Ratio of $p_{\mathrm{T,ch\ jet}}$-differential cross section of charm jets tagged with $\mathrm{D^{0}}$ mesons for different $R$: $\sigma(R=0.2)/\sigma(R=0.4)$ and $\sigma(R=0.2)/\sigma(R=0.6)$ in pp collisions at $\sqrt{s}=13$ TeV.

Ratio of $p_{\mathrm{T,ch\ jet}}$-differential cross section of charm jets tagged with $\mathrm{D^{0}}$ mesons for different $R$: $\sigma(R=0.2)/\sigma(R=0.4)$ and $\sigma(R=0.2)/\sigma(R=0.6)$ in pp collisions at $\sqrt{s}=5.02$ TeV.

The fraction of $\mathrm{D^{0}}$ jets over inclusive charged-particle jets in pp collisions at $\sqrt{s}=5.02$ TeV for $R=0.2$, $0.4$, and $0.6$.

Distributions of $z^{\mathrm{ch}}_{||}$-differential yield of charm jets tagged with $\mathrm{D^{0}}$ mesons normalised by the number of $\mathrm{D^{0}}$ jets within each distribution in pp collisions at $\sqrt{s}=13$ TeV in four jet-$p_{\mathrm{T}}$ intervals $5<p_{\mathrm{T,ch\ jet}}<7$ GeV/$c$, $7<p_{\mathrm{T,ch\ jet}}<10$ GeV/$c$, $10<p_{\mathrm{T,ch\ jet}}<15$ GeV/$c$, and $15<p_{\mathrm{T,ch\ jet}}<50$ GeV/$c$ for jet radii $R=0.2$, $0.4$, and $0.6$.

Distributions of $z^{\mathrm{ch}}_{||}$-differential yield of charm jets tagged with $\mathrm{D^{0}}$ mesons normalised by the number of $\mathrm{D^{0}}$ jets within each distribution in pp collisions at $\sqrt{s}=5.02$ TeV in four jet-$p_{\mathrm{T}}$ intervals $5<p_{\mathrm{T,ch\ jet}}<7$ GeV/$c$, $7<p_{\mathrm{T,ch\ jet}}<10$ GeV/$c$, $10<p_{\mathrm{T,ch\ jet}}<15$ GeV/$c$, and $15<p_{\mathrm{T,ch\ jet}}<50$ GeV/$c$ for jet radii $R=0.2$, $0.4$, and $0.6$.

$p_{\mathrm{T,ch\ jet}}$-differential cross section of charm jets tagged with $\mathrm{D^{0}}$ mesons for $R=0.3$ in pp collisions at $\sqrt{s}=5.02$ TeV.

The fraction of $\mathrm{D^{0}}$ jets over inclusive charged-particle jets in pp collisions at $\sqrt{s}=5.02$ TeV for $R=0.3$.

Distributions of $z^{\mathrm{ch}}_{||}$-differential yield of charm jets tagged with $\mathrm{D^{0}}$ mesons normalised by the number of $\mathrm{D^{0}}$ jets within each distribution in pp collisions at $\sqrt{s}=5.02$ TeV in four jet-$p_{\mathrm{T}}$ intervals $5<p_{\mathrm{T,ch\ jet}}<7$ GeV/$c$, $7<p_{\mathrm{T,ch\ jet}}<10$ GeV/$c$, $10<p_{\mathrm{T,ch\ jet}}<15$ GeV/$c$, and $15<p_{\mathrm{T,ch\ jet}}<50$ GeV/$c$ for jet radius $R=0.3$.

Example of combinatorial background subtracted invariant mass distributions and the extracted yields as a function of $\cos \theta^*$ for $\phi$ and $K^{*0}$ mesons. \textbf{a)} example of $\phi \rightarrow K^+ + K^-$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{b)} example of $K^{*0} (\overline{K^{*0}}) \rightarrow K^{-} \pi^{+} (K^{+} \pi^{-})$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{c)} extracted yields of $\phi$ as a function of $\cos \theta^*$; \textbf{d)} extracted yields of $K^{*0}$ as a function of $\cos \theta^*$.

