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 $W_{\gamma \mathrm{N}}^{\mathrm{Pb}}$.

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.

The distribution of the BDT discriminants for the full 2016--2018 data set in the all-hadronic channel. The sample VR category shown is defined by $N_\textrm{RT} \geq 2$, $H_T > 1100$ GeV. The background from QCD multijet and $\textrm{t}\bar{\textrm{t}}$ production is derived from control regions in the data. Estimates for the $\textrm{t}\bar{\textrm{t}}\textrm{t}\bar{\textrm{t}}$ signal and other backgrounds are shown using simulated samples. The hatched bands correspond to the estimated total uncertainty.

The distribution of the BDT discriminants for the full 2016--2018 data set in the all-hadronic channel. The SR category shown in this figure is defined by $N_\textrm{RT}=1$, $N_\textrm{BT} \geq 1$, $H_T > 1400$ GeV. The background from QCD multijet and $\textrm{t}\bar{\textrm{t}}$ production is derived from control regions in the data. Estimates for the $\textrm{t}\bar{\textrm{t}}\textrm{t}\bar{\textrm{t}}$ signal and other backgrounds are shown using simulated samples. The hatched bands correspond to the estimated total uncertainty after the fit.

The distribution of the BDT discriminants for the full 2016--2018 data set in the all-hadronic channel. The SR category shown in this figure is defined by $N_\textrm{RT} = 2$, $H_T > 1100$ GeV. The background from QCD multijet and $\textrm{t}\bar{\textrm{t}}$ production is derived from control regions in the data. Estimates for the $\textrm{t}\bar{\textrm{t}}\textrm{t}\bar{\textrm{t}}$ signal and other backgrounds are shown using simulated samples. The hatched bands correspond to the estimated total uncertainty after the fit.

Expected and observed significance (in standard deviations) for $\textrm{t}\bar{\textrm{t}}\textrm{t}\bar{\textrm{t}}$ production from each final state and the combination with previous CMS results (EPJC 80 (2020) 75 and JHEP 11 (2019) 082). The same-sign dilepton and multilepton (SSDL\&ML) final state results are from EPJC 80 (2020) 75.

Measured signal strength ($\mu = \sigma_{\textrm{t}\bar{\textrm{t}}\textrm{t}\bar{\textrm{t}}}/ \sigma_{\textrm{t}\bar{\textrm{t}}\textrm{t}\bar{\textrm{t}}} ^{\textrm{SM}}$), corresponding cross section (in fb), and the expected and observed significance (in standard deviations) for $\textrm{t}\bar{\textrm{t}}\textrm{t}\bar{\textrm{t}}$ production from all analysis channels. This table shows production from each analysis channel in this Letter, the combination of those channels, the results from previously published results, and the full combination of all CMS 2016-2018 results.

Observed and expected 95% CL upper limits on ${{(\sigma_{\text{H}}/\sigma_{\text{H}}^{\mathrm{SM}}) \times {{\mathcal{B}(\text{H} \to \text{inv})}}}}$ for the combined VBF, ttH, VH and ggH channels using all available CMS data for 2016--2018, Run1, 2015, and their combination, assuming a SM Higgs boson with a mass of 125 GeV.

Observed and expected 95% CL upper limits on ${{(\sigma_{\text{H}}/\sigma_{\text{H}}^{\mathrm{SM}}) \times {{\mathcal{B}(\text{H} \to \text{inv})}}}}$ for the VBF, ttH(lep), ttH(had), V(qq)H, Z(ll)H, Z(bb)H and ggH channels using all available CMS data, and their combination, assuming a SM Higgs boson with a mass of 125 GeV.

The 90% CL upper limits on the spin-independent DM-nucleon scattering cross section in Higgs-portal models, assuming a scalar, fermionic or vectorial DM candidate (with a UV-complete vector model), compared to direct detection experimets CRESST-III, DarkSide-50, LUX_ZEPLIN and PandaX-4T (2022 results).

Postfit event yields in each category and hadronic recoil bin of the ttH category SR for the different background and signal processes summed across 2016, 2017 and 2018 samples. The background and signal yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR or CR-only. The Postfit signal contributions for a Higgs boson, produced in ttH, VH (split into WH and ZH), ggH and VBF, decaying to invisible particles with a branching fraction of $\mathcal{B}(\text{H} \to \text{inv}) = 1$, and the observed event yields are reported.

