Measured $R_\text{AA}$ for the $\Upsilon(3S)$ state as functions of PbPb collision centrality, integrated over the full kinematic range $p_\text{T}$ < 30 GeV/c and |y| < 2.4. The global uncertainty "PP MB" represents the pp luminosity and PbPb $N_\text{MB}$ combined uncertainties, whereas the global uncertainty "PP 3S" corresponds to the uncertainty on the $\Upsilon(3S)$ pp yields.

Measured $R_\text{AA}$ for the$\Upsilon(2S)$ state in the 0–90% centrality interval, integrated over the full kinematic range $p_\text{T}$ < 30 GeV/c and |y| < 2.4. The global uncertainty "PP MB" represents the pp luminosity and PbPb $N_\text{MB}$ combined uncertainties, whereas the global uncertainty "PP 2S" corresponds to the uncertainty on the $\Upsilon(2S)$ pp yields.

Measured $R_\text{AA}$ for the$\Upsilon(2S)$ state in the 0–90% centrality interval, integrated over the full kinematic range $p_\text{T}$ < 30 GeV/c and |y| < 2.4. The global uncertainty "PP MB" represents the pp luminosity and PbPb $N_\text{MB}$ combined uncertainties, whereas the global uncertainty "PP 2S" corresponds to the uncertainty on the $\Upsilon(2S)$ pp yields.

Measured $R_\text{AA}$ for the $\Upsilon(3S)$ state in the 0–90% centrality interval, integrated over the full kinematic range $p_\text{T}$ < 30 GeV/c and |y| < 2.4. The global uncertainty "PP MB" represents the pp luminosity and PbPb $N_\text{MB}$ combined uncertainties, whereas the global uncertainty "PP 3S" corresponds to the uncertainty on the$\Upsilon(3S)$ pp yields.

Measured $R_\text{AA}$ for the $\Upsilon(3S)$ state in the 0–90% centrality interval, integrated over the full kinematic range $p_\text{T}$ < 30 GeV/c and |y| < 2.4. The global uncertainty "PP MB" represents the pp luminosity and PbPb $N_\text{MB}$ combined uncertainties, whereas the global uncertainty "PP 3S" corresponds to the uncertainty on the$\Upsilon(3S)$ pp yields.

Measured $R_\text{AA}$ for the $\Upsilon(2S)$ state as functions of transverse momentum $p_\text{T}$, integrated over the rapidity range of |y| < 2.4 and the 0–90% centrality interval. The global uncertainty combines the uncertainties of $T_\text{AA}$ , pp luminosity, and PbPb $N_\text{MB}$.

Measured $R_\text{AA}$ for the $\Upsilon(2S)$ state as functions of transverse momentum $p_\text{T}$, integrated over the rapidity range of |y| < 2.4 and the 0–90% centrality interval. The global uncertainty combines the uncertainties of $T_\text{AA}$ , pp luminosity, and PbPb $N_\text{MB}$.

Measured $R_\text{AA}$ for the $\Upsilon(3S)$ state as functions of transverse momentum $p_\text{T}$, integrated over the rapidity range of |y| < 2.4 and the 0–90% centrality interval. The global uncertainty combines the uncertainties of $T_\text{AA}$ , pp luminosity, and PbPb $N_\text{MB}$.

Measured $R_\text{AA}$ for the $\Upsilon(3S)$ state as functions of transverse momentum $p_\text{T}$, integrated over the rapidity range of |y| < 2.4 and the 0–90% centrality interval. The global uncertainty combines the uncertainties of $T_\text{AA}$ , pp luminosity, and PbPb $N_\text{MB}$.

The double ratios of $\Upsilon(3S)$ /$\Upsilon(2S)$ as functions of PbPb collision centrality, integrated over the full kinematic range $p_\text{T}$ < 30 GeV/c and |y| < 2.4. The global uncertainty represents the combined systematic and statistical uncertainties from pp data.

The double ratios of $\Upsilon(3S)$ /$\Upsilon(2S)$ as functions of PbPb collision centrality, integrated over the full kinematic range $p_\text{T}$ < 30 GeV/c and |y| < 2.4. The global uncertainty represents the combined systematic and statistical uncertainties from pp data.

The double ratios of $\Upsilon(3S)$ /$\Upsilon(2S)$ in the 0–90% centrality interval, integrated over the full kinematic range $p_\text{T}$ < 30 GeV/c and |y| < 2.4. The global uncertainty represents the combined systematic and statistical uncertainties from pp data.

The double ratios of $\Upsilon(3S)$ /$\Upsilon(2S)$ in the 0–90% centrality interval, integrated over the full kinematic range $p_\text{T}$ < 30 GeV/c and |y| < 2.4. The global uncertainty represents the combined systematic and statistical uncertainties from pp data.

The double ratios of $\Upsilon(3S)$ /$\Upsilon(2S)$ as functions of transverse momentum $p_\text{T}$, integrated over the rapidity range of |y| < 2.4 and the 0–90% centrality interval.

The double ratios of $\Upsilon(3S)$ /$\Upsilon(2S)$ as functions of transverse momentum $p_\text{T}$, integrated over the rapidity range of |y| < 2.4 and the 0–90% centrality interval.