Example of combinatorial background subtracted invariant mass distributions and the extracted yields as a function of $\cos \theta^*$ for $\phi$ and $K^{*0}$ mesons. \textbf{a)} example of $\phi \rightarrow K^+ + K^-$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{b)} example of $K^{*0} (\overline{K^{*0}}) \rightarrow K^{-} \pi^{+} (K^{+} \pi^{-})$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{c)} extracted yields of $\phi$ as a function of $\cos \theta^*$; \textbf{d)} extracted yields of $K^{*0}$ as a function of $\cos \theta^*$.

Example of combinatorial background subtracted invariant mass distributions and the extracted yields as a function of $\cos \theta^*$ for $\phi$ and $K^{*0}$ mesons. \textbf{a)} example of $\phi \rightarrow K^+ + K^-$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{b)} example of $K^{*0} (\overline{K^{*0}}) \rightarrow K^{-} \pi^{+} (K^{+} \pi^{-})$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{c)} extracted yields of $\phi$ as a function of $\cos \theta^*$; \textbf{d)} extracted yields of $K^{*0}$ as a function of $\cos \theta^*$.

Efficiency corrected $\phi$-meson yields as a function of cos$\theta$* and corresponding fits with Eq.1 in the method section.

Efficiency and acceptance corrected $K^{*0}$-meson yields as a function of cos$\theta$* and corresponding fits with Eq.4 in the method section.

$\phi$-meson $\rho_{00}$ obtained from 1st- and 2nd-order event planes. The red stars (gray squares) show the $\phi$-meson $\rho_{00}$ as a function of beam energy, obtained with the 2nd-order (1st-order) EP.

$\phi$-meson $\rho_{00}$ with respect to different quantization axes. $\phi$-meson $\rho_{00}$ as a function of beam energy, for the out-of-plane direction (stars) and the in-plane direction (diamonds). Curves are fits based on theoretical calculations with a $\phi$-meson field. The corresponding $G_s^{(y)}$ values obtained from the fits are shown in the legend.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

Global spin alignment measurement of $\phi$ and $K^{*0}$ vector mesons in Au+Au collisions at 0-20\% centrality. The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for $K^{*0}$-meson, obtained with the 2nd-order EP.

Global spin alignment measurement of $\phi$ and $K^{*0}$ vector mesons in Au+Au collisions at 0-20\% centrality. The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for $K^{*0}$-meson, obtained with the 2nd-order EP.

Invariant yield of direct photons, every 20% centrality

Invariant yield of nonprompt photons, every 20% centrality

$T_{eff}$ vs charged particle multiplicity

Integrated direct photon yield of 1-5GeV vs charged particle multiplicity

Integrated nonprompt direct photon yield of different $p_T$ integration window vs charged particle multiplicity

Scaling factor $\alpha$ vs charged particle multiplicity

Direct photon spectra for minimum bias (0-86%) Au+Au collision at $\sqrt{s_{NN}} = 62.4$ GeV (a) and $39$ GeV (b). For $62.4$ GeV also centrality bins of 0-20% (c) and 20-40% (d) are shown. Data points are shown with statistical and systematic uncertainties, unless the central value is negative (arrows) or is consistent with zero within the statistical uncertainties (arrows with data point). In these cases upper limit with CL = 95$%$ are given.

Inverse slopes, $T_{eff}$ , obtained from fitting the combined data from central collisions shown in Fig. 11 is compared to the fit results of the individual data sets at $\sqrt{s_{NN}} = 62.4$ GeV, $200$ GeV, and $2760$ GeV. Also included is the value for $\sqrt{s_{NN}} = 39$ GeV obtained from fitting the min. bias data set in the lower $p_T$ range.

Integrated invariant direct-photon yields vs. charged particle multiplicity for $p_{T}$ integrated from (a) 0.4 GeV/c, (b) 1.0 GeV/c, (c) 1.5 GeV/c, and (d) 2.0 to 5.0 GeV/c for all available A+A datasets.

