Measured normalised differential fiducial cross sections of $\gamma\gamma \rightarrow \gamma\gamma$ production in Pb+Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV for diphoton $|cos(\theta*)|$ are shown as points with error bars giving the statistical uncertainty and grey bands indicating the size of the total uncertainty. The results are compared with the prediction from the SuperChic v3.0 MC generator (solid line).

Measured normalised differential fiducial cross sections of $\gamma\gamma \rightarrow \gamma\gamma$ production in Pb+Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV for average photon transverse momentum are shown as points with error bars giving the statistical uncertainty and grey bands indicating the size of the total uncertainty. The results are compared with the prediction from the SuperChic v3.0 MC generator (solid line) with bands denoting the theoretical uncertainty.

Measured normalised differential fiducial cross sections of $\gamma\gamma \rightarrow \gamma\gamma$ production in Pb+Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV for average photon transverse momentum are shown as points with error bars giving the statistical uncertainty and grey bands indicating the size of the total uncertainty. The results are compared with the prediction from the SuperChic v3.0 MC generator (solid line).

Measured differential fiducial cross sections of $\gamma\gamma \rightarrow \gamma\gamma$ production in Pb+Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV for diphoton rapidity are shown as points with error bars giving the statistical uncertainty and grey bands indicating the size of the total uncertainty. The results are compared with the prediction from the SuperChic v3.0 MC generator (solid line) with bands denoting the theoretical uncertainty.

Measured normalised differential fiducial cross sections of $\gamma\gamma \rightarrow \gamma\gamma$ production in Pb+Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV for diphoton rapidity are shown as points with error bars giving the statistical uncertainty and grey bands indicating the size of the total uncertainty. The results are compared with the prediction from the SuperChic v3.0 MC generator (solid line).

The 95% CL upper limit on the ALP cross section $\sigma_{\gamma\gamma\rightarrow a \rightarrow\gamma\gamma}$ for the $\gamma\gamma\rightarrow a \rightarrow \gamma\gamma$ process as a function of ALP mass m$_{a}$. The observed upper limit is shown as a solid black line and the expected upper limit is shown by the dashed black line with its $\pm1$ and $\pm2$ standard deviation bands. The discontinuity at $m_{a}=70 GeV$ is caused by the increase of the mass-bin width which brings an increase in signal acceptance.

The 95% CL upper limit on the ALP coupling $1/\Lambda_{a}$ for the $\gamma\gamma\rightarrow a \rightarrow \gamma\gamma$ process as a function of ALP mass m$_{a}$. The observed upper limit is shown as a solid black line and the expected upper limit is shown by the dashed black line with its $\pm1$ and $\pm2$ standard deviation bands. The discontinuity at $m_{a} = 70 GeV$ is caused by the increase of the mass-bin width which brings an increase in signal acceptance.

Fiducial cross section for light-by-light scattering

The number of data and fitted simulated events in each bin of the $|d_{0}^{\mu}|$ distribution in the $10<p_{\textrm{T}}^{\mu}<20$ GeV selection in the $\mu-\mu$ channel.

The number of data and fitted simulated events in each bin of the $|d_{0}^{\mu}|$ distribution in the $20<p_{\textrm{T}}^{\mu}<250$ GeV selection in the $e-\mu$ channel.

The number of data and fitted simulated events in each bin of the $|d_{0}^{\mu}|$ distribution in the $20<p_{\textrm{T}}^{\mu}<250$ GeV selection in the $\mu-\mu$ channel.

The measurement of the ratio of the rate of decay of W bosons to τ-leptons and muons, $R(\tau/\mu)=B(W\rightarrow\tau\nu_\tau)/B(W\rightarrow \mu\nu_\mu)$.

Observed and expected multivariate discriminant distribution in the $\ell\ell\ell\ell jj$ SR.

Observed and expected multivariate discriminant distribution in the $\ell\ell\nu\nu jj$ SR.

Correlation matrix between the fiducial cross sections for the four individual decay final states and the $ZZ^{*}$ normalisation factor.

Differential fiducial cross section for the transverse momentum $p_{T}^{4l}$ of the Higgs boson. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 . Measured value in the last bin is un upper limit at 95% CL.

