Fiducial differential cross section of the electroweak $W^\pm W^\pm jj$ production as a function of $N_{\mathrm{gap}\,\mathrm{jets}}$. The correlation of uncertainties of the measured cross section across bins is presented in Table 14.

Fiducial differential cross section of the electroweak $W^\pm W^\pm jj$ production as a function of $\xi_{\mathrm{j}3}$. The correlation of uncertainties of the measured cross section across bins is presented in Table 15.

Fiducial differential cross section of the inclusive $W^\pm W^\pm jj$ production as a function of $m_{\ell\ell}$. The correlation of uncertainties of the measured cross section across bins is presented in Table 16.

Fiducial differential cross section of the inclusive $W^\pm W^\pm jj$ production as a function of $m_{\mathrm{T}}$. The correlation of uncertainties of the measured cross section across bins is presented in Table 17.

Fiducial differential cross section of the inclusive $W^\pm W^\pm jj$ production as a function of $m_{\mathrm{jj}}$. The correlation of uncertainties of the measured cross section across bins is presented in Table 18.

Fiducial differential cross section of the inclusive $W^\pm W^\pm jj$ production as a function of $N_{\mathrm{gap}\,\mathrm{jets}}$. The correlation of uncertainties of the measured cross section across bins is presented in Table 19.

Fiducial differential cross section of the inclusive $W^\pm W^\pm jj$ production as a function of $\xi_{\mathrm{j}3}$. The correlation of uncertainties of the measured cross section across bins is presented in Table 20.

Observed correlations between the bins of the LH-unfolded cross section of the electroweak $W^\pm W^\pm jj$ production as a function of $m_{\ell\ell}$. See Table 1.

Observed correlations between the bins of the LH-unfolded cross section of the electroweak $W^\pm W^\pm jj$ production as a function of $m_{\mathrm{T}}$. See Table 2.

Observed correlations between the bins of the LH-unfolded cross section of the electroweak $W^\pm W^\pm jj$ production as a function of $m_{\mathrm{jj}}$. See Table 3.

Observed correlations between the bins of the LH-unfolded cross section of the electroweak $W^\pm W^\pm jj$ production as a function of $N_{\mathrm{gap}\,\mathrm{jets}}$. See Table 4.

Observed correlations between the bins of the LH-unfolded cross section of the electroweak $W^\pm W^\pm jj$ production as a function of $\xi_{\mathrm{j}3}$. See Table 5.

Observed correlations between the bins of the LH-unfolded cross section of the inclusive $W^\pm W^\pm jj$ production as a function of $m_{\ell\ell}$. See Table 6.

Observed correlations between the bins of the LH-unfolded cross section of the inclusive $W^\pm W^\pm jj$ production as a function of $m_{\mathrm{T}}$. See Table 7.

Observed correlations between the bins of the LH-unfolded cross section of the inclusive $W^\pm W^\pm jj$ production as a function of $m_{\mathrm{jj}}$. See Table 8.

Observed correlations between the bins of the LH-unfolded cross section of the inclusive $W^\pm W^\pm jj$ production as a function of $N_{\mathrm{gap}\,\mathrm{jets}}$. See Table 9.

Observed correlations between the bins of the LH-unfolded cross section of the inclusive $W^\pm W^\pm jj$ production as a function of $\xi_{\mathrm{j}3}$. See Table 10.

Evolution of the one-dimensional expected and observed limits at 95% CL on the parameters corresponding to the quartic operators with label M0 as a function of the cut-off scale. The unitarity bounds as a function of the cut-off scale are defined for one non-zero Wilson coefficient.

Evolution of the one-dimensional expected and observed limits at 95% CL on the parameters corresponding to the quartic operators with label M1 as a function of the cut-off scale. The unitarity bounds as a function of the cut-off scale are defined for one non-zero Wilson coefficient.

Evolution of the one-dimensional expected and observed limits at 95% CL on the parameters corresponding to the quartic operators with label M7 as a function of the cut-off scale. The unitarity bounds as a function of the cut-off scale are defined for one non-zero Wilson coefficient. The limits on M7 were obtained without taking into account the SM-EFT interference for the EW W$^\pm$Zjj final state.

Evolution of the one-dimensional expected and observed limits at 95% CL on the parameters corresponding to the quartic operators with label S02 as a function of the cut-off scale. The unitarity bounds as a function of the cut-off scale are defined for one non-zero Wilson coefficient.

Evolution of the one-dimensional expected and observed limits at 95% CL on the parameters corresponding to the quartic operators with label S1 as a function of the cut-off scale. The unitarity bounds as a function of the cut-off scale are defined for one non-zero Wilson coefficient.