Integrated invariant direct-photon yields vs. charged particle multiplicity for $p_{T}$ integrated from (a) 0.4 GeV/c, (b) 1.0 GeV/c, (c) 1.5 GeV/c, and (d) 2.0 to 5.0 GeV/c for all available A+A datasets.

Integrated invariant direct-photon yields vs. charged particle multiplicity for $p_{T}$ integrated from (a) 0.4 GeV/c, (b) 1.0 GeV/c, (c) 1.5 GeV/c, and (d) 2.0 to 5.0 GeV/c for all available A+A datasets.

Integrated invariant direct-photon yields vs. charged particle multiplicity for $p_{T}$ integrated from (a) 0.4 GeV/c, (b) 1.0 GeV/c, (c) 1.5 GeV/c, and (d) 2.0 to 5.0 GeV/c for all available A+A datasets.

Integrated direct-photon yields from A+A collisions for $p_{T,min}$ of $5$ GeV/c (a) and $8$ GeV/c. The representation is the same as in Fig. 13. Also shown are the results from pQCD calculations scaled by $N_{coll}$

Integrated direct-photon yields from A+A collisions for $p_{T,min}$ of $5$ GeV/c (a) and $8$ GeV/c. The representation is the same as in Fig. 13. Also shown are the results from pQCD calculations scaled by $N_{coll}$

The $\alpha$ values extracted using fits to integrated direct photon yields. The dashed line gives the average $\alpha$ value for the 4 lower $p_{T,min}$ points. Also shown is a model calculation for $\alpha$ discussed in the text.

Azimuthal anisotropy $v_2\{BF\}$ as a function of transverse momentum $p_T$ in $d$+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.

Azimuthal anisotropy $v_2\{BB\}$ as a function of transverse momentum $p_T$ in $^3$He+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.

Azimuthal anisotropy $v_2\{BF\}$ as a function of transverse momentum $p_T$ in $^3$He+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.

Azimuthal anisotropy $v_2$ as a function of transverse momentum $p_T$ in $p$+$p$ collisions at $\sqrt{s_{NN}} =$ 200 GeV.

Azimuthal anisotropy $v_2$ as a function of centrality in $p$+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.

Azimuthal anisotropy $v_2$ as a function of centrality in $d$+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.

Azimuthal anisotropy $v_2$ as a function of centrality in $^3$He+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.

Azimuthal anisotropy $v_2$ as a function of charged particle multiplicity $dN_{ch}/d\eta$ in $p$+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.

Azimuthal anisotropy $v_2$ as a function of charged particle multiplicity $dN_{ch}/d\eta$ in $d$+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.

Azimuthal anisotropy $v_2$ as a function of charged particle multiplicity $dN_{ch}/d\eta$ in $^3$He+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.

Azimuthal anisotropy $v_2$ as a function of charged particle multiplicity $dN_{ch}/d\eta$ in $p$+$p$ collisions at $\sqrt{s_{NN}} =$ 200 GeV.

Azimuthal anisotropy ratio $R=v_2\{BF\}/v_2\{BB\}$ as a function of charged particle multiplicity $dN_{ch}/d\eta$ in $p$+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.

Azimuthal anisotropy ratio $R=v_2\{BF\}/v_2\{BB\}$ as a function of charged particle multiplicity $dN_{ch}/d\eta$ in $d$+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.

Azimuthal anisotropy ratio $R=v_2\{BF\}/v_2\{BB\}$ as a function of charged particle multiplicity $dN_{ch}/d\eta$ in $^3$He+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.

Azimuthal anisotropy ratio $R=v_2\{BF\}/v_2\{BB\}$ as a function of charged particle multiplicity $dN_{ch}/d\eta$ in $p$+$p$ collisions at $\sqrt{s_{NN}} =$ 200 GeV.

Summary of the total efficiencies. Quoted uncertainties correspond to statistical uncertainties of the simulated samples used. For the $B_c^+\to J/\psi \pi^+$ channel, the efficiency $\epsilon_{B_c^+\to J/\psi \pi^+}$ entering the equations for $R_{D_s^{(*)+}/\pi^+}$ is shown, while the efficiency for the full dataset is not defined.