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the transverse momentum $p_{T}^{4l}$ of the Higgs boson.

Differential fiducial cross section for the invariant mass $m_{12}$ of the leading Z boson. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the invariant mass $m_{12}$ of the leading Z boson.

Differential fiducial cross section for the invariant mass $m_{34}$ of the subleading Z boson. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the invariant mass $m_{34}$ of the subleading Z boson.

Differential fiducial cross section for the rapidity $|y_{4l}|$ of the Higgs boson. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the rapidity $|y_{4l}|$ of the Higgs boson.

Differential fiducial cross section for the production angle $|\cos\theta^{*}|$ of the leading Z boson. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the production angle $|\cos\theta^{*}|$ of the leading Z boson.

Differential fiducial cross section for the production angle $\cos\theta_{1}$ of the anti-lepton from the leading Z boson. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the production angle $\cos\theta_{1}$ of the anti-lepton from the leading Z boson.

Differential fiducial cross section for the production angle $\cos\theta_{2}$ of the anti-lepton from the subleading Z boson. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the production angle $\cos\theta_{2}$ of the anti-lepton from the subleading Z boson.

Differential fiducial cross section for the azimuthal angle $\phi$ of the decay planes of the two reconstructed Z bosons. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the azimuthal angle $\phi$ of the decay planes of the two reconstructed Z bosons.

Differential fiducial cross section for the azimuthal angle $\phi_{1}$ of the decay plane of the leading Z boson and the plane formed between its four-momentum and the z-axis. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the azimuthal angle $\phi_{1}$ of the decay plane of the leading Z boson and the plane formed between its four-momentum and the z-axis.

Differential fiducial cross section for the jet multiplicity $N_{jets}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the jet multiplicity $N_{jets}$.

Differential fiducial cross section for the inclusive jet multiplicity $N_{jets}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Differential fiducial cross section for the number of b-quark initiated jets $N_{b-jets}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the number of b-quark initiated jets $N_{b-jets}$.

Differential fiducial cross section for the transverse momentum of the leading jet $p_{T}^{lead.jet}$ in events with at least one jet. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the transverse momentum of the leading jet $p_{T}^{lead.jet}$ in events with at least one jet.

Differential fiducial cross section for the transverse momentum of the subleading jet $p_{T}^{sublead.jet}$ in events with at least two jets. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the transverse momentum of the subleading jet $p_{T}^{sublead.jet}$ in events with at least two jets.

Differential fiducial cross section for the invariant mass of the two highest-pT jets $m_{jj}$ in events with at least two jets. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the invariant mass of the two highest-pT jets $m_{jj}$ in events with at least two jets.

Differential fiducial cross section for the distance between the two highest-pT jets in pseudorapidity $\Delta\eta_{jj}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the distance between the two highest-pT jets in pseudorapidity $\Delta\eta_{jj}$.

Differential fiducial cross section for the distance between the two highest-pT jets in $\phi$ $\Delta\phi_{jj}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the distance between the two highest-pT jets in $\phi$ $\Delta\phi_{jj}$.

Differential fiducial cross section for the transverse momentum of the four lepton plus jet system, in events with at least one jet $p_{T}^{4lj}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the transverse momentum of the four lepton plus jet system, in events with at least one jet $p_{T}^{4lj}$.

Differential fiducial cross section for the transverse momentum of the four lepton plus di-jet system, in events with at least two jets $p_{T}^{4ljj}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 . Measured value in the last bin is un upper limit at 95% CL.

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the transverse momentum of the four lepton plus di-jet system, in events with at least two jets $p_{T}^{4ljj}$.

Differential fiducial cross section for the invariant mass of the four lepton plus jet system in events with at least one jet $m_{4lj}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the invariant mass of the four lepton plus jet system in events with at least one jet $m_{4lj}$.

Differential fiducial cross section for the invariant mass of the four lepton plus di-jet system in events with at least two jets $m_{4ljj}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the invariant mass of the four lepton plus di-jet system in events with at least two jets $m_{4ljj}$.

Differential fiducial cross section for the leading vs. subleading Z boson mass $m_{12}$vs.$m_{34}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the leading vs. subleading Z boson mass $m_{12}$vs.$m_{34}$.