Yields for $\Upsilon(2S)$ mesons in PbPb collisions in centrality $0--90\%$ and $|y| < 2.4$, corrected for acceptance and efficiency, and normalized by the nuclear thickness function $\langle T_{AA} \rangle$ and the number of minimum bias events $N_{MB}$. The numbers are in units of pb$/GeV/c$.

Yields for $\Upsilon(2S)$ mesons in PbPb collisions in $p_\text{T} < 30GeV/c$ and $|y| < 2.4$, corrected for acceptance and efficiency, and normalized by the nuclear thickness function $\langle T_{AA} \rangle$ and the number of minimum bias events $N_{MB}$. The numbers are in units of pb$/GeV/c$.

Yields for $\Upsilon(3S)$ mesons in PbPb collisions in centrality $0--90\%$ and $|y| < 2.4$, corrected for acceptance and efficiency, and normalized by the nuclear thickness function $\langle T_{AA} \rangle$ and the number of minimum bias events $N_{MB}$. The numbers are in units of pb$/GeV/c$.

Yields for $\Upsilon(3S)$ mesons in PbPb collisions in $p_\text{T} < 30GeV/c$ and $|y| < 2.4$, corrected for acceptance and efficiency, and normalized by the nuclear thickness function $\langle T_{AA} \rangle$ and the number of minimum bias events $N_{MB}$. The numbers are in units of pb$/GeV/c$.

Yields for $\Upsilon(1S)$ mesons in PbPb collisions in $p_\text{T} < 30GeV/c$ and $|y| < 2.4$, corrected for acceptance and efficiency, and normalized by the nuclear thickness function $\langle T_{AA} \rangle$ and the number of minimum bias events $N_{MB}$. The numbers are in units of pb$/GeV/c$. The values and global integrated luminosity uncertainty are quoted from data taken from CMS in 2018 LHC PbPb run.

The total coherent $\mathrm{J}/\psi$ photoproduction cross section as a function of photon-nuclear center-of-mass energy per nucleon $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$, measured in PbPb ultra-peripheral collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV. The $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$ values used correspond to the center of each rapidity range. The theoretical uncertainties is due to the uncertainties in the photon flux.

The nuclear gluon suppression factor $R_{\mathrm{g}}^{\mathrm{Pb}}$ as a function of Bjorken $x$ extracted from the CMS measurement of the coherent $\mathrm{J}/\psi$ photoproduction in PbPb ultra-peripheral collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV. The $x$ values are evaluated at the centers of their corresponding rapidity ranges. The theoretical uncertainties are due to the uncertainties in the photon flux and the impulse approximation model.

The nuclear gluon suppression factor $R_{\mathrm{g}}^{\mathrm{Pb}}$ as a function of Bjorken $x$ extracted from the CMS measurement of the coherent $\mathrm{J}/\psi$ photoproduction in PbPb ultra-peripheral collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV. The $x$ values are evaluated at the centers of their corresponding rapidity ranges. The theoretical uncertainties are due to the uncertainties in the photon flux and the impulse approximation model.

The total covariance matrix of the total coherent photoproduction cross section as a function of photon-nuclear center-of-mass energy per nucleon $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$. The covariance matrix includes both the experimental and theoretical (photon flux) uncertainties. The bins are ordered as increasing in $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$.

The photon flux values from STARLight as a function of rapidity, in different neutron multiplicity classes: 0n0n, 0nXn, and XnXn.

The experimental covariance matrix of the total coherent photoproduction cross section as a function of photon-nuclear center-of-mass energy per nucleon $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$. The bins are ordered as increasing in $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$.

The covariance matrix for the flux in the 0n0n neutron multiplicity class.

The theoretical (photon flux) covariance matrix of the total coherent photoproduction cross section as a function of photon-nuclear center-of-mass energy per nucleon $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$. The bins are ordered as increasing in $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$.

The covariance matrix for the flux in the 0nXn neutron multiplicity class.

The covariance matrix for the flux in the XnXn neutron multiplicity class.

The total covariance matrix of the total coherent photoproduction cross section as a function of photon-nuclear center-of-mass energy per nucleon $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$. The covariance matrix includes both the experimental and theoretical (photon flux) uncertainties. The bins are ordered as increasing in $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$.

The experimental covariance matrix of the total coherent photoproduction cross section as a function of photon-nuclear center-of-mass energy per nucleon $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$. The bins are ordered as increasing in $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$.

The theoretical (photon flux) covariance matrix of the total coherent photoproduction cross section as a function of photon-nuclear center-of-mass energy per nucleon $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$. The bins are ordered as increasing in $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$.

Post-fit distributions for the number of jets ($N_{j}$) in CR 1b(-). The QmisID represents the backgrounds with a mis-assigned charge. HF e and HF $\mu$ are the backgrounds with fake/non-prompt leptons. Mat. Conv. and Low $m_{\gamma*}$ are the material and virtual photon conversions.

Post-fit distribution for the difference between the number of positive events and the number of negative events ($N_{+}-N_{-}$) as a function of the number of jets ($N_{j}$) in the sum of four $t\bar{t}W$ CRs and the SR.