Trigger efficiency for simulated signal events as a function of the LLP decay position in the x&ndash;y plane (L_xy) for LLPs decaying in the barrel (|&eta;|&lt;1.4) for one of the low-E_T signal samples for HLT CalRatio triggers seeded by the high-E_T L1 triggers with E_T thresholds of 60 GeV and 100 GeV and by the two versions of the low-E_T L1 triggers. Only statistical uncertainties are shown.

Trigger efficiency for simulated signal events as a function of the LLP decay position in the x&ndash;y plane (L_xy) for LLPs decaying in the barrel (|&eta;|&lt;1.4) for one of the high-E_T signal samples for HLT CalRatio triggers seeded by the high-E_T L1 triggers with E_T thresholds of 60 GeV and 100 GeV and by the two versions of the low-E_T L1 triggers. Only statistical uncertainties are shown.

The NN output scores in the dijet control region for the low-E_T training with no adversary network. Statistical uncertainties are shown in all plots. In cases where training with adversary networks is considered, the systematic uncertainty related to modelling discrepancies is included as well.

The NN output scores in the dijet control region for the low-E_T training with an adversary network included. Statistical uncertainties are shown in all plots. In cases where training with adversary networks is considered, the systematic uncertainty related to modelling discrepancies is included as well.

The NN output scores in the dijet control region for the high-E_T training with no adversary network. Statistical uncertainties are shown in all plots. In cases where training with adversary networks is considered, the systematic uncertainty related to modelling discrepancies is included as well.

The NN output scores in the dijet control region for the high-E_T training with an adversary network included. Statistical uncertainties are shown in all plots. In cases where training with adversary networks is considered, the systematic uncertainty related to modelling discrepancies is included as well.

Distribution of the low-E_T per-event BDT in main data, BIB data and some of the benchmark signal samples after preselection. Only statistical uncertainties are shown.

Distribution of the high-E_T per-event BDT outputs in main data, BIB data and some of the benchmark signal samples after preselection. Only statistical uncertainties are shown.

Sequential impact of each requirement on the number of events passing the selection for the high-E_T selections. The signal columns represent the cumulative fraction of events passing the selection than the number of events.

Sequential impact of each requirement on the number of events passing the selection for the low-E_T selections. The signal columns represent the cumulative fraction of events passing the selection than the number of events.

Application of the modified ABCD method to the final high-E_T selections. The a priori estimate refers to the "pre-unblinding" case, where the data in region A are ignored by removing the Poisson constraint in that region and the signal strength is fixed to zero. This matches the simple N^bkg_A=(N^bkg_B&middot; N^bkg_C)/N^bkg_D relation. The a posteriori estimate refers to the "post-unblinding" case, including the observed data in region A in the background-only global fit, obtained by fixing the signal strength to 0 (background-only fit) or allowing it to float (signal-plus-background fit). The table also shows one set of representative signal yields in each selection for the signal-plus-background fit. Only statistical uncertainties are included in the quoted error of the background, while the uncertainties in the signal include those from both statistical and experimental sources.

Application of the modified ABCD method to the final low-E_T selections. The a priori estimate refers to the "pre-unblinding" case, where the data in region A are ignored by removing the Poisson constraint in that region and the signal strength is fixed to zero. This matches the simple N^bkg_A=(N^bkg_B&middot; N^bkg_C)/N^bkg_D relation. The a posteriori estimate refers to the "post-unblinding" case, including the observed data in region A in the background-only global fit, obtained by fixing the signal strength to 0 (background-only fit) or allowing it to float (signal-plus-background fit). The table also shows one set of representative signal yields in each selection for the signal-plus-background fit. Only statistical uncertainties are included in the quoted error of the background, while the uncertainties in the signal include those from both statistical and experimental sources.

95% CL expected and observed limits on the BR of SM Higgs bosons to pairs of neutral LLPs (B_{H&rarr; ss}), showing the &plusmn; 1 &sigma; (green) and &plusmn; 2 &sigma; (yellow) expected limit bands, as well as a comparison with the results from previous ATLAS searches [36,78]. The cross-section for SM Higgs boson gluon--gluon fusion production is assumed to be 48.6 pb.