Postfit event yields in each category and hadronic recoil bin of the VH category SR for the different background and signal processes summed across 2016, 2017 and 2018 samples. The background and signal yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR or CR-only. The Postfit signal contributions for a Higgs boson, produced in ttH, VH (split into WH and ZH), ggH and VBF, decaying to invisible particles with a branching fraction of $\mathcal{B}(\text{H} \to \text{inv}) = 1$, and the observed event yields are reported.

Postfit event yields in each category and $p\mathrm{_{T}^{miss}}$ bin of the ttH category e$+$jets CR for the different background processes summed across 2016, 2017 and 2018 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR or CR-only.

Postfit event yields in each category and $p\mathrm{_{T}^{miss}}$ bin of the VH category e$+$jets CR for the different background processes summed across 2016, 2017 and 2018 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR or CR-only.

Postfit event yields in each category and $p\mathrm{_{T}^{miss}}$ bin of the ttH category $\mu+$jets CR for the different background processes summed across 2016, 2017 and 2018 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR or CR-only.

Postfit event yields in each category and $p\mathrm{_{T}^{miss}}$ bin of the VH category $\mu+$jets CR for the different background processes summed across 2016, 2017 and 2018 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR or CR-only.

Postfit event yields in each category and $p\mathrm{_{T}^{miss}}$ bin of the ttH category ee$+$jets, $\mu\mu+$jets, and $\ell\ell+$jets CRs for the different background processes summed across 2016, 2017 and 2018 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR or CR-only.

Postfit event yields in each category and $p\mathrm{_{T}^{miss}}$ bin of the VH category ee$+$jets, $\mu\mu+$jets, and $\gamma+$jets CRs for the different background processes summed across 2016, 2017 and 2018 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR or CR-only.

The expected (dotted black) and observed (solid black) upper limits at 95% CL on $\sigma_{T^\prime bq(T^\prime \rightarrow tH)}$ in the hadronic channel displayed as a function of $\rm{M}_{T^\prime}$. The green (yellow) band represents the 68% (95%) of the limit values expected under the background-only hypothesis. The theoretical cross sections for the singlet $T^\prime$ production with representative $\kappa_T$-values fixed at 0.1, 0.15, 0.2 and 0.25 (for $\Gamma/\rm{M}_{T^\prime} < 5\%$) are shown as solid red lines.

Selection of the hadronic signal region for the three BDTs and $\rm{M}_{T^\prime}$ windows.

Selection of the leptonic signal region for the three BDTs and $\rm{M}_{T^\prime}$ windows.

The expected yields of different processes in each signal window for events with a $T^{\prime}$ with mass in the range $\rm{M}_{T^\prime} \in [600, 1200]$ GeV, and the observed number of events in the signal region $m_{\gamma\gamma} \in [115, 135]$. Here, the yields for the $T^\prime$ are for $\kappa_{T}$ fixed at 0.2.

Signal efficiency for the hadronic channel (left) and the leptonic channel (right) in the signal regions as optimized for each of the three different $\rm{M}_{T^\prime}$ ranges, [600, 700], [700, 1000] and [1000, 1200] GeV, represented as red, green and blue curves respectively. The efficiency is defined as the ratio of the events after the final selection to the total expected events.

Reconstruction level differential cross section spectla, obtained for the central acceptance, $|\eta| < 3$, for events with Pomeron-Proton ($\mathrm{I\!P}\mathrm{p} + \gamma \mathrm{p}$) topology compared to the to the EPOS-LHC predictions, broken down into the non-diffractive (ND), central diffractive (CD), single diffractive (SD) and double diffractive (DD) components. Forward Rapidity Gap definition: $|\eta| < 2.5$: $p_{T}^{track} < 200$ MeV and $\sum \limits_{bin} E^{PF} < 6$ GeV $|\eta| \in [2.5,3.0]$: $\sum \limits_{bin} E_{neutral}^{PF} < 13.4$ GeV