Post-fit distributions for the fitted variables in the CRs for the fake/non-prompt lepton background - CR HF e. The QmisID represents the backgrounds with a mis-assigned charge. HF e and HF $\mu$ are the backgrounds with fake/non-prompt leptons. Mat. Conv. and Low $m_{\gamma*}$ are the material and virtual photon conversions.

Post-fit distributions for the fitted variables in the CRs for the fake/non-prompt lepton background - CR HF $\mu$. The QmisID represents the backgrounds with a mis-assigned charge. HF e and HF $\mu$ are the backgrounds with fake/non-prompt leptons. Mat. Conv. and Low $m_{\gamma*}$ are the material and virtual photon conversions.

Post-fit distributions for the fitted variables in the CRs for the fake/non-prompt lepton background - CR Mat. Conv.. The QmisID represents the backgrounds with a mis-assigned charge. HF e and HF $\mu$ are the backgrounds with fake/non-prompt leptons. Mat. Conv. and Low $m_{\gamma*}$ are the material and virtual photon conversions.

Post-fit distributions for the fitted variables in the CRs for the fake/non-prompt lepton background - CR Low $m_{\gamma*}$. The QmisID represents the backgrounds with a mis-assigned charge. HF e and HF $\mu$ are the backgrounds with fake/non-prompt leptons. Mat. Conv. and Low $m_{\gamma*}$ are the material and virtual photon conversions.

Comparison between data and the predictions after a fit to data for the GNN distribution in the SR. The QmisID represents the backgrounds with a mis-assigned charge. HF e and HF $\mu$ are the backgrounds with fake/non-prompt leptons. Mat. Conv. and Low $m_{\gamma*}$ are the material and virtual photon conversions.

Comparison between data and prediction after the fit to data in the signal-enriched region with GNN >= 0.6 for the distributions of the number of jets. The QmisID represents the backgrounds with a mis-assigned charge. HF e and HF $\mu$ are the backgrounds with fake/non-prompt leptons. Mat. Conv. and Low $m_{\gamma*}$ are the material and virtual photon conversions.

Comparison between data and prediction after the fit to data in the signal-enriched region with GNN >= 0.6 for the distributions of the number of b-jets. The QmisID represents the backgrounds with a mis-assigned charge. HF e and HF $\mu$ are the backgrounds with fake/non-prompt leptons. Mat. Conv. and Low $m_{\gamma*}$ are the material and virtual photon conversions.

Comparison between data and prediction after the fit to data in the signal-enriched region with GNN >= 0.6 for the distributions of the sum of the four highest PCBT scores of jets in the event. The QmisID represents the backgrounds with a mis-assigned charge. HF e and HF $\mu$ are the backgrounds with fake/non-prompt leptons. Mat. Conv. and Low $m_{\gamma*}$ are the material and virtual photon conversions.

Comparison between data and prediction after the fit to data in the signal-enriched region with GNN >= 0.6 for the distributions of the sum of transverse momenta over all jets and leptons in the event. The QmisID represents the backgrounds with a mis-assigned charge. HF e and HF $\mu$ are the backgrounds with fake/non-prompt leptons. Mat. Conv. and Low $m_{\gamma*}$ are the material and virtual photon conversions.

Two-dimensional negative log-likelihood contour for the $t\bar{t}t$ cross section ($\sigma_{t\bar{t}t}$) versus the $t\bar{t}t\bar{t}$ cross section ($\sigma_{t\bar{t}t\bar{t}}$) when the normalisation of both processes are treated as free parameters in the fit.

The negative log-likelihood values as a function of the Higgs oblique parameter $\hat{H}$.

The measured and expected cross-sections of $t\bar{t}t\bar{t}$ production.

Observed 68% CL Limit Contour in $\kappa_t,\alpha$ with $t\bar tt\bar t$ parameterized as a function of $\kappa_t,\alpha$, and the $t\bar tH$ parameterization profiled. This is the lower part of the contour.

Observed 68% CL Limit Contour in $\kappa_t,\alpha$ with $t\bar tt\bar t$ parameterized as a function of $\kappa_t,\alpha$, and the $t\bar tH$ parameterization profiled. This is the upper part of the contour.

Observed 95% CL Limit Contour in $\kappa_t,\alpha$ with $t\bar tt\bar t$ parameterized as a function of $\kappa_t,\alpha$, and the $t\bar tH$ parameterization profiled.

Expected 68% CL Limit Contour in $\kappa_t,\alpha$ with $t\bar tt\bar t$ parameterized as a function of $\kappa_t,\alpha$, and the $t\bar tH$ parameterization profiled.

Expected 95% CL Limit Contour in $\kappa_t,\alpha$ with $t\bar tt\bar t$ parameterized as a function of $\kappa_t,\alpha$, and the $t\bar tH$ parameterization profiled.

Observed 68% CL Limit Contour in $\kappa_t,\alpha$ with $t\bar tt\bar t$ parameterized as a function of $\kappa_t,\alpha$, and the $t\bar tH$ parameterization profiled. This is the lower part of the contour.

Observed 68% CL Limit Contour in $\kappa_t,\alpha$ with $t\bar tt\bar t$ parameterized as a function of $\kappa_t,\alpha$, and the $t\bar tH$ parameterization profiled. This is the upper part of the contour.

