The spin transfer $D_{LL}$ to (a) $\Lambda$ and (b) $\bar{\Lambda}$ hyperons produced at positive pseudorapidity with respect to the polarized proton beam from $MB$, $JP$, and $HT$ data versus hyperon transverse momenta $p_{T}$. The sizes of the statistical and systematic uncertainties are indicated by the vertical bars and bands, respectively. For clarity, the HT data points have been shifted slightly in $p_{T}$. The dotted vertical lines indicate the $p_{T}$ intervals in the analysis of HT and JP data.

Comparison of $\Lambda$ and $\bar{\Lambda}$ spin transfer $D_{LL}$ in polarized proton-proton collisions at $\sqrt{s} = 200 GeV$ for (a) positive and (b) negative $\eta$ versus $p_{T}$. The vertical bars and bands indicate the sizes of the statistical and systematic uncertainties, respectively. The $\bar{\Lambda}$ data points have been shifted slightly in $p_{T}$ for clarity. The dotted vertical lines indicate the $p_{T}$ intervals in the analysis of HT and JP data. The horizontal lines show model predictions evaluated at $\eta$ and largest $p_{T}$ of the data.

Comparison of $\Lambda$ and $\bar{\Lambda}$ spin transfer $D_{LL}$ in polarized proton-proton collisions at $\sqrt{s} = 200$ GeV for (a) positive and (b) negative $\eta$ versus $p_{T}$. The vertical bars and bands indicate the sizes of the statistical and systematic uncertainties, respectively. The $\bar{\Lambda}$ data points have been shifted slightly in $p_{T}$ for clarity. The dotted vertical lines indicate the $p_{T}$ intervals in the analysis of HT and JP data. The horizontal lines show model predictions evaluated at $\eta$ and largest $p_{T}$ of the data.

The spin transfer $D_{LL}$ to (a) $\Lambda$ and (b) $\bar{\Lambda}$ hyperons, calculated using the new $\alpha_\Lambda=0.732$ updated on PDG2020, produced at positive pseudorapidity with respect to the polarized proton beam from $MB$, $JP$, and $HT$ data versus hyperon transverse momenta $p_{T}$. The sizes of the statistical and systematic uncertainties are indicated by the vertical bars and bands, respectively. For clarity, the HT data points have been shifted slightly in $p_{T}$. The dotted vertical lines indicate the $p_{T}$ intervals in the analysis of HT and JP data.

The spin transfer $D_{LL}$ to (a) $\Lambda$ and (b) $\bar{\Lambda}$ hyperons, calculated using the new $\alpha_\Lambda=0.732$ updated on PDG2020, produced at positive pseudorapidity with respect to the polarized proton beam from $MB$, $JP$, and $HT$ data versus hyperon transverse momenta $p_{T}$. The sizes of the statistical and systematic uncertainties are indicated by the vertical bars and bands, respectively. For clarity, the HT data points have been shifted slightly in $p_{T}$. The dotted vertical lines indicate the $p_{T}$ intervals in the analysis of HT and JP data.

Comparison of $\Lambda$ and $\bar{\Lambda}$ spin transfer $D_{LL}$, calculated using the new $\alpha_\Lambda=0.732$ updated on PDG2020, in polarized proton-proton collisions at $\sqrt{s} = 200$ GeV for (a) positive and (b) negative $\eta$ versus $p_{T}$. The vertical bars and bands indicate the sizes of the statistical and systematic uncertainties, respectively. The $\bar{\Lambda}$ data points have been shifted slightly in $p_{T}$ for clarity. The dotted vertical lines indicate the $p_{T}$ intervals in the analysis of HT and JP data. The horizontal lines show model predictions evaluated at $\eta$ and largest $p_{T}$ of the data.

Expected and observed 95% CL upper limits on $|V_\mathrm{N}|^2$ as a function of $m_\mathrm{N}$ for the mixing scenario ($r_e$, $r_\mu$, $r_\tau$) = (0.33, 0.33, 0.33) and in the Majorana scenario.

Expected and observed 95% CL upper limits on $|V_\mathrm{N}|^2$ as a function of $m_\mathrm{N}$ for the mixing scenario ($r_e$, $r_\mu$, $r_\tau$) = (0.0, 1.0, 0.0) and in the Dirac-like scenario.

Expected and observed 95% CL upper limits on $|V_\mathrm{N}|^2$ as a function of $m_\mathrm{N}$ for the mixing scenario ($r_e$, $r_\mu$, $r_\tau$) = (0.0, 0.5, 0.5) and in the Dirac-like scenario.

Expected and observed 95% CL upper limits on $|V_\mathrm{N}|^2$ as a function of $m_\mathrm{N}$ for the mixing scenario ($r_e$, $r_\mu$, $r_\tau$) = (0.5, 0.5, 0.0) and in the Dirac-like scenario.