The number of high purity tracksin the first $\eta$ bin after a gap of $4.5 \leq \Delta\eta^F < 5.0$ for events with the Pomeron-Proton ($\mathrm{I\!P}\mathrm{p} + \gamma \mathrm{p}$) topology Forward Rapidity Gap definition: $|\eta| < 2.5$: $p_{T}^{track} < 200$ MeV and $\sum \limits_{bin} E^{PF} < 6$ GeV $|\eta| \in [2.5,3.0]$: $\sum \limits_{bin} E_{neutral}^{PF} < 13.4$ GeV

The transeverse momentum of high purity tracksin the first $\eta$ bin after a gap of $4.5 \leq \Delta\eta^F < 5.0$ for events with the Pomeron-Proton ($\mathrm{I\!P}\mathrm{p} + \gamma \mathrm{p}$) topology Forward Rapidity Gap definition: $|\eta| < 2.5$: $p_{T}^{track} < 200$ MeV and $\sum \limits_{bin} E^{PF} < 6$ GeV $|\eta| \in [2.5,3.0]$: $\sum \limits_{bin} E_{neutral}^{PF} < 13.4$ GeV

The total energy of all Particle Flow candidatesin the first $\eta$ bin after a gap of $4.5 \leq \Delta\eta^F < 5.0$ for events with the Pomeron-Proton ($\mathrm{I\!P}\mathrm{p} + \gamma \mathrm{p}$) topology Forward Rapidity Gap definition: $|\eta| < 2.5$: $p_{T}^{track} < 200$ MeV and $\sum \limits_{bin} E^{PF} < 6$ GeV $|\eta| \in [2.5,3.0]$: $\sum \limits_{bin} E_{neutral}^{PF} < 13.4$ GeV

Unfolded diffraction enhanced differential cross section for events with Pomeron-Lead ($\mathrm{I\!P}\mathrm{Pb}$) topology, defined on the region $|\eta| < 5.2$, compared to hadron level predictions of the MC generators. The data are corrected for the contribution from events with undetectable energy in the HF calorimeter adjacent to the rapidity gap. The corrections are obtained using the EPOS-LHC MC sample. Forward Rapidity Gap definition: $|\eta| < 2.5$: $p_{T}^{track} < 200$ MeV and $\sum \limits_{bin} E^{PF} < 6$ GeV $|\eta| \in [2.5,3.0]$: $\sum \limits_{bin} E_{neutral}^{PF} < 13.4$ GeV $|\eta| > 3.0$: No particles

Unfolded diffraction enhanced differential cross section for events with Pomeron-Proton ($\mathrm{I\!P}\mathrm{p} + \gamma \mathrm{p}$) topology, defined on the region $|\eta| < 5.2$, compared to hadron level predictions of the MC generators. The data are corrected for the contribution from events with undetectable energy in the HF calorimeter adjacent to the rapidity gap. The corrections are obtained using the EPOS-LHC MC sample. Forward Rapidity Gap definition: $|\eta| < 2.5$: $p_{T}^{track} < 200$ MeV and $\sum \limits_{bin} E^{PF} < 6$ GeV $|\eta| \in [2.5,3.0]$: $\sum \limits_{bin} E_{neutral}^{PF} < 13.4$ GeV $|\eta| > 3.0$: No particles

Unfolded diffractive enhanced differential cross section spectla for events with Pomeron-Lead ($\mathrm{I\!P}\mathrm{Pb}$) topology, compared to the to the hadron-level EPOS-LHC predictions, broken down into the non-diffractive (ND), central diffractive (CD), single diffractive (SD) and double diffractive (DD) components. Forward Rapidity Gap definition: $|\eta| < 2.5$: $p_{T}^{track} < 200$ MeV and $\sum \limits_{bin} E^{PF} < 6$ GeV $|\eta| \in [2.5,3.0]$: $\sum \limits_{bin} E_{neutral}^{PF} < 13.4$ GeV $|\eta| > 3.0$: No particles

Unfolded diffractive enhanced differential cross section spectla for events with Pomeron-Proton ($\mathrm{I\!P}\mathrm{p} + \gamma \mathrm{p}$) topology, compared to the to the hadron-level EPOS-LHC predictions, broken down into the non-diffractive (ND), central diffractive (CD), single diffractive (SD) and double diffractive (DD) components. Forward Rapidity Gap definition: $|\eta| < 2.5$: $p_{T}^{track} < 200$ MeV and $\sum \limits_{bin} E^{PF} < 6$ GeV $|\eta| \in [2.5,3.0]$: $\sum \limits_{bin} E_{neutral}^{PF} < 13.4$ GeV $|\eta| > 3.0$: No particles