Evolution of the one-dimensional expected and observed limits at 95% CL on the parameters corresponding to the quartic operators with label T0 as a function of the cut-off scale. The unitarity bounds as a function of the cut-off scale are defined for one non-zero Wilson coefficient.

Evolution of the one-dimensional expected and observed limits at 95% CL on the parameters corresponding to the quartic operators with label T1 as a function of the cut-off scale. The unitarity bounds as a function of the cut-off scale are defined for one non-zero Wilson coefficient.

Evolution of the one-dimensional expected and observed limits at 95% CL on the parameters corresponding to the quartic operators with label T2 as a function of the cut-off scale. The unitarity bounds as a function of the cut-off scale are defined for one non-zero Wilson coefficient.

Expected and observed exclusion limits at 95% CL for $\sigma_{\mathrm{VBF}}(\mathrm{H}^{\pm\pm}_5) \times \mathcal{B}(\mathrm{H}^{\pm\pm}_5 \rightarrow W^{\pm}W^{\pm})$ as a function of the doubly-charged Higgs mass.

Expected and observed exclusion limits at 95% CL for $\sin\theta_{\mathrm{H}}$ as a function of the doubly-charged Higgs mass in the Georgi-Machacek model.

Observed differential $m_{\Gamma\Gamma}$ mass spectrum for 0.4$ < \alpha < $0.44%, where $\alpha = m_\phi/m_X$. The cross-section is calculated by dividing the event yield by the bin width and luminosity.

Observed differential $m_{\Gamma\Gamma}$ mass spectrum for 0.49$ < \alpha < $0.55%, where $\alpha = m_\phi/m_X$. The cross-section is calculated by dividing the event yield by the bin width and luminosity.

Observed differential $m_{\Gamma\Gamma}$ mass spectrum for 0.55$ < \alpha < $0.6%, where $\alpha = m_\phi/m_X$. The cross-section is calculated by dividing the event yield by the bin width and luminosity.

Observed differential $m_{\Gamma\Gamma}$ mass spectrum for 0.6$ < \alpha < $0.7%, where $\alpha = m_\phi/m_X$. The cross-section is calculated by dividing the event yield by the bin width and luminosity.

Observed differential $m_{\Gamma\Gamma}$ mass spectrum for 0.7$ < \alpha < $0.81%, where $\alpha = m_\phi/m_X$. The cross-section is calculated by dividing the event yield by the bin width and luminosity.

Observed differential $m_{\Gamma\Gamma}$ mass spectrum for 0.81$ < \alpha < $3.0%, where $\alpha = m_\phi/m_X$. The cross-section is calculated by dividing the event yield by the bin width and luminosity.

Two dimensional plot where the Z-axis is the observed (paper Fig. 3) or expected (Supp. Fig. 20) 95% CL upper limits on the product of the cross section for $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$. 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 $m_X N / f$.

Expected exclusion limits for $m_X N / f = 1/9$ for signal cross sections for for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$.

Expected exclusion limits for $m_X N / f = 1$ for signal cross sections for for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.005$. 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 $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.006$. 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 $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.007$. 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 $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.008$. 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 $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.009$. 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 $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.01$. 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 $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.011$. 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 $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.012$. 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 $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.013$. 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 $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.014$. 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 $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.015$. 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 $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.016$. 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 $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.017$. 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 $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.018$. 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 $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.019$. 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 $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.02$. 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 $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.021$. 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 $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.022$. 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 $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.023$. 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 $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.024$. 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 $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.025$. 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 $m_X N / f$.

Signal fractional efficiencies

Local significance in units of standard deviations in the $(m_\phi/m_X) − m_X$ plane.

The double ratio of particle yield of f0((980) to K*(892)0

Transverse-momentum-differential particle yield ratio of f$_{0}$(980) to charged pions and its double ratio

Transverse-momentum-differential particle yield ratio of f$_{0}$(980) to K$^{*}(892)$^{0}$ and its double ratio

Nuclear modification factor of f0(980) in p-Pb collisions at 5.02 TeV

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

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

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

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

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

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

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

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

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

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

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

Summary of the observed and expected 95% CL upper limits on the cross section for $\mathrm{LQ}_{\mathrm{mix}}^{\mathrm{d}}$ pair production as a function of $m_{\mathrm{LQ}_{\mathrm{mix}}^{\mathrm{d}}}$ under the assumptions of B(LQ$\rightarrow t\mu$)=1.

Summary of observed and predicted yields in the four signal region categories. The background prediction is shown after the combined likelihood fit to data under the background-only hypothesis across all control region and signal region categories. The expected signal yields that are obtained by using their theoretical cross sections are also shown with their pre-fit uncertainties, assuming B=1 and $\mu$=1. The "Other" contribution is dominated by $t\bar{t}t\bar{t}$ and $t\bar{t}WW$ in the $3\ell$ SRs, whereas it is dominated by $tWZ$ and $t\bar{t}WW$ in the $4\ell$ SRs. Dashes refer to components that are negligible or not applicable.

