Observed and expected 95% credibility-level upper limits on the cross-section times branching ratio for the simplified dark-matter model. The table also shows the corresponding $1\sigma$ and $2\sigma$ bands for the expected limits. The limits are calculated using jets in events with at least one isolated lepton ($e$ or $\mu$) with $p_\text{T}^\ell \ge 60$ GeV.

The 95% CL upper limits on the cross-section times acceptance times efficiency times branching ratio, as a function of the resonance mass, $m_X$. The limits are calculated using jets in events with at least one isolated lepton ($e$ or $\mu$) with $p_\text{T}^\ell \ge 60$ GeV. The limits are shown for a generic Gaussian signal with the width $\sigma_{X}/m_{X} =0$. The table also shows the expected limits and the corresponding $1\sigma$ and $2\sigma$ bands. The tabulated data has been used in Figure 04 of the publication.

The 95% CL upper limits on the cross-section times acceptance times efficiency times branching ratio, as a function of the resonance mass, $m_X$. The limits are calculated using jets in events with at least one isolated lepton ($e$ or $\mu$) with $p_\text{T}^\ell \ge 60$ GeV. The limits are shown for a generic Gaussian signal with the width $\sigma_{X}/m_{X} =0.05$. The table also shows the expected limits and the corresponding $1\sigma$ and $2\sigma$ bands. The tabulated data has been used in Figure 04 of the publication.

The 95% CL upper limits on the cross-section times acceptance times efficiency times branching ratio, as a function of the resonance mass, $m_X$. The limits are calculated using jets in events with at least one isolated lepton ($e$ or $\mu$) with $p_\text{T}^\ell \ge 60$ GeV. The limits are shown for a generic Gaussian signal with the width $\sigma_{X}/m_{X} =0.10$. The table also shows the expected limits and the corresponding $1\sigma$ and $2\sigma$ bands. The tabulated data has been used in Figure 04 of the publication.

The 95% CL upper limits on the cross-section times acceptance times efficiency times branching ratio, as a function of the resonance mass, $m_X$. The limits are calculated using jets in events with at least one isolated lepton ($e$ or $\mu$) with $p_\text{T}^\ell \ge 60$ GeV. The limits are shown for a generic Gaussian signal with the width $\sigma_{X}/m_{X} =0.15$. The table also shows the expected limits and the corresponding $1\sigma$ and $2\sigma$ bands. The tabulated data has been used in Figure 04 of the publication.

Truth-level cross-sections ($\sigma$), acceptances ($A$), detector efficiencies ($\epsilon$) and the detector-level visible cross-sections ($\sigma^{vis}$) for different masses of the $\rho_T$ model. Only statistical uncertainties on the acceptances and efficiencies are shown. The acceptance is defined by requiring jets with $m_{jj} >216$ GeV and $|\eta|<2.4$, as well as isolated leptons ($e$ or $\mu$) with $p_\text{T}^\ell \ge 60$ GeV and $|\eta^\mu|<2.5$ ($|\eta^e|<2.47$, excluding of the gap region 1.37--1.52) for muons (electrons). The tabulated data has been used in Figure 05a of the publication.

Truth-level cross-sections ($\sigma$), acceptances ($A$), detector efficiencies ($\epsilon$) and the detector-level visible cross-sections ($\sigma^{vis}$) for different masses of the $W'/Z'$ SSM model. Only statistical uncertainties on the acceptances and efficiencies are shown. The acceptance is defined by requiring jets with $m_{jj} >216$ GeV and $|\eta|<2.4$, as well as leptons with $p_\text{T}^\ell \ge 60$ GeV and $|\eta^\mu|<2.5$ ($|\eta^e|<2.47$ with exclusion of the gap region 1.37-1.52) for muons (electrons). The tabulated data has been used in Figure 05b of the publication.

Truth-level cross-sections ($\sigma$), acceptances ($A$), detector efficiencies ($\epsilon$) and the detector-level visible cross-sections ($\sigma^{vis}$) for different masses of the $H^+$ model for $\tan \beta=1$. Only statistical uncertainties on the acceptances and efficiencies are shown. The acceptance correction was calculated assuming $\tan \beta=1$ and the narrow-width approximation. The acceptance is defined by requiring jets with $m_{jj} >216$ GeV and $|\eta|<2.4$, as well as leptons with $p_\text{T}^\ell \ge 60$ GeV and $|\eta^\mu|<2.5$ ($|\eta^e|<2.47$ with exclusion of the gap region 1.37-1.52) for muons (electrons). The tabulated data has been used in Figure 05c of the publication.

