Background-only fit to the observed numbers of events (black points) as a function of the diphoton invariant mass $m_{\gamma\gamma}$.

Expected and observed 95% CL upper limits on the signal fiducial cross section $\sigma_{\textrm{fid}}$, assuming 100% branching ratio for ALP decay into two photons, as a function of the hypothetical ALP mass $m_{\textrm{X}}$. The 1$\sigma$ and 2$\sigma$ confidence intervals are shown by the coloured bands.

Expected and observed 95% CL upper limits on the the ALP coupling constant, assuming 100% branching ratio for ALP decay into two photons, as a function of the hypothetical ALP mass $m_{\textrm{X}}$. The 1$\sigma$ and 2$\sigma$ confidence intervals are shown by the coloured bands. Contours of the ALP natural width $\Gamma$ are illustrated by the smooth blue solid lines.

Fiducial region acceptance of signal events for coupling constant f$^{-1}=0.05$ TeV$^{-1}$. EL, SD, and DD stand for the exclusive, single-dissociative, and double-dissociative processes. The acceptances are parameterised as $p_0 + p^{i}_{1} e^{p_{2}^{i} m_{\textrm{X}}} + p_{3}^{i} e^{p_{4}^{i} m_{\textrm{X}}} $ , where $i$ specifies the process type, exclusive, single-dissociative, or double-dissociative.

Correction factors $A_{\textrm{X}}/A_{0}$ and $C_{\textrm{X}}$ for the exclusive signal events with ALP coupling constant f$^{-1}$=0.05 TeV$^{-1}$, where acceptance $A_{\textrm{X}}$ and efficiency $C_{\textrm{X}}$ are defined in arXiv:2102.13405. $A_{\textrm{X}}$/$A_{0}$ and $C_{\textrm{X}}$ are parameterised as $p_0 + p^{i}_{1} e^{p_{2}^{i} m_{\textrm{X}}} + p_{3}^{i} e^{p_{4}^{i} m_{\textrm{X}}}$, where $i$ specifies the process type.

Simulated ALP signal cutflow for $m_{\rm{X}}$=300 GeV and $m_{\rm{X}}$=1200 GeV. The yields are normalized to a luminosity of 14.6 fb$^{-1}$. Selections are applied for each side after the selection on acoplanarity. The union of the sets of selected events is taken finally.

Parametrization of the $A_{X}$ factor, defined as the fraction of diphoton resonances satisfying the fiducial acceptance at the particle level, as function of $m_{X}$ obtained from the narrow width simulated signal samples produced in gluon fusion.

The correction factor, $C_{X}$, defined as the ratio between the number of reconstructed signal events passing the analysis cuts and the number of signal events at the particle level generated within the fiducial volume, and acceptance correction factor, $A_{X}$, defined as the fraction of diphoton resonances satisfying the fiducial acceptance at the particle level. Both are computed for NWA spin-0 models as a function of $m_{X}$.

Effect of event selections on a scalar MC signal sample generated for $m_{X}$ = 15 GeV and on the data. For the MC sample, the efficiencies are shown after applying event weights and a truth level filter that requires two photons with $p^{\gamma\gamma}_{T}>40$ GeV; for the data, the absolute yields are shown. The initial yields for data include a trigger preselection that is the OR of a list of single photon and diphoton triggers. The "2 $loose$ photons" step includes the kinematic acceptance cuts.

Parameterization of the Double Sided Crystal Ball function parameters describing the scalar mass resolution model as a function of $m_{X}$ [GeV].

Excluded signal cross section at $95\%$ CL for Hut coupling. Each jet category and their combination are shown separately.

Excluded signal cross section at $95\%$ CL for Hut coupling. Each jet category and their combination are shown separately.

Observed upper limits on the branching fractions $\mathcal{B}(\mathrm{t}\to\mathrm{Hu})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{Hc})$ at $95\%$ CL.

Expected upper limits on the branching fractions $\mathcal{B}(\mathrm{t}\to\mathrm{Hu})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{Hc})$ at $95\%$ CL.

Expected +1 standard deviation upper limits on the branching fractions $\mathcal{B}(\mathrm{t}\to\mathrm{Hu})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{Hc})$ at $95\%$ CL.

