}^+\mathrm{e}^- $ events passing our analysis requirements (Table 1) in the data (black points) and in SUPERCHIC + PHOTOS++ and STARLIGHT simulations (histograms). The MC simulations are normalised to match $ \sigma_\text{fid,MC}\mathcal{L}_\text{int} $, and corrected with the scale factors listed in Table 2. Ratios of the data to MC expectation are shown in the bottom panels. Error bars (boxes) around the data points indicate statistical (square sum of systematic and MC statistical) uncertainties. |
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Figure 2-h:
Detector-level kinematic distributions for exclusive $ \mathrm{e}^+\mathrm{e}^- $ events passing our analysis requirements (Table 1) in the data (black points) and in SUPERCHIC + PHOTOS++ and STARLIGHT simulations (histograms). The MC simulations are normalised to match $ \sigma_\text{fid,MC}\mathcal{L}_\text{int} $, and corrected with the scale factors listed in Table 2. Ratios of the data to MC expectation are shown in the bottom panels. Error bars (boxes) around the data points indicate statistical (square sum of systematic and MC statistical) uncertainties. |
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Figure 3:
Probability for different neutron multiplicity classes (0n, 1n, and Xn with $ X > $ 2) measured on each ZDC side, for B-W process events within the fiducial phase space of Table 1. The measured ratios are compared with SUPERCHIC 4.2 and STARLIGHT predictions. |
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Figure 4:
Differential cross sections for exclusive dielectron production, in the fiducial phase space of Table 1, as a function of pair $ p_{\mathrm{T}} $ (upper left), rapidity (upper right), invariant mass (lower left), and $ |\cos\theta^{*}| $ (lower right). Data (black dots) are compared with SUPERCHIC + FSR( PHOTOS++), STARLIGHT, and gamma-UPC + FSR(PY8) predictions. Vertical bars (boxes) show statistical (systematic) uncertainties. |
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Figure 4-a:
Differential cross sections for exclusive dielectron production, in the fiducial phase space of Table 1, as a function of pair $ p_{\mathrm{T}} $ (upper left), rapidity (upper right), invariant mass (lower left), and $ |\cos\theta^{*}| $ (lower right). Data (black dots) are compared with SUPERCHIC + FSR( PHOTOS++), STARLIGHT, and gamma-UPC + FSR(PY8) predictions. Vertical bars (boxes) show statistical (systematic) uncertainties. |
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Figure 4-b:
Differential cross sections for exclusive dielectron production, in the fiducial phase space of Table 1, as a function of pair $ p_{\mathrm{T}} $ (upper left), rapidity (upper right), invariant mass (lower left), and $ |\cos\theta^{*}| $ (lower right). Data (black dots) are compared with SUPERCHIC + FSR( PHOTOS++), STARLIGHT, and gamma-UPC + FSR(PY8) predictions. Vertical bars (boxes) show statistical (systematic) uncertainties. |
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Figure 4-c:
Differential cross sections for exclusive dielectron production, in the fiducial phase space of Table 1, as a function of pair $ p_{\mathrm{T}} $ (upper left), rapidity (upper right), invariant mass (lower left), and $ |\cos\theta^{*}| $ (lower right). Data (black dots) are compared with SUPERCHIC + FSR( PHOTOS++), STARLIGHT, and gamma-UPC + FSR(PY8) predictions. Vertical bars (boxes) show statistical (systematic) uncertainties. |
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Figure 4-d:
Differential cross sections for exclusive dielectron production, in the fiducial phase space of Table 1, as a function of pair $ p_{\mathrm{T}} $ (upper left), rapidity (upper right), invariant mass (lower left), and $ |\cos\theta^{*}| $ (lower right). Data (black dots) are compared with SUPERCHIC + FSR( PHOTOS++), STARLIGHT, and gamma-UPC + FSR(PY8) predictions. Vertical bars (boxes) show statistical (systematic) uncertainties. |
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Figure 5:
Diphoton acoplanarity distribution over $ A_{\phi}^{\gamma\gamma} = $ 0-0.1 in events passing the fiducial criteria of Table 1 (except the $ A_{\phi}^{\gamma\gamma} < $ 0.01 one) measured in data (black dots) compared with the predictions for the LbL signal (orange histogram), the B-W process (yellow histogram), and the CEP (blue histogram, normalised to data as explained in the text) backgrounds. Error bars on the data points show statistical uncertainties, and dashed bands on the stacked histograms (and at unity in the data/MC ratio) represent systematic uncertainties. |