Truth-level cross-sections ($\sigma$), acceptances ($A$), detector efficiencies ($\epsilon$) and the detector-level visible cross-sections ($\sigma^{vis}$) for different masses of the $Z'$ (DM) model. Only statistical uncertainties on the acceptances and efficiencies are shown. The acceptance is defined by requiring jets with $m_{jj} > 216$ GeV and $|\eta|<2.4$, as well as leptons with $p_\text{T}^\ell \ge 60$ GeV and $|\eta^\mu|<2.5$ ($|\eta^e|<2.47$ with exclusion of the gap region 1.37-1.52) for muons (electrons). The tabulated data has been used in Figure 05d of the publication.

Efficiency and N2LO volume-corrected proton cumulant ratio $K_4/K_2$ plotted as a function of the rapidity acceptance

Efficiency and N2LO volume-corrected proton cumulant ratio $K_2/K_1$ plotted as a function of the mean number of participants $<N_{part}>$ for two rapidity acceptances

Efficiency and N2LO volume-corrected proton cumulant ratio $K_3/K_2$ plotted as a function of the mean number of participants $<N_{part}>$ for two rapidity acceptances

Efficiency and N2LO volume-corrected proton cumulant ratio $K_4/K_2$ plotted as a function of the mean number of participants $<N_{part}>$ for two rapidity acceptances

Efficiency and N2LO volume-corrected proton cumulant $K_2$ plotted as a function of $\Delta y$

Efficiency and N2LO volume-corrected proton cumulant $K_3$ plotted as a function of $\Delta y$

Efficiency and N2LO volume-corrected proton cumulant $K_4$ plotted as a function of $\Delta y$

Efficiency and N2LO volume-corrected proton correlator $C_3$ plotted as a function of $\Delta y$

Efficiency and N2LO volume-corrected proton correlator $C_4$ plotted as a function of $\Delta y$

Efficiency and N2LO volume-corrected proton correlator $C_2$ plotted as a function of maximum $p_t$

Efficiency and N2LO volume-corrected proton correlator $C_3$ plotted as a function of maximum $p_t$

Efficiency and N2LO volume-corrected proton correlator $C_4$ plotted as a function of maximum $p_t$

Efficiency and N2LO volume-corrected proton correlator $C_2$ plotted as a function of the mean number of protons.

Efficiency and N2LO volume-corrected proton correlator $C_3$ plotted as a function of the mean number of protons.

Efficiency and N2LO volume-corrected proton correlator $C_4$ plotted as a function of the mean number of protons.

Efficiency and N2LO volume-corrected proton cumulant ratio $K_3/K_2$ plotted as a function of the center-of-mass energy for two centrality bins (0-10% and 30-40%).

Efficiency and N2LO volume-corrected proton cumulant ratio $K_4/K_2$ plotted as a function of the center-of-mass energy for two centrality bins (0-10% and 30-40%).

Post-fit BDT distributions after the VBF event selection for the $\tau_{\mathrm{had}}\tau_{\mathrm{had}}$ analysis channel. The VBF signal is shown for $\mu = 0.73$ and $\tilde d = -0.01$. ''Other bkg'' denotes all background contributions not listed explicitly in the legend. The size of the combined statistical, experimental, and theoretical uncertainties is given.

Post-fit $m_{\tau\tau}^{\mathrm{MMC}}$ distributions in the low BDT score CR for the $\tau_{\mathrm{lep}}\tau_{\mathrm{lep}}$ SF analysis channel. ''Other bkg'' denotes all background contributions not listed explicitly in the legend. The size of the combined statistical, experimental, and theoretical uncertainties is given. The exact value of the $p_{\mathrm{T}}$ cut on the leptons depends on the trigger.

Post-fit $m_{\tau\tau}^{\mathrm{MMC}}$ distributions in the low BDT score CR for the $\tau_{\mathrm{lep}}\tau_{\mathrm{lep}}$ DF analysis channel. ''Other bkg'' denotes all background contributions not listed explicitly in the legend. The size of the combined statistical, experimental, and theoretical uncertainties is given.