Expected -1 standard deviation upper limits on the branching fractions $\mathcal{B}(\mathrm{t}\to\mathrm{Hu})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{Hc})$ at $95\%$ CL.

Expected +2 standard deviation upper limits on the branching fractions $\mathcal{B}(\mathrm{t}\to\mathrm{Hu})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{Hc})$ at $95\%$ CL.

Expected -2 standard deviation upper limits on the branching fractions $\mathcal{B}(\mathrm{t}\to\mathrm{Hu})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{Hc})$ at $95\%$ CL.

Observed upper limits on the anomalous couplings $\kappa_{\mathrm{Hut}}$ and $\kappa_{\mathrm{Hut}}$ at $95\%$ CL.

Expected upper limits on the anomalous couplings $\kappa_{\mathrm{Hut}}$ and $\kappa_{\mathrm{Hut}}$ at $95\%$ CL.

Expected +1 standard deviation upper limits on the anomalous couplings $\kappa_{\mathrm{Hut}}$ and $\kappa_{\mathrm{Hut}}$ at $95\%$ CL.

Expected -1 standard deviation upper limits on the anomalous couplings $\kappa_{\mathrm{Hut}}$ and $\kappa_{\mathrm{Hut}}$ at $95\%$ CL.

Expected +2 standard deviation upper limits on the anomalous couplings $\kappa_{\mathrm{Hut}}$ and $\kappa_{\mathrm{Hut}}$ at $95\%$ CL.

Expected -2 standard deviation upper limits on the anomalous couplings $\kappa_{\mathrm{Hut}}$ and $\kappa_{\mathrm{Hut}}$ at $95\%$ CL.

Expected and observed limits computed using asymptotic formulas as a function of the signal mass m_{G*} and k/Mpl for the spin-2 resonance search.

The expected and observed upper limits at 95\% CL on the fiducial cross-section times branching ratio to two photons of a spin-0 resonance as a function of its mass m_X. The decay width of the resonance is equal to 2% of m_X. For masses greater than 1000 GeV, pseudo-experiments are used to verify the expected and observed limits, and used in place of the asymptotic limit when differences are observed.

The expected and observed upper limits at 95\% CL on the fiducial cross-section times branching ratio to two photons of a spin-0 resonance as a function of its mass m_X. The decay width of the resonance is equal to 6% of m_X. For masses greater than 1000 GeV, pseudo-experiments are used to verify the expected and observed limits, and used in place of the asymptotic limit when differences are observed.

The expected and observed upper limits at 95\% CL on the fiducial cross-section times branching ratio to two photons of a spin-0 resonance as a function of its mass m_X. The decay width of the resonance is equal to 10% of m_X. For masses greater than 1000 GeV, pseudo-experiments are used to verify the expected and observed limits, and used in place of the asymptotic limit when differences are observed.

The expected and observed upper limits at 95\% CL on the production cross-section times branching ratio to two photons of the lightest KK graviton as a function of its mass for k/Mpl=0.01. For masses greater than 1000 GeV, pseudo-experiments are used to verify the expected and observed limits, and used in place of the asymptotic limit when differences are observed.

The expected and observed upper limits at 95\% CL on the production cross-section times branching ratio to two photons of the lightest KK graviton as a function of its mass for k/Mpl=0.05. For masses greater than 1000 GeV, pseudo-experiments are used to verify the expected and observed limits, and used in place of the asymptotic limit when differences are observed.

Diphoton invariant mass in the signal region using a binning based on the invariant mass resolution.

Diphoton invariant mass in the signal region binned in 1 GeV bins..

Effect of event selections on a NWA spin-0 and a spin-2 ($k/Mpl=0.01$) MC samples generated for m_X = 1 TeV and on the data. For the MC samples, the event yield is shown after applying event weights; for the data, the absolute yields are shown. The initial yields for data include a trigger preselection that is the OR of a list of single photon and diphoton triggers. The "2 $loose$ photons" step includes the kinematic acceptance cuts. The cross-section times branching ratio for the spin-0 sample is normalized to the MadGraph NLO prediction of 112~fb and the cross-section times branching ratio for the graviton corresponds to the Pythia8 prediction of 12~fb.

Parameterization for the CX and AX factors as function of mX for a scalar particle, as obtained from the narrow-width MC signal samples.