Observed 95% CL Limit Contour in $\kappa_t,\alpha$ with $t\bar tt\bar t$ parameterized as a function of $\kappa_t,\alpha$, and the $t\bar tH$ parameterization profiled.

Expected 68% CL Limit Contour in $\kappa_t,\alpha$ with $t\bar tt\bar t$ parameterized as a function of $\kappa_t,\alpha$, and the $t\bar tH$ parameterization profiled.

Expected 95% CL Limit Contour in $\kappa_t,\alpha$ with $t\bar tt\bar t$ parameterized as a function of $\kappa_t,\alpha$, and the $t\bar tH$ parameterization profiled.

Breakdown of systematic uncertainties in the measured inclusive cross-section. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper.

Data bootstrap post unfolding for the inclusive cross-section. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry, and are in units of [fb].

Differential absolute cross-section for $\textrm{p}_{\textrm{T}}^{l}$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper. The last bin of the distribution contains the overflow.

Covariance Matrix (statistical uncertainties only) for the differential absolute cross-section for $\textrm{p}_{\textrm{T}}^{l}$. The last bin of the distribution contains the overflow.

Data bootstrap post unfolding for the differential absolute cross-section for $\textrm{p}_{\textrm{T}}^{l}$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry, and are in units of [fb/GeV]. The last bin of the distribution contains the overflow.

Differential absolute cross-section for $|\eta^{l}|$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper.

Covariance Matrix (statistical uncertainties only) for the differential absolute cross-section for $|\eta^{l}|$.

Data bootstrap post unfolding for the differential absolute cross-section for $|\eta^{l}|$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry, and are in units of [fb].

Differential absolute cross-section for $\textrm{E}^{e} + \textrm{E}^{\mu}$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper. The last bin of the distribution contains the overflow.

Covariance Matrix (statistical uncertainties only) for the differential absolute cross-section for $\textrm{E}^{e} + \textrm{E}^{\mu}$. The last bin of the distribution contains the overflow.

Data bootstrap post unfolding for the differential absolute cross-section for $\textrm{E}^{e} + \textrm{E}^{\mu}$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry, and are in units of [fb/GeV]. The last bin of the distribution contains the overflow.

Differential absolute cross-section for $m^{e\mu}$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper. The last bin of the distribution contains the overflow.

Covariance Matrix (statistical uncertainties only) for the differential absolute cross-section for $m^{e\mu}$. The last bin of the distribution contains the overflow.

Data bootstrap post unfolding for the differential absolute cross-section for $m^{e\mu}$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry, and are in units of [fb/GeV]. The last bin of the distribution contains the overflow.

Differential absolute cross-section for $\textrm{p}_{\textrm{T}}^{e} + \textrm{p}_{\textrm{T}}^{\mu}$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper. The last bin of the distribution contains the overflow.

Covariance Matrix (statistical uncertainties only) for the differential absolute cross-section for $\textrm{p}_{\textrm{T}}^{e} + \textrm{p}_{\textrm{T}}^{\mu}$. The last bin of the distribution contains the overflow.

Data bootstrap post unfolding for the differential absolute cross-section for $\textrm{p}_{\textrm{T}}^{e} + \textrm{p}_{\textrm{T}}^{\mu}$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry, and are in units of [fb/GeV]. The last bin of the distribution contains the overflow.

Differential absolute cross-section for $\textrm{p}_{\textrm{T}}^{e\mu}$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper. The last bin of the distribution contains the overflow.

Covariance Matrix (statistical uncertainties only) for the differential absolute cross-section for $\textrm{p}_{\textrm{T}}^{e\mu}$. The last bin of the distribution contains the overflow.

Data bootstrap post unfolding for the differential absolute cross-section for $\textrm{p}_{\textrm{T}}^{e\mu}$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry, and are in units of [fb/GeV]. The last bin of the distribution contains the overflow.

Differential absolute cross-section for $|\Delta\phi^{e\mu}|$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper.

Covariance Matrix (statistical uncertainties only) for the differential absolute cross-section for $|\Delta\phi^{e\mu}|$.

Data bootstrap post unfolding for the differential absolute cross-section for $|\Delta\phi^{e\mu}|$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry, and are in units of [fb/rad].

Differential absolute cross-section for $|y^{e\mu}|$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper.

Covariance Matrix (statistical uncertainties only) for the differential absolute cross-section for $|y^{e\mu}|$.

Data bootstrap post unfolding for the differential absolute cross-section for $|y^{e\mu}|$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry, and are in units of [fb].

Double differential absolute cross-section for $|y^{e\mu}|$ x $m^{e\mu}$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper. The highest invariant mass bin of the two distributions contains the overflows.

Covariance Matrix (statistical uncertainties only) for the double differential absolute cross-section for $|y^{e\mu}|$ x $m^{e\mu}$. The highest invariant mass bin of the two distributions contains the overflows.

Data bootstrap post unfolding for the double differential absolute cross-section for $|y^{e\mu}|$ x $m^{e\mu}$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry, and are in units of [fb/GeV]. The highest invariant mass bin of the two distributions contains the overflows.