Unfolded diffractive enhanced differential cross section spectla for events with Pomeron-Lead ($\mathrm{I\!P}\mathrm{Pb}$) topology, compared to the to the hadron-level QGSJET II predictions, broken down into the non-diffractive (ND), central diffractive (CD), single diffractive (SD) and double diffractive (DD) components. Forward Rapidity Gap definition: $|\eta| < 2.5$: $p_{T}^{track} < 200$ MeV and $\sum \limits_{bin} E^{PF} < 6$ GeV $|\eta| \in [2.5,3.0]$: $\sum \limits_{bin} E_{neutral}^{PF} < 13.4$ GeV $|\eta| > 3.0$: No particles

Unfolded diffractive enhanced differential cross section spectla for events with Pomeron-Proton ($\mathrm{I\!P}\mathrm{p} + \gamma \mathrm{p}$) topology, compared to the to the hadron-level QGSJET II predictions, broken down into the non-diffractive (ND), central diffractive (CD), single diffractive (SD) and double diffractive (DD) components. Forward Rapidity Gap definition: $|\eta| < 2.5$: $p_{T}^{track} < 200$ MeV and $\sum \limits_{bin} E^{PF} < 6$ GeV $|\eta| \in [2.5,3.0]$: $\sum \limits_{bin} E_{neutral}^{PF} < 13.4$ GeV $|\eta| > 3.0$: No particles

Reconstruction level diffraction enhanced differential cross section spectrum for Pomeron-Proton ($\mathrm{I\!P}\mathrm{p} + \gamma \mathrm{p}$) topology corrected for the contribution from events with undetectable energy in the HF calorimeter adjacent to the rapidity gap, compared with the spectrum obtained with events satisfying the ZDC veto requirement $E_{ZDC−} < 1 \mathrm{~TeV}$ which selects only the events without lead nuclear break up (without correction for HF undetectable energy). Forward Rapidity Gap definition: $|\eta| < 2.5$: $p_{T}^{track} < 200$ MeV and $\sum \limits_{bin} E^{PF} < 6$ GeV $|\eta| \in [2.5,3.0]$: $\sum \limits_{bin} E_{neutral}^{PF} < 13.4$ GeV $|\eta| > 3.0$: No particles

$K^{0}_{S} K^{0}_{S}$ correlation meassurement in $10-20\%$ centrality.

$K^{0}_{S} K^{0}_{S}$ correlation meassurement in $20-30\%$ centrality.

$K^{0}_{S} K^{0}_{S}$ correlation meassurement in $30-40\%$ centrality.

$K^{0}_{S} K^{0}_{S}$ correlation meassurement in $40-50\%$ centrality.

$K^{0}_{S} K^{0}_{S}$ correlation meassurement in $50-60\%$ centrality.

$\Lambda K^{0}_{S} \oplus \overline{\Lambda} K^{0}_{S}$ correlation meassurement in $0-80\%$ centrality.

$\Lambda\Lambda\oplus\overline{\Lambda}\overline{\Lambda}$ correlation meassurement in $0-80\%$ centrality.

The extracted $R_{inv}$ from $K^{0}_{S} K^{0}_{S}$ correlations as a function of centrality.

The extracted $\lambda$ parameters from $K^{0}_{S} K^{0}_{S}$ correlations as a function of centrality.

Extracted effective range ($d_{0}$) and real components of the complex scattering length ($\Re f_{0}$) from the $\Lambda\Lambda\oplus\overline{\Lambda}\overline{\Lambda}$ and $\Lambda K^{0}_{S} \oplus \overline{\Lambda} K^{0}_{S}$ correlations.

Extracted imaginary components of the complex scattering length ($\Im f_{0}$) and real components of the complex scattering length ($\Re f_{0}$) from the $\Lambda K^{0}_{S} \oplus \overline{\Lambda} K^{0}_{S}$ correlation.

Electron $p_{T}$ distribution using 2016-2018 data sets. The complete set of selection criteria were applied. Two examples of SSM WPRIME boson signal samples with masses of 3.8 and 5.6 TeV are shown. The lower panel shows the ratio of data to SM prediction, and the shaded band represents the systematic uncertainties.