Differential fiducial cross section for the leading vs. subleading Z boson mass $m_{12}$vs.$m_{34}$ in $ll\mu\mu$ final states. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Differential fiducial cross section for the leading vs. subleading Z boson mass $m_{12}$vs.$m_{34}$ in $llee$ final states. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the leading vs. subleading Z boson mass m12 vs. m34 in $ll\mu\mu$ and $llee$ final states.

Differential fiducial cross section of the $p_{T}^{4l}$ distribution in $|y_{4l}|$ bins. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section of the $p_{T}^{4l}$ distribution in $|y_{4l}|$ bins.

Differential fiducial cross section of the $p_{T}^{4l}$ distribution in $N_{jets}$ bins. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section of the $p_{T}^{4l}$ distribution in $N_{jets}$ bins.

Differential fiducial cross section for transverse momentum of the four lepton system vs. the transverse momentum of the four lepton plus jet system $p_{T}^{4l}$vs.$p_{T}^{4lj}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for transverse momentum of the four lepton system vs. the transverse momentum of the four lepton plus jet system $p_{T}^{4l}$vs.$p_{T}^{4lj}$.

Differential fiducial cross section for the transverse momentum of the four lepton plus jet system vs the invariant mass of the four lepton plus jet system $p_{T}^{4l}$vs.$m_{4lj}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the transverse momentum of the four lepton plus jet system vs the invariant mass of the four lepton plus jet system $p_{T}^{4l}$vs.$m_{4lj}$.

Differential fiducial cross section for the transverse momentum of the four lepton vs the transverse momentum of the leading jet $p_{T}^{4l}$vs.$p_{T}^{l.jet}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the transverse momentum of the four lepton vs the transverse momentum of the leading jet $p_{T}^{4l}$vs.$p_{T}^{lead.jet}$.

Differential fiducial cross section for the transverse momentum of the leading jet vs the rapidity of the leading jet $p_{T}^{lead.jet}$vs.$|y^{lead.jet}|$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the transverse momentum of the leading jet vs the rapidity of the leading jet $p_{T}^{lead.jet}$vs.$|y^{lead.jet}|$.

Differential fiducial cross section for the transverse momentum of the leading jet vs the transverse momentum of the subleading jet $p_{T}^{lead.jet}$vs.$p_{T}^{sublead.jet}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the transverse momentum of the leading jet vs the transverse momentum of the subleading jet $p_{T}^{lead.jet}$vs.$p_{T}^{sublead.jet}$.

Differential fiducial cross section for the leading Z boson mass $m_{12}$ in $4\mu$ and $4e$ final states. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Differential fiducial cross section for the leading Z boson mass $m_{12}$ in $2e2\mu$ and $2\mu2e$ final states. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the leading Z boson mass $m_{12}$ in $4l$ and $2l2l$ final states.

Differential fiducial cross section for the subleading Z boson mass $m_{34}$ in $4\mu$ and $4e$ final states. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Differential fiducial cross section for the subleading Z boson mass $m_{34}$ in $2e2\mu$ and $2\mu2e$ final states. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the subleading Z boson mass $m_{34}$ in $4l$ and $2l2l$ final states.

Differential fiducial cross section for the azimuthal angle $\phi$ of the decay planes of the two reconstructed Z bosons in $4\mu$ and $4e$ final states. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Differential fiducial cross section for the azimuthal angle $\phi$ of the decay planes of the two reconstructed Z bosons in $2e2\mu$ and $2\mu2e$ final states. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the azimuthal angle $\phi$ of the decay planes of the two reconstructed Z bosons in $4l$ and $2l2l$ final states.

Differential fiducial cross section for the leading vs. subleading Z boson mass $m_{12}$vs.$m_{34}$ in $4\mu$ and $4e$ final states. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Differential fiducial cross section for the leading vs. subleading Z boson mass $m_{12}$vs.$m_{34}$ in $2\mu2e$ and $2e2\mu$ final states. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the leading vs. subleading Z boson mass $m_{12}$vs.$m_{34}$ in $4l$ and $2l2l$ final states.

Charged particle multiplicity distribution.

Average charged particle transverse momentum as a function of the number of charged particles in the event.