Post-fit $m_{\tau\tau}^{\mathrm{MMC}}$ distributions in the low BDT score CR for the $\tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ analysis channel. ''Other bkg'' denotes all background contributions not listed explicitly in the legend. The size of the combined statistical, experimental, and theoretical uncertainties is given. The exact value of the $p_{\mathrm{T}}$ cut on the leading lepton depends on the trigger.

Post-fit $m_{\tau\tau}^{\mathrm{MMC}}$ distributions in the low BDT score CR for the $\tau_{\mathrm{had}}\tau_{\mathrm{had}}$ analysis channel. ''Other bkg'' denotes all background contributions not listed explicitly in the legend. The size of the combined statistical, experimental, and theoretical uncertainties is given.

Post-fit Optimal Observable distributions in the low BDT score CR for the $\tau_{\mathrm{lep}}\tau_{\mathrm{lep}}$ SF analysis channel. ''Other bkg'' denotes all background contributions not listed explicitly in the legend. The size of the combined statistical, experimental, and theoretical uncertainties is given. The exact value of the $p_{\mathrm{T}}$ cut on the leptons depends on the trigger.

Post-fit Optimal Observable distributions in the low BDT score CR for the $\tau_{\mathrm{lep}}\tau_{\mathrm{lep}}$ DF analysis channel. ''Other bkg'' denotes all background contributions not listed explicitly in the legend. The size of the combined statistical, experimental, and theoretical uncertainties is given.

Post-fit Optimal Observable distributions in the low BDT score CR for the $\tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ analysis channel. ''Other bkg'' denotes all background contributions not listed explicitly in the legend. The size of the combined statistical, experimental, and theoretical uncertainties is given. The exact value of the $p_{\mathrm{T}}$ cut on the leading lepton depends on the trigger.

Post-fit Optimal Observable distributions in the low BDT score CR for the $\tau_{\mathrm{had}}\tau_{\mathrm{had}}$ analysis channel. ''Other bkg'' denotes all background contributions not listed explicitly in the legend. The size of the combined statistical, experimental, and theoretical uncertainties is given.

Post-fit distributions of the event yields as a function of the Optimal Observable in the SR for the $\tau_{\mathrm{lep}}\tau_{\mathrm{lep}}$ SF analysis channel. The values of $\tilde d$, the signal strength $\mu$, the normalization of background processes, and nuisance parameters for the event yield prediction are set to those which minimize the NLL. The size of the combined statistical, experimental and theoretical uncertainties is given.

Post-fit distributions of the event yields as a function of the Optimal Observable in the SR for the $\tau_{\mathrm{lep}}\tau_{\mathrm{lep}}$ DF analysis channel. The values of $\tilde d$, the signal strength $\mu$, the normalization of background processes, and nuisance parameters for the event yield prediction are set to those which minimize the NLL. The size of the combined statistical, experimental and theoretical uncertainties is given.

Post-fit distributions of the event yields as a function of the Optimal Observable in the SR for the $\tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ analysis channel. The values of $\tilde d$, the signal strength $\mu$, the normalization of background processes, and nuisance parameters for the event yield prediction are set to those which minimize the NLL. The size of the combined statistical, experimental and theoretical uncertainties is given. The exact value of the $p_{\mathrm{T}}$ cut on the leading lepton depends on the trigger.

Post-fit distributions of the event yields as a function of the Optimal Observable in the SR for the $\tau_{\mathrm{had}}\tau_{\mathrm{had}}$ analysis channel. The values of $\tilde d$, the signal strength $\mu$, the normalization of background processes, and nuisance parameters for the event yield prediction are set to those which minimize the NLL. The size of the combined statistical, experimental and theoretical uncertainties is given.

The observed $\Delta\mathrm{NLL}$ curve as a function of $\tilde d$ values. For comparison, expected $\Delta\mathrm{NLL}$ curves are also shown. The constraints on the nuisance parameters and normalization factors are first determined in a CR-only fit, and then a fit to pseudo-data corresponding to these nuisance parameters, normalization factors, and to $\tilde d=0, \mu = 1$ or $\tilde d =0, \mu = 0.73$ is performed to obtain these $\Delta\mathrm{NLL}$ curves. Moreover, a pre-fit expected $\Delta\mathrm{NLL}$ is shown, using pseudo-data corresponding to $\tilde d =0$ and $\mu = 1$ in the signal and control regions.

The expected $\Delta\mathrm{NLL}$ curves comparing the sensitivity of the fit with and without systematic uncertainties. For comparison, other curves are shown which remove the effect of jet-based systematic uncertainties, $\tau$-based systematic uncertainties, and MC statistical uncertainties.