Summary of the data, background and signal yields in the four signal region categories. The background prediction is shown before the combined likelihood fit to data. Dashes (--) refer to components that are negligible or not applicable.

Summary of the data and background yields in the seven control region categories. The background prediction is shown before the combined likelihood fit to data. Dashes (--) refer to components that are negligible or not applicable.

Summary of the data and background yields in the seven control region categories. The background prediction is shown after the combined likelihood fit to data under the background-only hypothesis across all control region categories. Dashes (--) refer to components that are negligible or not applicable.

Data requested from authors.

Fully corrected assorted $\pi^{0}$-hadron conditional pair distributions for $d$+Au collisions centrality 0-88% and $p$+$p$ collisions. The trigger $\pi^0$s are within 5 < $p_{T,trig}$ < 10 GeV/$c$ and are correlated with hadrons with $p_{T,assoc}$ of 1.5-2 GeV/$c$, 2-3GeV/$c$, 3-4 GeV/$c$, and 4-5 GeV/$c$.

Near- and far-side widths as a function of $p_{T, assoc}$ for charged hadron azimuthal correlations from minimumbias $d$+Au collisions.

Near-side width, far-side width as a function of $p_{T,assoc}$ for a charged pion and neutral pion triggers from the $p_{T,trig}$ range of 5-10 GeV/$c$ in minimum bias $d$+Au collisions.

Near-side width, far-side width as a function of $p_{T,assoc}$ for a charged pion and neutral pion triggers from the $p_{T,trig}$ range of 5-10 GeV/$c$ in minimum bias $d$+Au collisions.

Near- and far-side conditional yields as a function of $p_{T, assoc}$ for charged hadron triggers (2.5−4 GeV/$c$) and associated charged hadrons from $d$+Au collisions.

Near- and far-side conditional yields as a function of $p_{T, assoc}$ for charged hadron triggers (4−6 GeV/$c$) and associated charged hadrons from $d$+Au collisions.

Near- and far-side conditional yields as a function of $p_{T, assoc}$ for charged pion triggers (5−10 GeV/$c$) and associated charged hadrons from minimum-bias $d$+Au collisions.

Near- and far-side conditional yields as a function of $p_{T, assoc}$ for neutral pion triggers (5−10 GeV/$c$) and associated charged hadrons from minimum-bias $d$+Au collisions.

Near- and far-side widths and conditional yields as a function of $N_{coll}$ for charged hadron triggers (2.5−4 GeV/$c$) and associated charged hadrons (1–2.5 GeV/$c$) from $d$+Au collisions.

Near- and far-side widths and conditional yields as a function of centrality for neutral pion triggers (5−10 GeV/$c$) and associated charged hadrons (2–3 GeV/$c$) from $d$+Au collisions.

The extracted $\sqrt{<j^2_T>}$ for minimum-bias $d$+Au collisions from all four dihadron correlations. The trigger $p_T$ ranges are 3 - 5 GeV/$c$, 5 - 10 GeV/$c$ and 5 - 10 GeV/$c$ for $h^{\pm}$ - $h^{\pm}$, $\pi^0$ - $h^{\pm}$ and $\pi^{\pm}$ - $h^{\pm}$ assorted-$p_T$ correlations.

The extracted $\sqrt{<j^2_T>}$ for minimum-bias $d$+Au collisions from all four dihadron correlations. The trigger $p_T$ ranges are 3 - 5 GeV/$c$, 5 - 10 GeV/$c$ and 5 - 10 GeV/$c$ for $h^{\pm}$ - $h^{\pm}$, $\pi^0$ - $h^{\pm}$ and $\pi^{\pm}$ - $h^{\pm}$ assorted-$p_T$ correlations.

The extracted $\sqrt{<j^2_T>}$ for minimum-bias $d$+Au collisions from all four dihadron correlations. The trigger $p_T$ ranges are 3 - 5 GeV/$c$, 5 - 10 GeV/$c$ and 5 - 10 GeV/$c$ for $h^{\pm}$ - $h^{\pm}$, $\pi^0$ - $h^{\pm}$ and $\pi^{\pm}$ - $h^{\pm}$ assorted-$p_T$ correlations.