Double differential absolute cross-section for $|\Delta\phi^{e\mu}|$ x $m^{e\mu}$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper. The highest invariant mass bin of the two distributions contains the overflows.

Covariance Matrix (statistical uncertainties only) for the double differential absolute cross-section for $|\Delta\phi^{e\mu}|$ x $m^{e\mu}$. The highest invariant mass bin of the two distributions contains the overflows.

Data bootstrap post unfolding for the double differential absolute cross-section for $|\Delta\phi^{e\mu}|$ x $m^{e\mu}$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry, and are in units of [fb/GeV/rad]. The highest invariant mass bin of the two distributions contains the overflows.

Double differential absolute cross-section for $|\Delta\phi^{e\mu}|$ x $\textrm{p}_{\textrm{T}}^{e\mu}$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper. The highest $\textrm{p}_{\textrm{T}}^{e\mu}$ bin contains the overflows.

Covariance Matrix (statistical uncertainties only) for the double differential absolute cross-section for $|\Delta\phi^{e\mu}|$ x $\textrm{p}_{\textrm{T}}^{e\mu}$. The highest $\textrm{p}_{\textrm{T}}^{e\mu}$ bin contains the overflows.

Data bootstrap post unfolding for the double differential absolute cross-section for $|\Delta\phi^{e\mu}|$ x $\textrm{p}_{\textrm{T}}^{e\mu}$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry, and are in units of [fb/GeV/rad]. The highest $\textrm{p}_{\textrm{T}}^{e\mu}$ bin contains the overflows.

Double differential absolute cross-section for $|\Delta\phi^{e\mu}|$ x $\textrm{E}^{e} + \textrm{E}^{\mu}$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper. The highest $\textrm{E}^{e} + \textrm{E}^{\mu}$ bin contains the overflows.

Covariance Matrix (statistical uncertainties only) for the double differential absolute cross-section for $|\Delta\phi^{e\mu}|$ x $\textrm{E}^{e} + \textrm{E}^{\mu}$. The highest $\textrm{E}^{e} + \textrm{E}^{\mu}$ bin contains the overflows.

Data bootstrap post unfolding for the double differential absolute cross-section for $|\Delta\phi^{e\mu}|$ x $\textrm{E}^{e} + \textrm{E}^{\mu}$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry, and are in units of [fb/GeV/rad]. The highest $\textrm{E}^{e} + \textrm{E}^{\mu}$ bin contains the overflows.

Differential normalised cross-section for $\textrm{p}_{\textrm{T}}^{l}$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper. The last bin of the distribution contains the overflow.

Covariance Matrix (statistical uncertainties only) for the differential normalised cross-section for $\textrm{p}_{\textrm{T}}^{l}$. The last bin of the distribution contains the overflow.

Data bootstrap post unfolding for the differential normalised cross-section for $\textrm{p}_{\textrm{T}}^{l}$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry, and are in units of [1/GeV]. The last bin of the distribution contains the overflow.

Differential normalised cross-section for $|\eta^{l}|$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper.

Covariance Matrix (statistical uncertainties only) for the differential normalised cross-section for $|\eta^{l}|$.

Data bootstrap post unfolding for the differential normalised cross-section for $|\eta^{l}|$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry.

Differential normalised cross-section for $\textrm{E}^{e} + \textrm{E}^{\mu}$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper. The last bin of the distribution contains the overflow.

Covariance Matrix (statistical uncertainties only) for the differential normalised cross-section for $\textrm{E}^{e} + \textrm{E}^{\mu}$. The last bin of the distribution contains the overflow.

Data bootstrap post unfolding for the differential normalised cross-section for $\textrm{E}^{e} + \textrm{E}^{\mu}$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry. The last bin of the distribution contains the overflow.

Differential normalised cross-section for $m^{e\mu}$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper. The last bin of the distribution contains the overflow.

Covariance Matrix (statistical uncertainties only) for the differential normalised cross-section for $m^{e\mu}$. The last bin of the distribution contains the overflow.

Data bootstrap post unfolding for the differential normalised cross-section for $m^{e\mu}$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry. The last bin of the distribution contains the overflow.

Differential normalised cross-section for $\textrm{p}_{\textrm{T}}^{e} + \textrm{p}_{\textrm{T}}^{\mu}$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper. The last bin of the distribution contains the overflow.

Covariance Matrix (statistical uncertainties only) for the differential normalised cross-section for $\textrm{p}_{\textrm{T}}^{e} + \textrm{p}_{\textrm{T}}^{\mu}$. The last bin of the distribution contains the overflow.

Data bootstrap post unfolding for the differential normalised cross-section for $\textrm{p}_{\textrm{T}}^{e} + \textrm{p}_{\textrm{T}}^{\mu}$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry, and are in units of [1/GeV]. The last bin of the distribution contains the overflow.

Differential normalised cross-section for $\textrm{p}_{\textrm{T}}^{e\mu}$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper. The last bin of the distribution contains the overflow.

Covariance Matrix (statistical uncertainties only) for the differential normalised cross-section for $\textrm{p}_{\textrm{T}}^{e\mu}$. The last bin of the distribution contains the overflow.

Data bootstrap post unfolding for the differential normalised cross-section for $\textrm{p}_{\textrm{T}}^{e\mu}$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry, and are in units of [1/GeV]. The last bin of the distribution contains the overflow.