Expected and observed 95% CL upper limits on $|V_\mathrm{N}|^2$ as a function of $m_\mathrm{N}$ for the mixing scenario ($r_e$, $r_\mu$, $r_\tau$) = (0.33, 0.33, 0.33) and in the Dirac-like scenario.

Observed 95% CL lower limits on $c\tau_\mathrm{N}$ as functions of the mixing ratios ($r_e$, $r_\mu$, $r_\tau$) for a fixed N mass of 1.0 GeV in the Majorana scenario.

Observed 95% CL lower limits on $c\tau_\mathrm{N}$ as functions of the mixing ratios ($r_e$, $r_\mu$, $r_\tau$) for a fixed N mass of 1.5 GeV in the Majorana scenario.

Observed 95% CL lower limits on $c\tau_\mathrm{N}$ as functions of the mixing ratios ($r_e$, $r_\mu$, $r_\tau$) for a fixed N mass of 2.0 GeV in the Majorana scenario.

Observed 95% CL lower limits on $c\tau_\mathrm{N}$ as functions of the mixing ratios ($r_e$, $r_\mu$, $r_\tau$) for a fixed N mass of 1.0 GeV in the Dirac-like scenario.

Observed 95% CL lower limits on $c\tau_\mathrm{N}$ as functions of the mixing ratios ($r_e$, $r_\mu$, $r_\tau$) for a fixed N mass of 1.5 GeV in the Dirac-like scenario.

Observed 95% CL lower limits on $c\tau_\mathrm{N}$ as functions of the mixing ratios ($r_e$, $r_\mu$, $r_\tau$) for a fixed N mass of 2.0 GeV in the Dirac-like scenario.

Observed limits at 95% CL on $\sigma \mathcal{B} (X \to Y(gg)g) \mathcal{A}$ for a cascade decay trijet resonance. The acceptance $\mathcal{A}$ is defined as $\mathcal{A} = N$(events with $m_{X}^{GEN} > 85\% m_{X}^{input}$) / $N$(events generated in the full phase space defined by the CMS default generator settings). Only 2016 data are used to derive limits below 2.0 TeV because of higher trigger thresholds in 2017 and 2018. Mass exclusion ranges of the benchmark signal scenarios are depicted with hatched areas inside the black contours.

Observed limits at 95% CL on $\sigma \mathcal{B} (X \to Y(qq)q) \mathcal{A}$ for a cascade decay trijet resonance. The acceptance $\mathcal{A}$ is defined as $\mathcal{A} = N$(events with $m_{X}^{GEN} > 85\% m_{X}^{input}$) / $N$(events generated in the full phase space defined by the CMS default generator settings). Only 2016 data are used to derive limits below 2.0 TeV because of higher trigger thresholds in 2017 and 2018. Mass exclusion ranges of the benchmark signal scenarios are depicted with hatched areas inside the black contours.

Efficiencies of the selection requirements on the benchmark signal processes: $Z_{R} \to ggg$ with nominal width ($\Gamma_{X}/m_{X}\sim 3\%$). A value of -1 means that the corresponding efficiency is not calculated for this year.

Efficiencies of the selection requirements on the benchmark signal processes: $Z_{R} \to ggg$ with narrow width ($\Gamma_{X}/m_{X}\sim 0.01\%$). A value of -1 means that the corresponding efficiency is not calculated for this year.

Efficiencies of the selection requirements on the benchmark signal processes: $G_{KK} \to {\varphi}(gg)g$, where $\varphi$ is the radion. A value of -1 means that the corresponding efficiency is not calculated for this year.

Efficiencies of the selection requirements on the benchmark signal processes: $q^{*} \to V(qq)q$, where $V$ is a beyond-the-SM vector boson. A value of -1 means that the corresponding efficiency is not calculated for this year.

Acceptance of the signal selection requirement $m_{X}^{\text{GEN}}/m_{X}^{\text{input}} > 85\%$ on the benchmark signal process $Z_{R} \to ggg$. The acceptance is defined as $\mathcal{A} = N$(events with $m_{X}^{\text{GEN}}/m_{X}^{\text{input}} > 85\%$)/$N$(events generated in the full phase space defined by the CMS default generator settings).

Acceptance of the signal selection requirement $m_{X}^{\text{GEN}}/m_{X}^{\text{input}} > 85\%$ on the benchmark signal process $G_{KK} \to {\varphi}(gg)g$.

Acceptance of the signal selection requirement $m_{X}^{\text{GEN}}/m_{X}^{\text{input}} > 85\%$ on the benchmark signal process $q^{*} \to V(qq)q$.