Trigger efficiency of simulated signal events as a function of the LLP decay position in the z direction for LLPs decaying in the calorimeter endcaps (1.4 &le; |&eta;| &lt; 2.5) for one of the low-E_T signal samples for HLT CalRatio triggers seeded by the 60 GeV-high-E_T trigger and by the two versions of the low-E_T triggers.

Trigger efficiency of simulated signal events as a function of the LLP decay position in the z direction for LLPs decaying in the calorimeter endcaps (1.4 &le; |&eta;| &lt; 2.5) for one of the high-E_T signal samples for HLT CalRatio triggers seeded by the 60 GeV-high-E_T trigger and by the two versions of the low-E_T triggers.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The event BDT in the dijet control region for the low-E_T training training. The uncertainties are combined statistical and ML modelling systematic uncertainty.

The event BDT in the dijet control region for the high-E_T training. The uncertainties are combined statistical and ML modelling systematic uncertainty.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; mass of 60 GeV compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; mass of 60 GeV compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; mass 125 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; mass 125 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available. The 125 GeV mediator is assumed to be the SM Higgs boson.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; mass 125 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available. The 125 GeV mediator is assumed to be the SM Higgs boson.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; mass of 200 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; mass of 400 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; mass 600 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; mass of 600 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; masses of of 1000 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; masses of of 1000 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; masses of of 1000 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; masses of of 1000 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

Efficiency for an event to enter Region A of the high-E_T selection, as a function of the two LLP kinematics, decay type and decay position. LLP p_T is binned in the ranges of [0, 50 , 100, 200 , 400, 1600] GeV (5 bins), the LLP decay position is binned in decay position in L_xy in [0, 1.5, 2, 2.5, 3, 3.5, 3.9, &infin;] m for LLPs with |&eta;| &lt; 1.5 and L_z in [0, 3.6, 4.2, 4.8, 5.5, 6, &infin; ] m for LLPs with |&eta;|geq1.5, 13 bins in all. Finally, four decay types are considered: LLPs decaying to pairs of c, b, t, or &tau; in bins 0, 1, 2, 3 respectively. The efficiency is presented as a function of "Bin Index", which is calculated as follows: Bin Index = (decay position bin index ) &times; (number of p_T bins &times; number of decay type bins) + p_T bin index * (number of decay type bin) + decay type bin index. The efficiency for a given pair-produced LLP sample can be obtained by summing the efficiency values for each event as extracted from this map, and dividing it by the total number of events in the sample. The efficiency map is symmetric between the LLPs, so the choice of LLP1 and LLP2 is arbitrary. For the high-E_T selections, for overall efficiencies above 0.5%, the results are typically accurate to around 25%, but below this the efficiency can be overestimated and therefore should not be used for re-interpration.

Efficiency for an event to enter Region A of the low-E_T selection, as a function of the two LLP kinematics, decay type and decay position. LLP p_T is binned in the ranges of [0, 50 , 100, 200 , 400, 1600] GeV (5 bins), the LLP decay position is binned in L_xy in [0, 1.5, 2, 2.5, 3, 3.5, 3.9, &infin;] m for LLPs with |&eta;| &lt; 1.5 and L_z in [0, 3.6, 4.2, 4.8, 5.5, 6, &infin; ] m for LLPs with |&eta;|geq1.5, 13 bins in all. Finally, four decay types are considered: LLPs decaying to pairs of c, b, t, or &tau; in bins 0, 1, 2, 3 respectively. The efficiency is presented as a function of "Bin Index", which is calculated as follows: Bin Index = (decay position bin index ) &times; (number of p_T bins &times; number of decay type bins) + p_T bin index * (number of decay type bin) + decay type bin index. The efficiency for a given pair-produced LLP sample can be obtained by summing the efficiency values for each event as extracted from this map, and dividing it by the total number of events in the sample. The efficiency map is symmetric between the LLPs, so the choice of LLP1 and LLP2 is arbitrary. For the low-E_T selections, for overall efficiencies above 0.15%, the results are typically accurate to around 33%, and below this the efficiency is typically accurate up to a factor of 3.