The observed $\Delta\mathrm{NLL}$ curves for each analysis channel as a function of $\tilde d$, compared to the combined result. For the individual analysis channel $\Delta\mathrm{NLL}$ curves, only event yield information in the other SRs is used, ensuring that the Optimal Observable distributions in the other SRs do not influence the preferred value of $\tilde d$. The signal strength is constrained to be positive in these individual channel $\Delta\mathrm{NLL}$ curves. The exact value of the $p_{\mathrm{T}}$ cut on the leading lepton depends on the trigger.

Post-fit BDT distributions in the top-quark CR for the $\tau_{\mathrm{lep}}\tau_{\mathrm{lep}}$ SF channel. The size of the combined statistical, experimental, and theoretical uncertainties is given. The exact value of the $p_{\mathrm{T}}$ cut on the leptons depends on the trigger.

Post-fit BDT distributions in the top-quark CR for the $\tau_{\mathrm{lep}}\tau_{\mathrm{lep}}$ DF channel. The size of the combined statistical, experimental, and theoretical uncertainties is given.

Post-fit BDT distributions in the $Z\to \ell\ell$ CR for the $\tau_{\mathrm{lep}}\tau_{\mathrm{lep}}$ SF analysis channel. The size of the combined statistical, experimental, and theoretical uncertainties is given. The exact value of the $p_{\mathrm{T}}$ cut on the leptons depends on the trigger.

Post-fit Optimal Observable distributions in the top-quark CR for the $\tau_{\mathrm{lep}}\tau_{\mathrm{lep}}$ SF channel. The size of the combined statistical, experimental, and theoretical uncertainties is given. The exact value of the $p_{\mathrm{T}}$ cut on the leptons depends on the trigger.

Post-fit Optimal Observable distributions in the top-quark CR for the $\tau_{\mathrm{lep}}\tau_{\mathrm{lep}}$ DF channel. The size of the combined statistical, experimental, and theoretical uncertainties is given.

Post-fit Optimal Observable distributions in the $Z\to \ell\ell$ CR for the $\tau_{\mathrm{lep}}\tau_{\mathrm{lep}}$ SF analysis channel. The size of the combined statistical, experimental, and theoretical uncertainties is given. The exact value of the $p_{\mathrm{T}}$ cut on the leptons depends on the trigger.

Post-fit distribution of weighted event yields as a function of the Optimal Observable for all four SRs combined. The contributions of the different SRs are weighted by a factor of ln(1 + S/B), where S and B are the post-fit expected numbers of signal and background events in that region, respectively. The size of the combined statistical, experimental, and theoretical uncertainties is given.

Fit correlations between the physical parameters of interest, obtained from the fit for solution (b).

Values of the physical parameters extracted in the combination of solution (a) of 13 TeV results with those obtained from 7 TeV and 8 TeV data.

Values of the physical parameters extracted in the combination of solution (b) of 13 TeV results with those obtained from 7 TeV and 8 TeV data.

Correlation matrix of the BLUE combination of the 7 TeV and 8 TeV results and the solution (a) of the 13 TeV result.

Correlation matrix of the BLUE combination of the 7 TeV and 8 TeV results and the solution (b) of the 13 TeV result.

Summary of systematic uncertainties assigned to the physical parameters of interest.

Numerical values of double-differential yields $d^{2}n/dydp_{T}$ presented in Fig. 10, given in units of $10^{−3} (GeV/c)^{−1}$. The first uncertainty is statistical, while the second one is systematic

Numerical values of double-differential yields $1/m_T d^{2}n/dm_{T}dy$ given in units of $10^{−3}(GeV)^{−2}$ and presented in Fig. 11; the values of $m_T−m_0$ specify the bin centers. The first uncertainty is statistical, while the second one is systematic

Numerical values of double-differential yields $1/m_T d^{2}n/dm_{T}dy$ given in units of $10^{−3}(GeV)^{−2}$ and presented in Fig. 11; the values of $m_T−m_0$ specify the bin centers. The first uncertainty is statistical, while the second one is systematic

Numerical values of double-differential yields $1/m_T d^{2}n/dm_{T}dy$ given in units of $10^{−3}(GeV)^{−2}$ and presented in Fig. 11; the values of $m_T−m_0$ specify the bin centers. The first uncertainty is statistical, while the second one is systematic