Observed local significance for a 3-body decay $ggg$ resonance, shown for resonances with nominal width (blue solid line) and narrow width (red dashed line).

Observed local significance for a cascade decay $ggg$ resonance.

Observed local significance for a cascade decay $qqq$ resonance.

Expected and observed limits at 95% CL on $\sigma \mathcal{B} (X \to Y(gg)g) \mathcal{A}$ for a cascade decay trijet resonance with $m_{Y} / m_{X} = 0.2$. Only 2016 data are used to derive limits below 2.0 TeV because of higher trigger thresholds in 2017 and 2018. Theoretical predictions of the benchmark are depicted with the red curve. A value of -1 in the table means that the corresponding theoretical prediction is not calculated for this signal.

Expected and observed limits at 95% CL on $\sigma \mathcal{B} (X \to Y(gg)g) \mathcal{A}$ for a cascade decay trijet resonance with $m_{Y} / m_{X} = 0.3$. Only 2016 data are used to derive limits below 2.0 TeV because of higher trigger thresholds in 2017 and 2018. Theoretical predictions of the benchmark are depicted with the red curve. A value of -1 in the table means that the corresponding theoretical prediction is not calculated for this signal.

Expected and observed limits at 95% CL on $\sigma \mathcal{B} (X \to Y(gg)g) \mathcal{A}$ for a cascade decay trijet resonance with $m_{Y} / m_{X} = 0.4$. Only 2016 data are used to derive limits below 2.0 TeV because of higher trigger thresholds in 2017 and 2018. Theoretical predictions of the benchmark are depicted with the red curve. A value of -1 in the table means that the corresponding theoretical prediction is not calculated for this signal.

Expected and observed limits at 95% CL on $\sigma \mathcal{B} (X \to Y(gg)g) \mathcal{A}$ for a cascade decay trijet resonance with $m_{Y} / m_{X} = 0.5$. Only 2016 data are used to derive limits below 2.0 TeV because of higher trigger thresholds in 2017 and 2018. Theoretical predictions of the benchmark are depicted with the red curve. A value of -1 in the table means that the corresponding theoretical prediction is not calculated for this signal.

Expected and observed limits at 95% CL on $\sigma \mathcal{B} (X \to Y(gg)g) \mathcal{A}$ for a cascade decay trijet resonance with $m_{Y} / m_{X} = 0.6$. Only 2016 data are used to derive limits below 2.0 TeV because of higher trigger thresholds in 2017 and 2018. Theoretical predictions of the benchmark are depicted with the red curve. A value of -1 in the table means that the corresponding theoretical prediction is not calculated for this signal.

Expected and observed limits at 95% CL on $\sigma \mathcal{B} (X \to Y(gg)g) \mathcal{A}$ for a cascade decay trijet resonance with $m_{Y} / m_{X} = 0.7$. Only 2016 data are used to derive limits below 2.0 TeV because of higher trigger thresholds in 2017 and 2018. Theoretical predictions of the benchmark are depicted with the red curve. A value of -1 in the table means that the corresponding theoretical prediction is not calculated for this signal.

Expected and observed limits at 95% CL on $\sigma \mathcal{B} (X \to Y(gg)g) \mathcal{A}$ for a cascade decay trijet resonance with $m_{Y} / m_{X} = 0.8$. Only 2016 data are used to derive limits below 2.0 TeV because of higher trigger thresholds in 2017 and 2018. Theoretical predictions of the benchmark are depicted with the red curve. A value of -1 in the table means that the corresponding theoretical prediction is not calculated for this signal.

Expected and observed limits at 95% CL on $\sigma \mathcal{B} (X \to Y(qq)q) \mathcal{A}$ for a cascade decay trijet resonance $m_{Y} / m_{X} = 0.2$. Only 2016 data are used to derive limits below 2.0 TeV because of higher trigger thresholds in 2017 and 2018. Theoretical predictions of the benchmark are depicted with the red curve. A value of -1 in the table means that the corresponding theoretical prediction is not calculated for this signal.

Expected and observed limits at 95% CL on $\sigma \mathcal{B} (X \to Y(qq)q) \mathcal{A}$ for a cascade decay trijet resonance with $m_{Y} / m_{X} = 0.3$. Only 2016 data are used to derive limits below 2.0 TeV because of higher trigger thresholds in 2017 and 2018. Theoretical predictions of the benchmark are depicted with the red curve. A value of -1 in the table means that the corresponding theoretical prediction is not calculated for this signal.