Helicity-dependent differential cross section on deuteron at Egamma= 196. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 213. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 230. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 247. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 264. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 281. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 299. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 316. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 333. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 351. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 368. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 386. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 403. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 421. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 438. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 456. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 473. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 491. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 508. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 526. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 543. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 561. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 578. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 596. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 613. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 631. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 648. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 666. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 683. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 700. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 718. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 735. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 752. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 769. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 786. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 803. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 820. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 837. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 853. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 870. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 887. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 903. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 919. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 936. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 952. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 968. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 983. MeV

Helicity-dependent differential cross section on deuteron at Egamma= 999. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1015. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1030. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1046. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1061. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1076. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1091. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1105. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1120. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1134. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1148. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1162. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1176. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1190. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1203. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1217. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1230. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1243. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1256. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1268. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1281. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1293. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1305. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1317. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1328. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1340. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1351. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1362. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1374. MeV

Helicity-dependent differential cross section on deuteron at Egamma=1387. MeV

Helicity asymmetry E for quasi-free proton at W=1165. MeV

Helicity asymmetry E for quasi-free proton at W=1195. MeV

Helicity asymmetry E for quasi-free proton at W=1225. MeV

Helicity asymmetry E for quasi-free proton at W=1255. MeV

Helicity asymmetry E for quasi-free proton at W=1285. MeV

Helicity asymmetry E for quasi-free proton at W=1315. MeV

Helicity asymmetry E for quasi-free proton at W=1339. MeV

Helicity asymmetry E for quasi-free proton at W=1357. MeV

Helicity asymmetry E for quasi-free proton at W=1375. MeV

Helicity asymmetry E for quasi-free proton at W=1393. MeV

Helicity asymmetry E for quasi-free proton at W=1411. MeV

Helicity asymmetry E for quasi-free proton at W=1429. MeV

Helicity asymmetry E for quasi-free proton at W=1447. MeV

Helicity asymmetry E for quasi-free proton at W=1465. MeV

Helicity asymmetry E for quasi-free proton at W=1483. MeV

Helicity asymmetry E for quasi-free proton at W=1501. MeV

Helicity asymmetry E for quasi-free proton at W=1519. MeV

Helicity asymmetry E for quasi-free proton at W=1537. MeV

Helicity asymmetry E for quasi-free proton at W=1555. MeV

Helicity asymmetry E for quasi-free proton at W=1573. MeV