Numerical values of the $p_T$-integrated and extrapolated $dn/dy$ distribution presented in Fig. 12. The first uncertainty is statistical, while the second one is systematic. Additionally, the width of the Gaussian fit to the $dn/dy$ distribution, as well as the mean multiplicity of $K^{*}(892)^0$ mesons are shown (see the text for details)

The mean multiplicities $\langle K^{*}(892)^0\rangle$ and the widths of the rapidity distributions $\sigma_y$ obtained from $dn/dy$ distributions (see the text for details). The first uncertainty is statistical and the second systematic

The mean multiplicity of $K^{*}(892)^0$ mesons for 158 GeV/$c$ inelastic p+p interactions compared to theoretical multiplicities obtained within Hadron Gas Models

The mean multiplicities of different particle species measured in nucleus-nucleus collisions at 158$A$ GeV/$c$ by NA49 and NA61/SHINE. The total uncertainties of $\langle K^{*}(892)^0\rangle$, $\langle K^{+}\rangle$ and $\langle K^{-}\rangle$ were taken as the square roots of the sums of squares of statistical and systematic uncertainties. For NA49 p+p data, the $\langle K^{+}\rangle$ and $\langle K^{-}\rangle$ results include statistical uncertainties only($\langle K^{+}\rangle$ =0.2267$\pm$0.0006 and $\langle K^{-}\rangle$=0.1303$\pm$0.0004), whereas systematic uncertainties for total yields were not reported. Therefore, NA61/SHINE $\langle K^{+}\rangle$ and $\langle K^{-}\rangle$ values were used in the $\langle K^{*}(892)^0 \rangle / \langle K^{+} \rangle$ and $\langle K^{*}(892)^{0}\rangle / \langle K^{-} \rangle$ ratios. The numbers of $\langle K^{+} \rangle$ and $\langle K^{−}\rangle$ and their uncertainties for the 5% most central Pb+Pb collisions were multiplied by a factor 262/362 in orderto estimate charged kaon multiplicities in the 23.5% most central Pb+Pb reactions

Observed and expected limits at 95% CL on the cross-section of narrow resonance $X$ to $HH$ as a function of the mass $m_{X}$.

Observed and expected limits at 95% CL on the cross-section of broad resonance $X$ to $HH$ as a function of the mass $m_{X}$.

Observed and expected limits at 95% CL on the cross-sections of non-resonant $HH$ production via VBF as a function of the di-vector-boson-di-Higgs-boson coupling modifier $\kappa_{2V}$. The theory prediction of the cross-section as a function of $\kappa_{2V}$ is also shown. The minimum theory cross-section is 1.37 fb at $\kappa_{2V}=1.17$.

Parameters of the polynomial fit of net-proton C3/C2 and C4/C2 vs energy in 0-5$\%$ central Au+Au collisions. Polynomial of order 5 and 4 are used to fit C3/C2 and C4/C2 ratio vs energies, respectively.

Cumulant ratios C3/C2 and C4/C2 of net-proton distributions in STAR Au+Au collisions for nine energies from $\sqrt{s_{NN}} = 7.7 - 200 GeV for 0-5$\%$ and 70-80$\%$ centrality.

Cumulant ratios C3/C2 and C4/C2 of net-proton distributions in Au+Au collisions from UrQMD for 0-5$\%$ centrality.

Cumulant ratios C3/C2 and C4/C2 of net-proton distributions from HRG GCE, HRG GEC excluded volume, HRG CE model.

Cumulants and their ratios up to fourth order in Au+Au collisions at $\sqrt{s_{NN}} = 200 GeV using conventional analytical efficiency corrections and unfolding approaches with various cases of distribution of detector response.

Rapidity dependence of cumulant ratio C4/C2 of net-proton distributions for 0-5$\%$ central Au+Au collisions at nine energies from $\sqrt{s_{NN}} = 7.7 - 200 GeV.

Significance of deviations in net-proton C4/C2 (or kappa*sigma^2) for central 0-5$\%$ Au+Au collisions and those from UrQMD, HRG and peripheral 70-80$\%$ data.

Sum of invariant mass spectra of XI-PI-, XI-PI+, XI+PI-, XI+PI+.

Sum of invariant mass spectra of XI-PI-, XI-PI+, XI+PI-, XI+PI+ with mix-background subtracted compared with NA49 result.