Expected and observed limits at 95% CL on $\sigma \mathcal{B} (X \to Y(qq)q) \mathcal{A}$ for a cascade decay trijet resonance with $m_{Y} / m_{X} = 0.4$. Only 2016 data are used to derive limits below 2.0 TeV because of higher trigger thresholds in 2017 and 2018. Theoretical predictions of the benchmark are depicted with the red curve. A value of -1 in the table means that the corresponding theoretical prediction is not calculated for this signal.

Expected and observed limits at 95% CL on $\sigma \mathcal{B} (X \to Y(qq)q) \mathcal{A}$ for a cascade decay trijet resonance with $m_{Y} / m_{X} = 0.5$. Only 2016 data are used to derive limits below 2.0 TeV because of higher trigger thresholds in 2017 and 2018. Theoretical predictions of the benchmark are depicted with the red curve. A value of -1 in the table means that the corresponding theoretical prediction is not calculated for this signal.

Expected and observed limits at 95% CL on $\sigma \mathcal{B} (X \to Y(qq)q) \mathcal{A}$ for a cascade decay trijet resonance with $m_{Y} / m_{X} = 0.6$. Only 2016 data are used to derive limits below 2.0 TeV because of higher trigger thresholds in 2017 and 2018. Theoretical predictions of the benchmark are depicted with the red curve. A value of -1 in the table means that the corresponding theoretical prediction is not calculated for this signal.

Expected and observed limits at 95% CL on $\sigma \mathcal{B} (X \to Y(qq)q) \mathcal{A}$ for a cascade decay trijet resonance with $m_{Y} / m_{X} = 0.7$. Only 2016 data are used to derive limits below 2.0 TeV because of higher trigger thresholds in 2017 and 2018. Theoretical predictions of the benchmark are depicted with the red curve. A value of -1 in the table means that the corresponding theoretical prediction is not calculated for this signal.

Expected and observed limits at 95% CL on $\sigma \mathcal{B} (X \to Y(qq)q) \mathcal{A}$ for a cascade decay trijet resonance with $m_{Y} / m_{X} = 0.8$. Only 2016 data are used to derive limits below 2.0 TeV because of higher trigger thresholds in 2017 and 2018. Theoretical predictions of the benchmark are depicted with the red curve. A value of -1 in the table means that the corresponding theoretical prediction is not calculated for this signal

Cut flow table of the selection requirments for the $Z_{R}$ model scenarios. Values shown are absolute efficiencies, e.g., values shown in the column of 'Efficiency ($\Delta_{R}^{max} < 3.0$)' represent the cumulative efficiencies achieved through all selection requirements applied up to and including the current selection criterion.

Cut flow table of the selection requirments for the $G_{KK}$ model scenarios. Values shown are absolute efficiencies, e.g., values shown in the column of 'Efficiency ($\Delta_{R}^{max} < 3.0$)' represent the cumulative efficiencies achieved through all selection requirements applied up to and including the current selection criterion.

Cut flow table of the selection requirments for the $q^{*}$ model scenarios. Values shown are absolute efficiencies, e.g., values shown in the column of 'Efficiency ($\Delta_{R}^{max} < 3.0$)' represent the cumulative efficiencies achieved through all selection requirements applied up to and including the current selection criterion.

Predicted production cross section of the benchmark signal process $pp \to Z_{R} \to ggg$.

Predicted production cross section of the benchmark signal process $pp \to G_{KK} \to \varphi(gg)g$.

Predicted production cross section of the benchmark signal process $pp \to q^{*} \to V(qq)q$.

Correlation matrix for the differential branching fraction extraction between different $q^2$ bins in the simultaneous fit.

The product of acceptance and efficiency ($A\epsilon$) of the $\mathcal{B}(\mathrm{B}^+\to\mathrm{K}^+\mu^+\mu^-)$ channel, as a function of the muon pair $q^2$, as measured in simulated signal events, after all the corrections applied. In the figure, regions corresponding to resonances are displayed with red markers.

Same as Table 5, but for the bins containing the J$\psi$ and $\psi$(2S) resonances.

Integrated branching fraction $\mathcal{B}(\mathrm{B}^\pm \to \mathrm{K}^\pm\mu^+\mu^-)$ in the low-$q^2$ region.

Ratio of branching fractions $\mathcal{B}(\text{B}^\pm \to \text{K}^\pm\mu^+\mu^-)$ to $\mathcal{B}(\text{B}^\pm \to \text{K}^\pm\text{e}^+\text{e}^-)$, determined from the measured double ratio $R$(K) of these decays to the respective branching fractions of the decay chains $\text{B}^\pm\to\text{J/}\psi\text{K}^\pm$ with $\text{J/}\psi\to\mu^+\mu^-$ and $\text{e}^+\text{e}^-$.

Negative log likelihood function from the fit profiled as a function of the inverse ratio $R(\mathrm{K})^{-1}$.