Differential normalised cross-section for $|\Delta\phi^{e\mu}|$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper.

Covariance Matrix (statistical uncertainties only) for the differential normalised cross-section for $|\Delta\phi^{e\mu}|$.

Data bootstrap post unfolding for the differential normalised cross-section for $|\Delta\phi^{e\mu}|$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry, and are in units of [1/rad].

Differential normalised cross-section for $|y^{e\mu}|$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper.

Covariance Matrix (statistical uncertainties only) for the differential normalised cross-section for $|y^{e\mu}|$.

Data bootstrap post unfolding for the differential normalised cross-section for $|y^{e\mu}|$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry.

Double differential normalised cross-section for $|y^{e\mu}|$ x $m^{e\mu}$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper. The highest invariant mass bin of the two distributions contains the overflows.

Covariance Matrix (statistical uncertainties only) for the double differential normalised cross-section for $|y^{e\mu}|$ x $m^{e\mu}$. The highest invariant mass bin of the two distributions contains the overflows.

Data bootstrap post unfolding for the double differential normalised cross-section for $|y^{e\mu}|$ x $m^{e\mu}$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry, and are in units of [1/GeV]. The highest invariant mass bin of the two distributions contains the overflows.

Double differential normalised cross-section for $|\Delta\phi^{e\mu}|$ x $m^{e\mu}$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper. The highest invariant mass bin of the two distributions contains the overflows.

Covariance Matrix (statistical uncertainties only) for the double differential normalised cross-section for $|\Delta\phi^{e\mu}|$ x $m^{e\mu}$. The highest invariant mass bin of the two distributions contains the overflows.

Data bootstrap post unfolding for the double differential normalised cross-section for $|\Delta\phi^{e\mu}|$ x $m^{e\mu}$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry, and are in units of [1/GeV/rad]. The highest invariant mass bin of the two distributions contains the overflows.

Double differential normalised cross-section for $|\Delta\phi^{e\mu}|$ x $\textrm{p}_{\textrm{T}}^{e\mu}$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper. The highest $\textrm{p}_{\textrm{T}}^{e\mu}$ bin contains the overflows.

Covariance Matrix (statistical uncertainties only) for the double differential normalised cross-section for $|\Delta\phi^{e\mu}|$ x $\textrm{p}_{\textrm{T}}^{e\mu}$. The highest $\textrm{p}_{\textrm{T}}^{e\mu}$ bin contains the overflows.

Data bootstrap post unfolding for the double differential normalised cross-section for $|\Delta\phi^{e\mu}|$ x $\textrm{p}_{\textrm{T}}^{e\mu}$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry, and are in units of [1/GeV/rad]. The highest $\textrm{p}_{\textrm{T}}^{e\mu}$ bin contains the overflows.

Double differential normalised cross-section for $|\Delta\phi^{e\mu}|$ x $\textrm{E}^{e} + \textrm{E}^{\mu}$. The impact of the top-quark mass on the cross-section is included in the table and not counted in the total uncertainty entry in the paper. The highest $\textrm{E}^{e} + \textrm{E}^{\mu}$ bin contains the overflows.

Covariance Matrix (statistical uncertainties only) for the double differential normalised cross-section for $|\Delta\phi^{e\mu}|$ x $\textrm{E}^{e} + \textrm{E}^{\mu}$. The highest $\textrm{E}^{e} + \textrm{E}^{\mu}$ bin contains the overflows.

Data bootstrap post unfolding for the double differential normalised cross-section for $|\Delta\phi^{e\mu}|$ x $\textrm{E}^{e} + \textrm{E}^{\mu}$. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the BootstrapGenerator software package (https://gitlab.cern.ch/atlas-physics/sm/StandardModelTools_BootstrapGenerator/BootstrapGenerator), which implements a technique described in ATL-PHYS-PUB-2021-011 (https://cds.cern.ch/record/2759945). The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. All the provided numbers originate from pseudo-data, including the 0th entry, and are in units of [1/GeV/rad]. The highest $\textrm{E}^{e} + \textrm{E}^{\mu}$ bin contains the overflows.

The $\Delta p_{\mathrm{T}}$ of photon-tagged jets as a function of jet $p_{\mathrm{T}}$.

The double $R_{\mathrm{AA}}$ ratio of $R_{\mathrm{AA}}^{\gamma\text{-jet}}/R_{\mathrm{AA}}^{\text{inclusive jet}}$ as a function of jet $p_{\mathrm{T}}$.

The differential cross-section of photon-tagged jets as a function of jet $p_{\mathrm{T}}$ in pp collisions.

The yields of photon-tagged jets as a function of jet $p_{\mathrm{T}}$ in Pb+Pb collisions for different centrality intervals.

The nuclear modification factor of photon-tagged jets as a function of jet $p_{\mathrm{T}}$ for different centrality intervals.

The $\Delta p_{\mathrm{T}}$ of photon-tagged jets as a function of jet $p_{\mathrm{T}}$.

The $R_{\mathrm{CP}}$ of photon-tagged jets as a function of jet $p_{\mathrm{T}}$.