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Figure 6:
Detector-level kinematic distributions for candidate exclusive diphoton events passing all selection criteria (Table 1) in the data (black dots) compared with the simulated LbL scattering signal (orange histogram) and backgrounds from the B-W (yellow histogram) and CEP (blue histogram, scaled as described in the text) processes. All MC simulations are normalised as explained in the text. Error bars on the data points show statistical uncertainties, and dashed bands on the stacked histograms (and at unity in the data/MC ratios) represent systematic and MC statistical uncertainties added in quadrature. |
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Figure 6-a:
Detector-level kinematic distributions for candidate exclusive diphoton events passing all selection criteria (Table 1) in the data (black dots) compared with the simulated LbL scattering signal (orange histogram) and backgrounds from the B-W (yellow histogram) and CEP (blue histogram, scaled as described in the text) processes. All MC simulations are normalised as explained in the text. Error bars on the data points show statistical uncertainties, and dashed bands on the stacked histograms (and at unity in the data/MC ratios) represent systematic and MC statistical uncertainties added in quadrature. |
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Figure 6-b:
Detector-level kinematic distributions for candidate exclusive diphoton events passing all selection criteria (Table 1) in the data (black dots) compared with the simulated LbL scattering signal (orange histogram) and backgrounds from the B-W (yellow histogram) and CEP (blue histogram, scaled as described in the text) processes. All MC simulations are normalised as explained in the text. Error bars on the data points show statistical uncertainties, and dashed bands on the stacked histograms (and at unity in the data/MC ratios) represent systematic and MC statistical uncertainties added in quadrature. |
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Figure 6-c:
Detector-level kinematic distributions for candidate exclusive diphoton events passing all selection criteria (Table 1) in the data (black dots) compared with the simulated LbL scattering signal (orange histogram) and backgrounds from the B-W (yellow histogram) and CEP (blue histogram, scaled as described in the text) processes. All MC simulations are normalised as explained in the text. Error bars on the data points show statistical uncertainties, and dashed bands on the stacked histograms (and at unity in the data/MC ratios) represent systematic and MC statistical uncertainties added in quadrature. |
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Figure 6-d:
Detector-level kinematic distributions for candidate exclusive diphoton events passing all selection criteria (Table 1) in the data (black dots) compared with the simulated LbL scattering signal (orange histogram) and backgrounds from the B-W (yellow histogram) and CEP (blue histogram, scaled as described in the text) processes. All MC simulations are normalised as explained in the text. Error bars on the data points show statistical uncertainties, and dashed bands on the stacked histograms (and at unity in the data/MC ratios) represent systematic and MC statistical uncertainties added in quadrature. |
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Figure 6-e:
Detector-level kinematic distributions for candidate exclusive diphoton events passing all selection criteria (Table 1) in the data (black dots) compared with the simulated LbL scattering signal (orange histogram) and backgrounds from the B-W (yellow histogram) and CEP (blue histogram, scaled as described in the text) processes. All MC simulations are normalised as explained in the text. Error bars on the data points show statistical uncertainties, and dashed bands on the stacked histograms (and at unity in the data/MC ratios) represent systematic and MC statistical uncertainties added in quadrature. |
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Figure 6-f:
Detector-level kinematic distributions for candidate exclusive diphoton events passing all selection criteria (Table 1) in the data (black dots) compared with the simulated LbL scattering signal (orange histogram) and backgrounds from the B-W (yellow histogram) and CEP (blue histogram, scaled as described in the text) processes. All MC simulations are normalised as explained in the text. Error bars on the data points show statistical uncertainties, and dashed bands on the stacked histograms (and at unity in the data/MC ratios) represent systematic and MC statistical uncertainties added in quadrature. |