Helicity asymmetry E for quasi-free proton at W=1591. MeV

Helicity asymmetry E for quasi-free proton at W=1609. MeV

Helicity asymmetry E for quasi-free proton at W=1627. MeV

Helicity asymmetry E for quasi-free proton at W=1645. MeV

Helicity asymmetry E for quasi-free proton at W=1663. MeV

Helicity asymmetry E for quasi-free proton at W=1681. MeV

Helicity asymmetry E for quasi-free proton at W=1699. MeV

Helicity asymmetry E for quasi-free proton at W=1717. MeV

Helicity asymmetry E for quasi-free proton at W=1735. MeV

Helicity asymmetry E for quasi-free proton at W=1753. MeV

Helicity asymmetry E for quasi-free proton at W=1771. MeV

Helicity asymmetry E for quasi-free proton at W=1789. MeV

Helicity asymmetry E for quasi-free proton at W=1807. MeV

Helicity asymmetry E for quasi-free proton at W=1825. MeV

Helicity asymmetry E for quasi-free proton at W=1843. MeV

Helicity asymmetry E for quasi-free proton at W=1861. MeV

Helicity asymmetry E for quasi-free proton at W=1879. MeV

Helicity asymmetry E for quasi-free proton at W=1897. MeV

Helicity asymmetry E for quasi-free proton at W=1915. MeV

Helicity asymmetry E for quasi-free neutron at W=1165. MeV

Helicity asymmetry E for quasi-free neutron at W=1195. MeV

Helicity asymmetry E for quasi-free neutron at W=1225. MeV

Helicity asymmetry E for quasi-free neutron at W=1255. MeV

Helicity asymmetry E for quasi-free neutron at W=1285. MeV

Helicity asymmetry E for quasi-free neutron at W=1315. MeV

Helicity asymmetry E for quasi-free neutron at W=1339. MeV

Helicity asymmetry E for quasi-free neutron at W=1357. MeV

Helicity asymmetry E for quasi-free neutron at W=1375. MeV

Helicity asymmetry E for quasi-free neutron at W=1393. MeV

Helicity asymmetry E for quasi-free neutron at W=1411. MeV

Helicity asymmetry E for quasi-free neutron at W=1429. MeV

Helicity asymmetry E for quasi-free neutron at W=1447. MeV

Helicity asymmetry E for quasi-free neutron at W=1465. MeV

Helicity asymmetry E for quasi-free neutron at W=1483. MeV

Helicity asymmetry E for quasi-free neutron at W=1501. MeV

Helicity asymmetry E for quasi-free neutron at W=1519. MeV

Helicity asymmetry E for quasi-free neutron at W=1537. MeV

Helicity asymmetry E for quasi-free neutron at W=1555. MeV

Helicity asymmetry E for quasi-free neutron at W=1573. MeV

Helicity asymmetry E for quasi-free neutron at W=1591. MeV

Helicity asymmetry E for quasi-free neutron at W=1609. MeV

Helicity asymmetry E for quasi-free neutron at W=1627. MeV

Helicity asymmetry E for quasi-free neutron at W=1645. MeV

Helicity asymmetry E for quasi-free neutron at W=1663. MeV

Helicity asymmetry E for quasi-free neutron at W=1681. MeV

Helicity asymmetry E for quasi-free neutron at W=1699. MeV

Helicity asymmetry E for quasi-free neutron at W=1717. MeV

Helicity asymmetry E for quasi-free neutron at W=1735. MeV

Helicity asymmetry E for quasi-free neutron at W=1753. MeV

Helicity asymmetry E for quasi-free neutron at W=1771. MeV

Helicity asymmetry E for quasi-free neutron at W=1789. MeV

Helicity asymmetry E for quasi-free neutron at W=1807. MeV

Helicity asymmetry E for quasi-free neutron at W=1825. MeV

Helicity asymmetry E for quasi-free neutron at W=1843. MeV

Helicity asymmetry E for quasi-free neutron at W=1861. MeV

Helicity asymmetry E for quasi-free neutron at W=1879. MeV

Helicity asymmetry E for quasi-free neutron at W=1897. MeV

Helicity asymmetry E for quasi-free neutron at W=1915. MeV

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of X$\to\phi\phi\to$4b, with $m_\phi$ = 40 GeV. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_XN/f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of X$\to\phi\phi\to$4b, with $m_\phi$ = 45 GeV. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_XN/f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of X$\to\phi\phi\to$4b, with $m_\phi$ = 50 GeV. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_XN/f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of X$\to\phi\phi\to$4b, with $m_\phi$ = 55 GeV. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_XN/f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of X$\to\phi\phi\to$4b, with $m_\phi$ = 60 GeV. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_XN/f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of X$\to\phi\phi\to$4b, with $m_\phi$ = 65 GeV. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_XN/f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of X$\to\phi\phi\to$4b, with $m_\phi$ = 70 GeV. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_XN/f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of X$\to\phi\phi\to$4b, with $m_\phi$ = 75 GeV. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_XN/f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of X$\to\phi\phi\to$4b, with $m_\phi$ = 80 GeV. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_XN/f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of X$\to\phi\phi\to$4b, with $m_\phi$ = 85 GeV. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_XN/f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of X$\to\phi\phi\to$4b, with $m_\phi$ = 90 GeV. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_XN/f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of X$\to\phi\phi\to$4b, with $m_\phi$ = 95 GeV. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_XN/f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of X$\to\phi\phi\to$4b, with $m_\phi$ = 100 GeV. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_XN/f$.

Data event yields and predicted signal and background yields (including subdominant $t\bar{t}$) in bins of dijet and average jet mass.