The extracted $\sqrt{<j^2_T>}$ for minimum-bias $d$+Au collisions from all four dihadron correlations. The trigger $p_T$ ranges are 3 - 5 GeV/$c$, 5 - 10 GeV/$c$ and 5 - 10 GeV/$c$ for $h^{\pm}$ - $h^{\pm}$, $\pi^0$ - $h^{\pm}$ and $\pi^{\pm}$ - $h^{\pm}$ assorted-$p_T$ correlations.

$<sin^2(\phi_{jj})>$ for minimum bias $d$+Au collisions as function of associated particle $p_T$ for $\pi^{\pm}$ - $h^{\pm}$ and $\pi^0$ - $h^{\pm}$ correlations where the trigger particles have a $p_T$ between 5 - 10 GeV/$c$.

$<sin^2(\phi_{jj})>$ for minimum bias $d$+Au collisions as function of associated particle $p_T$ for $\pi^{\pm}$ - $h^{\pm}$ and $\pi^0$ - $h^{\pm}$ correlations where the trigger particles have a $p_T$ between 5 - 10 GeV/$c$.

$<sin^2(\phi_{jj})>$ for minimum bias $d$+Au collisions as function of trigger particle $p_T$ for $\pi^{\pm}$ - $h^{\pm}$ and $\pi^0$ - $h^{\pm}$ correlations.

$<sin^2(\phi_{jj})>$ for minimum bias $d$+Au collisions as function of trigger particle $p_T$ for $\pi^{\pm}$ - $h^{\pm}$ and $\pi^0$ - $h^{\pm}$ correlations.

Near-side and far-side $p_{out}$ distributions for minimum bias $d$+Au collisions obtained from $\pi^{\pm}$ - $h^{\pm}$ correlation. The trigger is 5 < $p_{T,trig}$ < 10 GeV/$c$, the associated particle is 0.5 < $p_{T,assoc}$ < 5.0 GeV/$c$.

Conditional yield as a function of $x_E$ for near-side and far-side for $\pi^{\pm}$ - $h^{\pm}$ and $\pi^0$ - $h^{\pm}$ from minimum-bias $d$+Au collisions.

Conditional yield as a function of $x_E$ for near-side and far-side for $\pi^{\pm}$ - $h^{\pm}$ and $\pi^0$ - $h^{\pm}$ from minimum-bias $d$+Au collisions.

Conditional yield as a function of $x_E$ for near-side and far-side correlations for $\pi^{\pm}$ - $h^{\pm}$ correlations from minimum-bias $d$+Au collisions. The trigger pions are 5 < $p_{T,trig}$ < 6 GeV/$c$.

Conditional yield as a function of $x_E$ for near-side and far-side correlation for $\pi^{\pm}$ - $h^{\pm}$ correlation for several different trigger $p_T$s for minimum-bias $d$+Au collisions.

Far-side conditional yield as a function of $p_{T,trig}$ for different ranges of $x_E$ for $\pi^{\pm}$ - $h^{\pm}$ correlation for minimum-bias $d$+Au collisions.

Far-side conditional yield as a function of $p_{T,trig}$ for different ranges of $x_E$ for $\pi^{\pm}$ - $h^{\pm}$ correlation for minimum-bias $d$+Au collisions.

Far-side conditional yield as a function of $p_{T,trig}$ for different ranges of $x_E$ for $\pi^{\pm}$ - $h^{\pm}$ correlation for minimum-bias $d$+Au collisions.

Far-side conditional yield as a function of $p_{T,trig}$ for different ranges of $x_E$ for $\pi^{\pm}$ - $h^{\pm}$ correlation for minimum-bias $d$+Au collisions.

The comparison of the $\sqrt{<j^2_T>}$ values between $d$+Au and $p$+$p$ for the $\pi^{\pm}$ - $h^{\pm}$ correlations and $\pi^0$ - $h^{\pm}$ correlations. The trigger pion range is 5 - 10 GeV/$c$.

The comparison of the $\sqrt{<j^2_T>}$ values between $d$+Au and $p$+$p$ for the $\pi^{\pm}$ - $h^{\pm}$ correlations and $\pi^0$ - $h^{\pm}$ correlations. The trigger pion range is 5 - 10 GeV/$c$.

Quadrature difference between minimum-bias $d$+Au and $p$+$p$ $<sin^2(\phi_{jj})>$ values.

Quadrature difference between minimum-bias $d$+Au and $p$+$p$ $<sin^2(\phi_{jj})>$ values.

The comparison of the $p_{out}$ distribution at the near-side and far-side between central $d$+Au collisions and $p$+$p$ collisions. Results are obtained for $\pi^{\pm}$ - $h^{\pm}$ correlations with the associated hadron range 0.5 < $p_{T,assoc}$ < 5 GeV/$c$ and trigger pion range of 5 < $p_{T,trig}$ < 10 GeV/$c$.