$p_{T}^{miss}$ distribution in the electron channel using 2016-2018 data sets. The complete set of selection criteria were applied. Two examples of SSM WPRIME boson signal samples with masses of 3.8 and 5.6 TeV are shown. The lower panel shows the ratio of data to SM prediction, and the shaded band represents the systematic uncertainties.

Muon $p_T$ distribution using 2016-2018 data sets. The complete set of selection criteria were applied. Two examples of SSM WPRIME boson signal samples with masses of 3.8 and 5.6 TeV are shown. The lower panel shows the ratio of data to SM prediction, and the shaded band represents the systematic uncertainties.

$p_T^{miss}$ distribution in the muon channel using 2016-2018 data sets. The complete set of selection criteria were applied. Two examples of SSM WPRIME boson signal samples with masses of 3.8 and 5.6 TeV are shown. The lower panel shows the ratio of data to SM prediction, and the shaded band represents the systematic uncertainties.

$M_T$ distribution for the E+INVISIBLE system using 2016-2018 data sets. The complete set of selection criteria were applied. Two examples of SSM WPRIME boson signal samples with masses of 3.8 and 5.6 TeV are shown. The lower panel shows the ratio of data to SM prediction, and the shaded band represents the systematic uncertainties.

$M_T$ distribution for the MU+INVISIBLE system using 2016-2018 data sets. The complete set of selection criteria were applied. Two examples of SSM WPRIME boson signal samples with masses of 3.8 and 5.6 TeV are shown. The lower panel shows the ratio of data to SM prediction, and the shaded band represents the systematic uncertainties.

Theoretical prediction for the production and decay cross-section of SSM WPRIME bosons (W --> LEPTON + NU) as a function of the WPRIME mass, for the range 200-6400 GeV and inclusive in phase-space (no cuts). The uncertainty shown covers PDF and ALPHAS uncertainties. These theoretical predictions are obtained with PYTHIA (LO) and corrected to NNLO in QCD using FEWZ program.

Observed (solid line) and expected (dashed line) upper limits at 95% CL on the product of WPRIME cross-section production and BF(WPRIME --> LEPTON + NU) for an SSM WPRIME boson, as a function of the boson mass, for the electron decay channel. The shaded bands represent the one (green) and two (yellow) standard deviation uncertainty bands for the expected limits. The theoretical predictions for the SSM at NNLO precision in QCD are shown with narrow gray bands corresponding to the PDF and ALPHAS uncertainties.

Observed (solid line) and expected (dashed line) upper limits at 95% CL on the product of WPRIME cross-section production and BF(WPRIME --> LEPTON + NU) for an SSM WPRIME boson, as a function of the boson mass, for the muon decay channel. The shaded bands represent the one (green) and two (yellow) standard deviation uncertainty bands for the expected limits. The theoretical predictions for the SSM at NNLO precision in QCD are shown with narrow gray bands corresponding to the PDF and ALPHAS uncertainties.

Observed (solid line) and expected (dashed line) upper limits at 95% CL on the product of WPRIME cross-section production and BF(WPRIME --> LEPTON + NU) for an SSM WPRIME boson, as a function of the boson mass, for the combined electron and muon decay channels. The shaded bands represent the one (green) and two (yellow) standard deviation uncertainty bands for the expected limits. The theoretical predictions for the SSM at NNLO precision in QCD are shown with narrow gray bands corresponding to the PDF and ALPHAS uncertainties.

The 95% CL observed (solid line) and expected (dashed line) model independent cross section upper limits as function of the $MT_{min}$ threshold, for the electron decay channel. The shaded bands represent the one (green) and two (yellow) standard deviation uncertainty bands for the expected limits.

The 95% CL observed (solid line) and expected (dashed line) model independent cross section upper limits as function of the $MT_{min}$ threshold, for the muon decay channel. The shaded bands represent the one (green) and two (yellow) standard deviation uncertainty bands for the expected limits.

The 95% CL observed (solid line) and expected (dashed line) model independent cross section upper limits as function of the $MT_{min}$ threshold, for the combined electron and muon decay channels. The shaded bands represent the one (green) and two (yellow) standard deviation uncertainty bands for the expected limits.