Cutflow for two representative signal samples used in this analysis. The excited tau mass $m_{\tau^\ast} = 2.75$ TeV and the contact interaction scale $\Lambda=10$ TeV. The LQ mass $m_\mathrm{LQ} = 1.3$ TeV. The event yields include all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$.

Acceptance x efficiency of the $\tau^\ast$ signal SR selection

Acceptance x efficiency of the LQ signal SR selection

HFE (electrons from semileptonic decays of heavy-flavor hadrons) invariant yields in different centrality intervals of Au+Au collisions at $\sqrt{s_{\rm NN}}=200$ GeV. The vertical bars and the boxes represent statistical and systematic uncertainties, respectively. The horizontal bars indicate the bin width.

HFE (electrons from semileptonic decays of heavy-flavor hadrons) $R_{\rm AA}$ (red circles) as a function of $p_{\rm T}$ in different centrality intervals of Au+Au collisions at $\sqrt{s_{\rm NN}}=200$ GeV, compared with STAR (yellow stars) and PHENIX (green squares) published results, and Duke ((modified Langevin transport model, blue line) and PHSD (parton-hadron-string dynamics model, orange line) model calculations. Vertical bars and boxes around data points represent combined statistical and systematic uncertainties from both Au+Au and $p$+$p$ measurements, respectively. Boxes at unity show the global uncertainties, which for this analysis include the 8% global uncertainty on $p$+$p$ reference and the $N_{\rm coll}$ uncertainties. The left box is for PHENIX and the right one for STAR.

HFE (electrons from semileptonic decays of heavy-flavor hadrons) $R_{\rm AA}$ (red circles) as a function of $N_{\rm part}$ in Au+Au collisions at $\sqrt{s_{\rm NN}}=200$ GeV, compared with PHENIX measurements (green squares), and Duke (blue line) and PHSD (orange line) model calculations. Vertical bars and boxes around data points represent statistical and systematic uncertainties from Au+Au measurements, respectively. The gray band represents the $N_{\rm coll}$ uncertainties. The boxes at unity show the global uncertainties including the total uncertainties of the $p$+$p$ reference.

Comparison of the $m_{miss}$ shapes for the simulated signal events within the fiducial region and those outside it, after including the effect of PU protons as describe in the text, for a generated $m_{X}$ mass of 1000 GeV. The distributions are shown for single(+z)-single(−z) proton reconstruction categories.

Product of the acceptance times the combined reconstruction and identification efficiency, as a function of $m_{X}$ , for events generated inside the fiducial volume defined in Table 1. The curves shown panel display the different final states. The definition of the fiducial region and signal model used to estimate the acceptance is provided in the text.

Product of the acceptance times the combined reconstruction and identification efficiency, as a function of $m_{X}$ , for different proton reconstruction categories in the $Z \rightarrow \mu\mu $ analysis, and for events generated inside the fiducial volume defined in Table 1. The curves shown panel display the different final states. The definition of the fiducial region and signal model used to estimate the acceptance is provided in the text.

Distributions of the reconstructed proton $\xi$ in the negative arm from the proton mixing procedure with simulated MC events, are compared to data. The ee final states are shown.The ee events are displayed without the Z boson $p_T$ requirement.For illustration, the simulated signal distributions are superimposed for various choices of $m_{X}$ , normalised to a generated fiducial cross section of 100 pb.

Distributions of the reconstructed proton $\xi$ in the positive arm from the proton mixing procedure with simulated MC events, are compared to data. The ee final states are shown.The ee events are displayed without the Z boson $p_T$ requirement.For illustration, the simulated signal distributions are superimposed for various choices of $m_{X}$ , normalised to a generated fiducial cross section of 100 pb.

Distributions of the reconstructed di-proton rapidity from the proton mixing procedure with simulated MC events, are compared to data. The ee final states are shown.The ee events are displayed without the Z boson $p_T$ requirement.For illustration, the simulated signal distributions are superimposed for various choices of $m_{X}$ , normalised to a generated fiducial cross section of 100 pb.

Distributions of the reconstructed proton $\xi$ in the negative arm from the proton mixing procedure with simulated MC events, are compared to data. The $\mu\mu$ final states are shown.The $\mu\mu$ events are displayed without the Z boson $p_T$ requirement.For illustration, the simulated signal distributions are superimposed for various choices of $m_{X}$ , normalised to a generated fiducial cross section of 100 pb.

Distributions of the reconstructed proton $\xi$ in the positive arm from the proton mixing procedure with simulated MC events, are compared to data. The $\mu\mu$ final states are shown.The $\mu\mu$ events are displayed without the Z boson $p_T$ requirement.For illustration, the simulated signal distributions are superimposed for various choices of $m_{X}$ , normalised to a generated fiducial cross section of 100 pb.

Distributions of the reconstructed di-proton rapidity from the proton mixing procedure with simulated MC events, are compared to data. The $\mu\mu$ final states are shown.The $\mu\mu$ events are displayed without the Z boson $p_T$ requirement.For illustration, the simulated signal distributions are superimposed for various choices of $m_{X}$ , normalised to a generated fiducial cross section of 100 pb.