Parameterization for the $C_{X}\cdot A_{X}$ factor as function of $m_{G^*}$ for the RS graviton, as obtained from k/MPl = 0.05 MC signal samples.

Parameterization of the Double Sided Crystal Ball function parameters describing the scalar mass resolution model as a function of m_{X} [GeV].

Parameterization of the Double Sided Crystal Ball function parameters describing the graviton mass resolution model as a function of m_{X} [GeV].

Upper limits on the fiducial cross section times branching ratio to two photons at centre-of-mass energy of 13 TeV of a narrow-width (Γ_X = 4 MeV) spin-0 resonance as a function of its mass m_X.

Upper limits on the production cross section times branching ratio to two photons at centre-of-mass energy of 13 TeV of the lightest KK graviton as a function of its mass m_G* for k/MPl=0.01.

Upper limits on the production cross section times branching ratio to two photons at centre-of-mass energy of 13 TeV of the lightest KK graviton as a function of its mass m_G* for k/MPl=0.10. Only the limits derived with the asymptotic formulae are quoted here.

Upper limits on the production cross section times branching ratio to two photons at centre-of-mass energy of 13 TeV of the lightest KK graviton as a function of its mass m_G* for k/MPl=0.20.

Upper limits on the production cross section times branching ratio to two photons at centre-of-mass energy of 13 TeV of the lightest KK graviton as a function of its mass m_G* for k/MPl=0.30.

Distribution of the diphoton invariant mass for data events passing the spin-0 selection. The data points are plotted at the centre of each bin. The error bars indicate statistical uncertainties. The distribution consists of not only genuine diphoton events, but also events where at least one photon is faked by a jet. There is no data event above 2700 GeV.

Distribution of the diphoton invariant mass for data events passing the spin-2 selection. The data points are plotted at the centre of each bin. The error bars indicate statistical uncertainties. The distribution consists of not only genuine diphoton events, but also events where at least one photon is faked by a jet. There is no data event above 2700 GeV.

Fiducial acceptance and product of the fiducial acceptance times the combined reconstruction and identification efficiency as a function of the mass for a spin-0 resonant signal with narrow width under the spin-0 selection. Only MC statistical uncertainties are included.

Fiducial acceptance and product of the fiducial acceptance times the combined reconstruction and identification efficiency as a function of the mass for a spin-2 resonant signal with k/MPl=0.1 under the spin-2 selection. The definition of fiducial region is provided in JHEP 09 (2016) 001. Only MC statistical uncertainties are included.

Fiducial acceptance and product of the fiducial acceptance times the combined reconstruction and identification efficiency as a function of the mass for an ADD excess (GRW formalism), calculated as the difference between the sum of ADD and SM contributions (including their interference) and the SM contribution, under the spin-2 selection in the signal region M(gamma gamma)>2240 GeV. The definition of fiducial region is provided in JHEP 09 (2016) 001, and M(gamma gamma)>2240 GeV is required in addition. Only MC statistical uncertainties are included.