Observed (solid line) and expected (dashed line) upper limits at 95% CL on the coupling strength ratio, gWprime/gW as a function of the mass of the WPRIME boson, for the electron channel. The one (green) and two (yellow) standard deviation uncertainty bands for the expected limits are shown. The area above the limit curve is excluded. The dotted line represents the case of SSM coupling, gWprime, being equal to gW, the SM coupling.

Observed (solid line) and expected (dashed line) upper limits at 95% CL on the coupling strength ratio, gWprime/gW, as a function of the mass of the WPRIME boson, for the muon channel. The one (green) and two (yellow) standard deviation uncertainty bands for the expected limits are shown. The area above the limit curve is excluded. The dotted line represents the case of SSM coupling, gWprime , being equal to gW, the SM coupling.

Exclusion limits in the 2D plane (1/R, $\mu$) for the split-UED interpretation for the n = 2 case, for the electron channel for the 2016-2018 data sets. R is the radius of the additional spatial dimension and $\mu$ the bulk mass for the fermion field in five dimensions. The expected limit is depicted as a black dashed line. The one (green) and two (yellow) standard deviation uncertainty bands for the expected limits are shown. The experimentally excluded region is the entire area to the left of the solid black line.

Exclusion limits in the 2D plane (1/R, $\mu$) for the split-UED interpretation for the n = 2 case, for the muon channel for the 2016-2018 data sets. R is the radius of the additional spatial dimension and $\mu$ the bulk mass for the fermion field in five dimensions. The expected limit is depicted as a black dashed line. The one (green) and two (yellow) standard deviation uncertainty bands for the expected limits are shown. The experimentally excluded region is the entire area to the left of the solid black line.

Exclusion limits in the 2D plane (1/R, $\mu$) for the split-UED interpretation for the n = 2 case, for the combined electron and muon channels for the 2016-2018 data sets. R is the radius of the additional spatial dimension and $\mu$ the bulk mass for the fermion field in five dimensions. The expected limit is depicted as a black dashed line. The one (green) and two (yellow) standard deviation uncertainty bands for the expected limits are shown. The experimentally excluded region is the entire area to the left of the solid black line.

Observed (solid line) and expected (dashed line) upper limits at 95% CL on the ${\lambda}_{231}$ coupling in the RPV SUSY model with a STAU mediator, as a function of the mass of STAU, for the electron channel and for the production coupling, ${\lambda}^{'}_{3ij}$=0.5 . The couplings ${\lambda}^{'}_{3ij}$, ${\lambda}_{231}$, and ${\lambda}_{132}$ are defined in Fig. 1. The one (green) and two (yellow) standard deviation uncertainty bands for the expected limits are shown. The area above the limit curve is excluded. Limits for other values of ${\lambda}^{'}_{3ij}$ are obtained multiplying the ones shown by the ratio ${\lambda}^{'}_{3ij}$/0.5

Observed (solid line) and expected (dashed line) upper limits at 95% CL on the ${\lambda}_{132}$ coupling in the RPV SUSY model with a stau mediator, as a function of the mass of the stau, for the muon channel and for the production coupling, ${\lambda}^{'}_{3ij}$ = 0.5 . The couplings ${\lambda}^{'}_{3ij}$, ${\lambda}_{231}$, and ${\lambda}_{132}$ are defined in Fig. 1. The one (green) and two (yellow) standard deviation uncertainty bands for the expected limits are shown. The area above the limit curve is excluded. Limits for other values of ${\lambda}^{'}_{3ij}$ are obtained multiplying these ones by the ratio ${\lambda}^{'}_{3ij}$/0.5

Region in the oblique (W,Y) parameter phase space allowed by the current analysis at 95% CL. The combination of the electron and muon channel distributions from the 2017 and 2018 data sets at sqrt(s) = 13 TeV is used, having 101 fb-1 of luminosity.

Negative Log-Likelihood for the determination of the oblique W parameter, for the combination of the electron and muon channel and for 2017 and 2018 data sets (L=101 fb-1) at sqrt(s) = 13 TeV.

Total background estimate and observed data in all bins used in the limit calculation for the SSM WPRIME limits. The total event sample is split into the three years of data taking and the two lepton flavors.The distributions being shown are $M_T$ ones. The associated integrated luminosities for each year are of 35.9, 41.5, and 59.4 fb$̣^{-1}. The mass bins are numbered in ascending order.