Distributions of the reconstructed proton $\xi$ in the negative arm from the proton mixing procedure with simulated MC events, are compared to data. The $\gamma$ final states are shown.For illustration, the simulated signal distributions are superimposed for various choices of $m_{X}$ , normalised to a generated fiducial cross section of 100 pb.

Distributions of the reconstructed proton $\xi$ in the positive arm from the proton mixing procedure with simulated MC events, are compared to data. The $\gamma$ final states are shown.For illustration, the simulated signal distributions are superimposed for various choices of $m_{X}$ , normalised to a generated fiducial cross section of 100 pb.

Distributions of the reconstructed di-proton rapidity from the proton mixing procedure with simulated MC events, are compared to data. The $\gamma$ final states are shown.For illustration, the simulated signal distributions are superimposed for various choices of $m_{X}$ , normalised to a generated fiducial cross section of 100 pb.

Validation of the background modelling method, using the $e\mu$ control sample. Selected $e\mu$ events are mixed with protons from $Z\rightarrow \mu \mu$ events with $p_{T}(Z)<10$ GeV to simulate the combinatorial background shape, while the data points are unaltered $e\mu$ events. The proton $\xi$ distribution for the positive CT-PPS arm is shown.

Validation of the background modelling method, using the $e\mu$ control sample. Selected $e\mu$ events are mixed with protons from $Z\rightarrow \mu \mu$ events with $p_{T}(Z)<10$ GeV to simulate the combinatorial background shape, while the data points are unaltered $e\mu$ events. The proton $\xi$ distribution for the negative CT-PPS arm is shown.

Validation of the background modelling method, using the $e\mu$ control sample. Selected $e\mu$ events are mixed with protons from $Z\rightarrow \mu \mu$ events with $p_{T}(Z)<10$ GeV to simulate the combinatorial background shape, while the data points are unaltered $e\mu$ events. The di-proton invariant mass is shown.

Validation of the background modelling method, using the $e\mu$ control sample. Selected $e\mu$ events are mixed with protons from $Z\rightarrow \mu \mu$ events with $p_{T}(Z)<10$ GeV to simulate the combinatorial background shape, while the data points are unaltered $e\mu$ events. The $m_{miss}$ is shown.

$m_{miss}$ distributions in the $pp\rightarrow ppZeeX$, with the protons reconstructed with the multi(+z)-multi(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 1 pb.

$m_{miss}$ distributions in the $pp\rightarrow ppZeeX$, with the protons reconstructed with the multi(+z)-single(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 1 pb.

$m_{miss}$ distributions in the $pp\rightarrow ppZeeX$, with the protons reconstructed with the single(+z)-multi(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 1 pb.

$m_{miss}$ distributions in the $pp\rightarrow ppZeeX$, with the protons reconstructed with the single(+z)-single(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 1 pb.

$m_{miss}$ distributions in the $pp\rightarrow ppZ\mu\mu X$, with the protons reconstructed with the multi(+z)-multi(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 1 pb.

$m_{miss}$ distributions in the $pp\rightarrow ppZ\mu\mu X$, with the protons reconstructed with the multi(+z)-single(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 1 pb.

$m_{miss}$ distributions in the $pp\rightarrow ppZ\mu\mu X$, with the protons reconstructed with the single(+z)-multi(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 1 pb.

$m_{miss}$ distributions in the $pp\rightarrow ppZ\mu\mu X$, with the protons reconstructed with the single(+z)-single(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 1 pb.

$m_{miss}$ distributions in the $pp\rightarrow pp\gamma X$, with the protons reconstructed with the multi(+z)-multi(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 10 pb.

$m_{miss}$ distributions in the $pp\rightarrow pp\gamma X$, with the protons reconstructed with the multi(+z)-single(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 10 pb.

$m_{miss}$ distributions in the $pp\rightarrow pp\gamma X$, with the protons reconstructed with the single(+z)-multi(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 10 pb.

$m_{miss}$ distributions in the $pp\rightarrow pp\gamma X$, with the protons reconstructed with the single(+z)-single(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 10 pb.

Upper limits on the $pp\rightarrow ppZ/\gamma X$ cross section at 95% CL, as a function of $m_X$. The 68 and 95% central intervals of the expected limits are represented by the green and yellow bands, respectively, while the observed limit is superimposed as a curve. The plot corresponds to the $Z\rightarrow ee$ analysis.

Upper limits on the $pp\rightarrow ppZ/\gamma X$ cross section at 95% CL, as a function of $m_X$. The 68 and 95% central intervals of the expected limits are represented by the green and yellow bands, respectively, while the observed limit is superimposed as a curve. The plot corresponds to the $Z\rightarrow \mu\mu$ analysis.

Upper limits on the $pp\rightarrow ppZ/\gamma X$ cross section at 95% CL, as a function of $m_X$. The 68 and 95% central intervals of the expected limits are represented by the green and yellow bands, respectively, while the observed limit is superimposed as a curve. The plot corresponds to the $Z$ analysis.

Upper limits on the $pp\rightarrow ppZ/\gamma X$ cross section at 95% CL, as a function of $m_X$. The 68 and 95% central intervals of the expected limits are represented by the green and yellow bands, respectively, while the observed limit is superimposed as a curve. The plot corresponds to the $\gamma$ analysis.