The comparison of the $x_E$ distribution from $\pi^{\pm}$ - $h^{\pm}$ correlation at the near-side and far-side between minimum bias $d$+Au collisions and $p$+$p$ collisions. The trigger $\pi^{\pm}$ are from 5 - 10 GeV/$c$.

Far-side conditional yield as a function of $p_{T,trig}$ for different ranges of $x_E$ from $p$+$p$ collisions, triggers are $\pi^{\pm}$ from 5 - 10 GeV/$c$.

Far-side conditional yield as a function of $p_{T,trig}$ for different ranges of $x_E$ from $p$+$p$ collisions, triggers are $\pi^{\pm}$ from 5 - 10 GeV/$c$.

Far-side conditional yield as a function of $p_{T,trig}$ for different ranges of $x_E$ from $p$+$p$ collisions, triggers are $\pi^{\pm}$ from 5 - 10 GeV/$c$.

The fitted fractional change in $dN/d_{x_E}$ per unit $p_{T,trig}$ of the far-side conditional yield for different ranges of $x_E$.

Centrality dependent near and far $CY(p_T)$ for $\pi^{\pm}$ - $h^{\pm}$ correlations and $\pi^0$ - $h^{\pm}$ correlations.

Centrality dependent near and far $CY(p_T)$ for $\pi^{\pm}$ - $h^{\pm}$ correlations and $\pi^0$ - $h^{\pm}$ correlations.

Centrality dependence to the ratio of near and far $CY(p_T)$ for $d$+Au to $p$+$p$.

Centrality dependence to the ratio of near and far $CY(p_T)$ for $d$+Au to $p$+$p$.

Near- and far-side widths as a function of $p_{T, trig}$ for charged pion triggers and associated charged hadrons (2–4.5 Gev/$c$) from minimum-bias $d$+Au collisions.

Near- and far-side widths as a function of $p_{T, trig}$ for neutral pion triggers and associated charged hadrons (2–4.5 Gev/$c$) from minimum-bias $d$+Au collisions.

The impact of the eight most important systematic uncertainties on \(R_t\), in %.

The post-fit yields in the two SRs. All uncertainties applied in the analysis are included.

Limits on EFT parameters and Vtb extracted from the analysis. The upper and lower limits correspond to 95% CL.

Results of the main analysis.

Pre-fit distribution of the NN discriminant \(D_{\text{nn}}\) in SR plus.

Post-fit distribution of the NN discriminant \(D_{\text{nn}}\) in SR plus.

Post-fit distribution of the \(\Delta\phi(\vec{p}_{T}^{miss},\mu)\) variable in the muon-plus CR.

Pre-fit distribution of the NN discriminant \(D_{\text{nn}}\) in SR minus.

Post-fit distribution of the NN discriminant \(D_{\text{nn}}\) in SR minus.

Post-fit distribution of the \(\Delta\phi(\vec{p}_{T}^{miss},\mu)\) variable in the muon-minus CR.

Pre-fit distribution of the invariant mass of the untagged jet and the b-tagged jet, \(m(jb)\), in SR plus.

Pre-fit distribution of the absolute value of the pseudorapidity of the untagged jet, \(|\eta(j)|\), in SR plus.

Pre-fit distribution of the absolute value of the difference in \(p_{\text{T}}\) between the reconstructed W boson and the jet pair, \(|\Delta p_{\text{T}}(W, jb)|\), in SR plus.

Pre-fit distribution of the difference in azimuth angle between the reconstructed W boson and the jet pair, \(|\Delta\phi(W, jb)|\), in SR plus.

Pre-fit distribution of the invariant mass of the reconstructed top quark, \(m(t)\), in SR plus.

Pre-fit distribution of the absolute value of the difference in pseudorapidity between the charged lepton and the untagged jet, \(|\Delta\eta(\ell ,j)|\), SR plus.

Pre-fit distribution of the angular distance of the charged lepton and the untagged jet, \(\Delta R(\ell ,j)\), in SR plus.

Pre-fit distribution of the absolute value of the difference in pseudorapidity between the b-tagged jet and the charged lepton, \(|\Delta\eta(b,\ell )|\), in SR plus.

Comparison of the observed (black points) and expected (histograms) numbers of events in nonoverlapping $m^{corr}_{\mu\mu}$ intervals in the STA-STA dimuon category, in the signal region optimized for the RPV SUSY model. Yellow and green stacked filled histograms represent mean expected background contributions from QCD and DY, respectively, while statistical uncertainties in the total expected background are shown as hatched histograms. Signal contributions expected from simulated signals indicated in the legends are shown in red and blue. Their yields are set to the corresponding median expected 95% CL exclusion limits obtained from the ensemble of both dimuon categories, scaled up as indicated in the legend to improve visibility. The last bin includes events in the histogram overflow.