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Figure 6-g:
Detector-level kinematic distributions for candidate exclusive diphoton events passing all selection criteria (Table 1) in the data (black dots) compared with the simulated LbL scattering signal (orange histogram) and backgrounds from the B-W (yellow histogram) and CEP (blue histogram, scaled as described in the text) processes. All MC simulations are normalised as explained in the text. Error bars on the data points show statistical uncertainties, and dashed bands on the stacked histograms (and at unity in the data/MC ratios) represent systematic and MC statistical uncertainties added in quadrature. |
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Figure 7:
Differential exclusive diphoton cross sections in the fiducial phase space of Table 1 as a function of diphoton rapidity (left) and invariant mass (right) measured in data (black dots) compared with SUPERCHIC, and gamma-UPC @ NLO predictions. Vertical bars (boxes) indicate statistical (systematic) uncertainties. |
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Figure 7-a:
Differential exclusive diphoton cross sections in the fiducial phase space of Table 1 as a function of diphoton rapidity (left) and invariant mass (right) measured in data (black dots) compared with SUPERCHIC, and gamma-UPC @ NLO predictions. Vertical bars (boxes) indicate statistical (systematic) uncertainties. |
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Figure 7-b:
Differential exclusive diphoton cross sections in the fiducial phase space of Table 1 as a function of diphoton rapidity (left) and invariant mass (right) measured in data (black dots) compared with SUPERCHIC, and gamma-UPC @ NLO predictions. Vertical bars (boxes) indicate statistical (systematic) uncertainties. |
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Figure 8:
Observed (full line) and expected (dotted line) 95% CL limits on the production cross section $ \sigma(\gamma\gamma \to \mathrm{a} \to \gamma\gamma) $ as a function of the ALP mass $ m_\mathrm{a} $ in ultraperipheral PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. The inner (green) and outer (yellow) bands indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. |
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Figure 9:
Exclusion limits at 95% CL in the axion-photon coupling $ g_{\mathrm{a}\gamma} $ versus axion mass $ m_\mathrm{a} $ plane, for the operator $ \frac{1}{4\Lambda}aF\tilde{F} $ (assuming ALP coupling to photons only) derived from multiple measurements compared with the limits extracted here (red area, the expected limits are indicated with a dashed line). |
| Tables | |
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Table 1:
Definition of the fiducial phase space for the B-W and LbL scattering processes, used in their respective cross section measurements. |
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Table 2:
Summary of the overall efficiencies from simulation ($ \varepsilon^{\gamma\gamma,\mathrm{e}\mathrm{e}} $), individual data-to-simulation scale factors (SF), and final correction factors ($ C^{\gamma\gamma,\mathrm{e}\mathrm{e}} $) obtained for the exclusive diphoton and dielectron analyses. The quoted uncertainties in $ \varepsilon^{\gamma\gamma,\mathrm{e}\mathrm{e}} $, SF, and $ C^{\gamma\gamma\mathrm{e}\mathrm{e}} $ are statistical, systematic, and statistical and systematic added in quadrature, respectively. |
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Table 3:
Exclusive dielectron yields after applying each selection criteria in data and MC simulations. The simulation yields are normalised to match $ \sigma_\text{fid,MC}\mathcal{L}_\text{int} $, and corrected by the scale factors listed in Table 2. The (%) column indicates the percentage of events remaining after applying the selection with respect to the previous one. |
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Table 4:
Summary of relative systematic uncertainties in the measurement of exclusive dielectron cross sections. |
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Table 5:
Probability of different neutron multiplicity classes measured in the exclusive dielectron events passing our fiducial criteria (Table 1), compared with the predictions of SUPERCHIC 4.2 and STARLIGHT 3.13 for the deexcitation of the Pb ions in concurrent EMD processes. (The MC predictions are not available for all XnYn categories). The experimental (MC model) uncertainties quoted are the square sum of statistical and systematic (MC statistical) sources. |
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Table 6:
Exclusive diphoton yields after applying each selection criteria in data and MC simulations. The simulation yields are scaled by the integrated luminosity of the measurement and corrected by the scale factors listed in Table 2. The (%) column indicates the percentage of events remaining after applying the selection with respect to the previous one. |
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Table 7:
Summary of relative systematic uncertainties in the measurement of the LbL scattering cross section. |
| Summary |
| Measurements of light-by-light scattering $ \gamma\gamma\to\gamma\gamma $, and the Breit-Wheeler process $ \gamma\gamma\to\mathrm{e}^+\mathrm{e}^- $, have been reported in ultraperipheral collisions of lead ions (PbPb). Both processes are among the simplest and most fundamental ones in quantum electrodynamics (QED). The data were collected in 2018 by the CMS experiment at the LHC at a centre-of-mass energy per nucleon pair of 5.02 TeV corresponding to an integrated luminosity of 1.647 nb$^{-1}$. The LbL and B-W processes are studied in events with exclusively produced $ \gamma\gamma $ and $ \mathrm{e}^+\mathrm{e}^- $ pairs, respectively. Each reconstructed particle is required to have a transverse energy of $ E_{\mathrm{T}}^{\gamma,\mathrm{e}} > $ 2 GeV, a pseudorapidity of $ |\eta^{\gamma,\mathrm{e}}| < $ 2.2, and the pairs to have an invariant mass of $ m^{\gamma\gamma,\mathrm{e}\mathrm{e}} > $ 5 GeV, a transverse momentum of $ p_{\mathrm{T}}^{\gamma\gamma,\mathrm{e}\mathrm{e}} < $ 1 GeV, and an acoplanarity $ A_{\phi}^{\gamma\gamma,\mathrm{e}\mathrm{e}} \equiv (1-\Delta \phi^{\gamma\gamma,\mathrm{e}\mathrm{e}}/\pi) < $ 0.01. The selected events are required to have no additional neutral particle produced within $ |\eta| < $ 5.2, as well as no charged particle with $ p_{\mathrm{T}} > $ 0.3 GeV over $ |\eta| < $ 2.4. More than 20\,000 B-W events pass the selection criteria, and their kinematic distributions are compared with simulated events generated with the STARLIGHT 3.13 and SUPERCHIC 3.03 Monte Carlo codes, including results for the probabilities of different multiplicities of forward neutrons emitted due to the electromagnetic excitation of the ions. The measured B-W cross section, $ \sigma_\text{fid}(\gamma\gamma \to \mathrm{e}^+\mathrm{e}^-)= $ 271.5 $ \pm $ 1.9 (stat) $ \pm $ 18.3 (syst) $ \mu$b, is consistent with the QED prediction at leading-order (LO) accuracy plus final-state photon radiation (FSR). The unfolded $ \mathrm{e}^+\mathrm{e}^- $ transverse momentum, rapidity and invariant mass distributions are compared with the predictions of STARLIGHT, SUPERCHIC, and \textttgamma-UPC/MadGraph-5_aMC@NLO MC event generators, including FSR simulated with the PHOTOS++ and PYTHIA8 codes. All predictions agree with the measured distributions within uncertainties, but the addition of photon FSR achieves a better accord. In the LbL final state, 26 exclusive diphoton candidate events are observed after all selection criteria, compared with an expectation of 12.8 events predicted for the signal and 12.0 for the background, the latter dominated by contributions from central exclusive (gluon mediated) production (10.1 events) with some remaining counts from the B-W QED process (1.9 events). The significance of the LbL signal against the background-only hypothesis is above five standard deviations. The measured fiducial light-by-light scattering cross section, $ \sigma_\text{fid}(\gamma\gamma \to \gamma\gamma)= $ 107 $ \pm $ 33 (stat) $ \pm $ 20 (syst) nb, is consistent with the theoretical prediction at NLO accuracy. The unfolded diphoton rapidity and invariant mass differential cross sections show a good agreement with the theoretical expectations. Exploiting the measured invariant mass distribution of exclusive diphoton events, new limits on the resonant production of axion-like particles (ALPs) coupling to photons are set for ALP masses $ m_\mathrm{a} = $ 5-100 GeV in the $ m_\mathrm{a} $ vs. axion-photon coupling plane. Couplings larger than $ g_{\mathrm{a}\gamma} \approx $ 0.1 TeV$^{-1} $ can be excluded over $ m_\mathrm{a} = $ 5-10 GeV. The latter are the most stringent constraints in this mass range to date. |
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