The expected 95% CL exclusion contour (-1$\sigma$) for a simplified model of dark-matter production involving an axial-vector operator, Dirac DM and couplings $g_{q}$ = 0.25, $g_{\chi}$ = 1 and $g_{l}$ = 0 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The expected 95% CL exclusion contour for a simplified model of dark-matter production involving an axial-vector operator, Dirac DM and couplings $g_{q}$ = 0.25, $g_{\chi}$ = 1 and $g_{l}$ = 0 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The observed 95% CL exclusion contour for a simplified model of dark-matter production involving an axial-vector operator, Dirac DM and couplings $g_{q}$ = 0.1, $g_{\chi}$ = 1 and $g_{l}$ = 0.1 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The expected 95% CL exclusion contour (+1$\sigma$) for a simplified model of dark-matter production involving an axial-vector operator, Dirac DM and couplings $g_{q}$ = 0.1, $g_{\chi}$ = 1 and $g_{l}$ = 0.1 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The expected 95% CL exclusion contour (-1$\sigma$) for a simplified model of dark-matter production involving an axial-vector operator, Dirac DM and couplings $g_{q}$ = 0.1, $g_{\chi}$ = 1 and $g_{l}$ = 0.1 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The expected 95% CL exclusion contour for a simplified model of dark-matter production involving an axial-vector operator, Dirac DM and couplings $g_{q}$ = 0.1, $g_{\chi}$ = 1 and $g_{l}$ = 0.1 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The observed 95% CL exclusion contour for a simplified model of dark-matter production involving a vector operator with couplings $g_{q}$ = 0.25, $g_{\chi}$ =1 and $g_{l}$ = 0 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The expected 95% CL exclusion contour ($+1\sigma$) for a simplified model of dark-matter production involving a vector operator with couplings $g_{q}$ = 0.25, $g_{\chi}$ =1 and $g_{l}$ = 0 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The expected 95% CL exclusion contour ($-1\sigma$) for a simplified model of dark-matter production involving a vector operator with couplings $g_{q}$ = 0.25, $g_{\chi}$ =1 and $g_{l}$ = 0 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The expected 95% CL exclusion contour for a simplified model of dark-matter production involving a vector operator with couplings $g_{q}$ = 0.25, $g_{\chi}$ =1 and $g_{l}$ = 0 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The observed 95% CL exclusion contour for a simplified model of dark-matter production involving for a vector operator with couplings $g_{q}$ = 0.1, $g_{\chi}$ = 1 and $g_{l}$ = 0.01 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The expected 95% CL exclusion contour ($+1\sigma$) for a simplified model of dark-matter production involving for a vector operator with couplings $g_{q}$ = 0.1, $g_{\chi}$ = 1 and $g_{l}$ = 0.01 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The expected 95% CL exclusion contour ($-1\sigma$) for a simplified model of dark-matter production involving for a vector operator with couplings $g_{q}$ = 0.1, $g_{\chi}$ = 1 and $g_{l}$ = 0.01 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The expected 95% CL exclusion contour for a simplified model of dark-matter production involving for a vector operator with couplings $g_{q}$ = 0.1, $g_{\chi}$ = 1 and $g_{l}$ = 0.01 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The 90% CL exclusion limit on the $\chi$-proton scattering cross section in a simplifed model of dark-matter production involving an axial-vector operator, Dirac DM and couplings $g_{q}$ = 0.25, $g_{\chi}$ = 1 and $g_{l}$ = 0 as a function of the dark-matter mass $m_{\chi}$.

The 90% CL exclusion limit on the $\chi$-nucleon scattering cross section in a simplifed model of dark-matter production involving a vector operator, Dirac DM and couplings $g_{q}$ = 0.25, $g_{\chi}$ = 1 and $g_{l}$ = 0 as a function of the dark-matter mass $m_{\chi}$.

The observed and expected 95% CL limits on M* for a dimension-7 operator EFT model with a contact interaction of type $\gamma\gamma\chi\chi$ as a function of dark-matter mass $m_{\chi}$.

The observed and expected limit at 95% CL on the production cross section of a $Z\gamma$ resonance as a function of its mass.

The observed 95% CL upper limits on signal strength $\mu$, the ratio of the experimental limit to the predicted signal cross section, for a simplified model of dark matter production involving an axial-vector operator, Dirac DM and couplings $g_{q}$ = 0.25 and $g_{\chi}$ = 1 as a function of the DM and the mediator particle masses. The bound on $\mu$ only applies for choices of couplings that yield the same kinematic distributions as the benchmark model.

Acceptance, in %, for a simplified model of dark matter production involving an axial-vector operator, Dirac DM and couplings $g_{q}$= 0.25 and $g_{\chi}$ = 1 for various $m_{\chi}$ and $m_{\textrm{med}}$ values. It is constant as a function of $m_{\chi}$ for a fixed $m_{\textrm{med}}$ in the region $m_{\textrm{med}}>2m_{\chi}$.

Fiducial reconstruction efficiencies in the three inclusive signal regions for a simplified model of dark matter production involving an axial-vector operator, Dirac DM and couplings $g_{q}$= 0.25 and $g_{\chi}$ = 1 for various $m_{\chi}$ and $m_{\textrm{med}}$ values. It is constant as a function of $m_{\chi}$ for a fixed $m_{\textrm{med}}$ in the region $m_{\textrm{med}}>2m_{\chi}$.