Distribution of min($d_0 / \sigma_{d_0}$) for TMS-TMS dimuons with $|\Delta\Phi| < \pi/30$, for events in all mass intervals combined, for both the validation (min($d_0 / \sigma_{d_0}$) < 6) and signal (min($d_0 / \sigma_{d_0}$) > 6) regions. The number of observed events (black circles) is overlaid with the stacked histograms showing the expected numbers of QCD (yellow) and DY (green) background events. Statistical uncertainties in the total expected background are shown as hatched histograms. Signal contributions expected from simulated signals indicated in the legends are shown in red and blue. Their yields are set to the corresponding median expected 95% CL exclusion limits obtained from the ensemble of both dimuon categories, scaled up as indicated in the legend to improve visibility. Events are required to satisfy all nominal selection criteria with the exception of the $d_0 / \sigma_{d_0}$ requirement. The last bin includes events in the histogram overflow.

Distribution of min($d_0 / \sigma_{d_0}$) for TMS-TMS dimuons with $|\Delta\Phi| < \pi/4$, for events in all mass intervals combined, for both the validation (min($d_0 / \sigma_{d_0}$) < 6) and signal (min($d_0 / \sigma_{d_0}$) > 6) regions. The number of observed events (black circles) is overlaid with the stacked histograms showing the expected numbers of QCD (yellow) and DY (green) background events. Statistical uncertainties in the total expected background are shown as hatched histograms. Signal contributions expected from simulated signals indicated in the legends are shown in red and blue. Their yields are set to the corresponding median expected 95% CL exclusion limits obtained from the ensemble of both dimuon categories, scaled up as indicated in the legend to improve visibility. Events are required to satisfy all nominal selection criteria with the exception of the $d_0 / \sigma_{d_0}$ requirement. The last bin includes events in the histogram overflow.

Comparison of observed and expected numbers of events in bins of $m^{corr}_{\mu\mu}$ in the TMS-TMS dimuon category, in the signal regions optimized for the RPV SUSY model. The number of observed events (black circles) is overlaid with the stacked filled histograms showing the expected numbers of QCD (yellow) and DY (green) background events in bins of $m^{corr}_{\mu\mu}$ in min($d_0 / \sigma_{d_0}$) bin: 6-10. Hatched histograms show statistical uncertainties in the total expected background. Contributions expected from signal events predicted by the RPV SUSY model with the parameters indicated in the legends are shown as red and blue histograms. Their yields are set to the corresponding median expected 95% CL exclusion limits obtained from the ensemble of both dimuon categories, scaled up as indicated in the legend to improve visibility. The last bin includes events in the histogram overflow.

Comparison of observed and expected numbers of events in bins of $m^{corr}_{\mu\mu}$ in the TMS-TMS dimuon category, in the signal regions optimized for the RPV SUSY model. The number of observed events (black circles) is overlaid with the stacked filled histograms showing the expected numbers of QCD (yellow) and DY (green) background events in bins of $m^{corr}_{\mu\mu}$ in min($d_0 / \sigma_{d_0}$) bin: 10-20. Hatched histograms show statistical uncertainties in the total expected background. Contributions expected from signal events predicted by the RPV SUSY model with the parameters indicated in the legends are shown as red and blue histograms. Their yields are set to the corresponding median expected 95% CL exclusion limits obtained from the ensemble of both dimuon categories, scaled up as indicated in the legend to improve visibility. The last bin includes events in the histogram overflow.

Comparison of observed and expected numbers of events in bins of $m^{corr}_{\mu\mu}$ in the TMS-TMS dimuon category, in the signal regions optimized for the RPV SUSY model. The number of observed events (black circles) is overlaid with the stacked filled histograms showing the expected numbers of QCD (yellow) and DY (green) background events in bins of $m^{corr}_{\mu\mu}$ in min($d_0 / \sigma_{d_0}$) bin: >20. Hatched histograms show statistical uncertainties in the total expected background. Contributions expected from signal events predicted by the RPV SUSY model with the parameters indicated in the legends are shown as red and blue histograms. Their yields are set to the corresponding median expected 95% CL exclusion limits obtained from the ensemble of both dimuon categories, scaled up as indicated in the legend to improve visibility. The last bin includes events in the histogram overflow.

Comparison of observed and expected numbers of events in bins of $m_{\mu\mu}$ in the TMS-TMS dimuon category, in the signal regions optimized for the HAHM. The number of observed events (black circles) is overlaid with the stacked filled histograms showing the expected numbers of QCD (yellow) and DY (green) background events in bins of $m_{\mu\mu}$ in min($d_0 / \sigma_{d_0}$) bin: 6-10. Hatched histograms show statistical uncertainties in the total expected background. Signal contributions expected from simulated $H \rightarrow Z_DZ_D$ events with the parameters indicated in the legends are shown as red and blue histograms. Their yields are set to the corresponding median expected 95% CL exclusion limits obtained from the ensemble of both dimuon categories, scaled up as indicated in the legend to improve visibility. The last bin includes events in the histogram overflow.

Comparison of observed and expected numbers of events in bins of $m_{\mu\mu}$ in the TMS-TMS dimuon category, in the signal regions optimized for the HAHM. The number of observed events (black circles) is overlaid with the stacked filled histograms showing the expected numbers of QCD (yellow) and DY (green) background events in bins of $m_{\mu\mu}$ in min($d_0 / \sigma_{d_0}$) bin: 10-20. Hatched histograms show statistical uncertainties in the total expected background. Signal contributions expected from simulated $H \rightarrow Z_DZ_D$ events with the parameters indicated in the legends are shown as red and blue histograms. Their yields are set to the corresponding median expected 95% CL exclusion limits obtained from the ensemble of both dimuon categories, scaled up as indicated in the legend to improve visibility. The last bin includes events in the histogram overflow.

Comparison of observed and expected numbers of events in bins of $m_{\mu\mu}$ in the TMS-TMS dimuon category, in the signal regions optimized for the HAHM. The number of observed events (black circles) is overlaid with the stacked filled histograms showing the expected numbers of QCD (yellow) and DY (green) background events in bins of $m_{\mu\mu}$ in min($d_0 / \sigma_{d_0}$) bin: >20. Hatched histograms show statistical uncertainties in the total expected background. Signal contributions expected from simulated $H \rightarrow Z_DZ_D$ events with the parameters indicated in the legends are shown as red and blue histograms. Their yields are set to the corresponding median expected 95% CL exclusion limits obtained from the ensemble of both dimuon categories, scaled up as indicated in the legend to improve visibility. The last bin includes events in the histogram overflow.

The 95% CL upper limits on $B(H \rightarrow Z_DZ_D)$ as a function of $c\tau(Z_D)$ in the HAHM model, for $m(Z_D) = 10\ GeV$, in the STA-STA and TMS-TMS dimuon categories in 2022 data and their combination.The median expected limits obtained from the STA-STA and TMS-TMS dimuon categories are shown as dashed blue and red curves, respectively; the combined median expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits.

The 95% CL upper limits on $B(H \rightarrow Z_DZ_D)$ as a function of $c\tau(Z_D)$ in the HAHM model, for $m(Z_D) = 20\ GeV$, in the STA-STA and TMS-TMS dimuon categories in 2022 data and their combination.The median expected limits obtained from the STA-STA and TMS-TMS dimuon categories are shown as dashed blue and red curves, respectively; the combined median expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits.

The 95% CL upper limits on $B(H \rightarrow Z_DZ_D)$ as a function of $c\tau(Z_D)$ in the HAHM model, for $m(Z_D) = 30\ GeV$, in the STA-STA and TMS-TMS dimuon categories in 2022 data and their combination.The median expected limits obtained from the STA-STA and TMS-TMS dimuon categories are shown as dashed blue and red curves, respectively; the combined median expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits.

The 95% CL upper limits on $B(H \rightarrow Z_DZ_D)$ as a function of $c\tau(Z_D)$ in the HAHM model, for $m(Z_D) = 40\ GeV$, in the STA-STA and TMS-TMS dimuon categories in 2022 data and their combination.The median expected limits obtained from the STA-STA and TMS-TMS dimuon categories are shown as dashed blue and red curves, respectively; the combined median expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits.

The 95% CL upper limits on $B(H \rightarrow Z_DZ_D)$ as a function of $c\tau(Z_D)$ in the HAHM model, for $m(Z_D) = 50\ GeV$, in the STA-STA and TMS-TMS dimuon categories in 2022 data and their combination.The median expected limits obtained from the STA-STA and TMS-TMS dimuon categories are shown as dashed blue and red curves, respectively; the combined median expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits.

The 95% CL upper limits on $B(H \rightarrow Z_DZ_D)$ as a function of $c\tau(Z_D)$ in the HAHM model, for $m(Z_D) = 60\ GeV$, in the STA-STA and TMS-TMS dimuon categories in 2022 data and their combination.The median expected limits obtained from the STA-STA and TMS-TMS dimuon categories are shown as dashed blue and red curves, respectively; the combined median expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits.

The 95% CL upper limits on $B(H \rightarrow Z_DZ_D)$ as a function of $c\tau(Z_D)$ in the HAHM model, for $m(Z_D) = 10\ GeV$, obtained in this analysis, the Run 2 analysis, and their combination. The observed limits in this analysis and in the Run 2 analysis are shown as blue and red curves, respectively; the median combined expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits.

The 95% CL upper limits on $B(H \rightarrow Z_DZ_D)$ as a function of $c\tau(Z_D)$ in the HAHM model, for $m(Z_D) = 20\ GeV$, obtained in this analysis, the Run 2 analysis, and their combination. The observed limits in this analysis and in the Run 2 analysis are shown as blue and red curves, respectively; the median combined expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits.

The 95% CL upper limits on $B(H \rightarrow Z_DZ_D)$ as a function of $c\tau(Z_D)$ in the HAHM model, for $m(Z_D) = 30\ GeV$, obtained in this analysis, the Run 2 analysis, and their combination. The observed limits in this analysis and in the Run 2 analysis are shown as blue and red curves, respectively; the median combined expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits.

The 95% CL upper limits on $B(H \rightarrow Z_DZ_D)$ as a function of $c\tau(Z_D)$ in the HAHM model, for $m(Z_D) = 40\ GeV$, obtained in this analysis, the Run 2 analysis, and their combination. The observed limits in this analysis and in the Run 2 analysis are shown as blue and red curves, respectively; the median combined expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits.

The 95% CL upper limits on $B(H \rightarrow Z_DZ_D)$ as a function of $c\tau(Z_D)$ in the HAHM model, for $m(Z_D) = 50\ GeV$, obtained in this analysis, the Run 2 analysis, and their combination. The observed limits in this analysis and in the Run 2 analysis are shown as blue and red curves, respectively; the median combined expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits.

The 95% CL upper limits on $B(H \rightarrow Z_DZ_D)$ as a function of $c\tau(Z_D)$ in the HAHM model, for $m(Z_D) = 60\ GeV$, obtained in this analysis, the Run 2 analysis, and their combination. The observed limits in this analysis and in the Run 2 analysis are shown as blue and red curves, respectively; the median combined expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits.

The 95% CL upper limits on $\sigma(pp \rightarrow \tilde{q}\bar{\tilde{q}})B(\tilde{q} \rightarrow q\tilde{\chi}^{0}_{1})$ as a function of $c\tau(\tilde{\chi}^{0}_{1})$ in the RPV SUSY model, for $B(\tilde{\chi}^{0}_{1} \rightarrow \mu^{+}\mu^{-}\nu) = 0.5$ and $m(\tilde{q}) = 125\ GeV$. The observed limits for various $m(\tilde{\chi}^{0}_{1})$ indicated in the legends are shown as solid curves. The median expected limits and their 68 and 95% quantiles are shown, respectively, as dashed black curves and green and yellow bands for the case of $m(\tilde{\chi}^{0}_{1}) = 50\ GeV$ and omitted for other neutralino masses for clarity. The predicted cross section for $m(\tilde{q}) = 125\ GeV$ is 7200 pb, and falls outside the y-axis range.

The 95% CL upper limits on $\sigma(pp \rightarrow \tilde{q}\bar{\tilde{q}})B(\tilde{q} \rightarrow q\tilde{\chi}^{0}_{1})$ as a function of $c\tau(\tilde{\chi}^{0}_{1})$ in the RPV SUSY model, for $B(\tilde{\chi}^{0}_{1} \rightarrow \mu^{+}\mu^{-}\nu) = 0.5$ and $m(\tilde{q}) = 200\ GeV$. The observed limits for various $m(\tilde{\chi}^{0}_{1})$ indicated in the legends are shown as solid curves. The median expected limits and their 68 and 95% quantiles are shown, respectively, as dashed black curves and green and yellow bands for the case of $m(\tilde{\chi}^{0}_{1}) = 50\ GeV$ and omitted for other neutralino masses for clarity. The predicted cross section for $m(\tilde{q}) = 200 GeV$ is 840 pb, and falls outside the y-axis range.

The 95% CL upper limits on $\sigma(pp \rightarrow \tilde{q}\bar{\tilde{q}})B(\tilde{q} \rightarrow q\tilde{\chi}^{0}_{1})$ as a function of $c\tau(\tilde{\chi}^{0}_{1})$ in the RPV SUSY model, for $B(\tilde{\chi}^{0}_{1} \rightarrow \mu^{+}\mu^{-}\nu) = 0.5$ and $m(\tilde{q}) = 350\ GeV$. The observed limits for various $m(\tilde{\chi}^{0}_{1})$ indicated in the legends are shown as solid curves. The median expected limits and their 68 and 95% quantiles are shown, respectively, as dashed black curves and green and yellow bands for the case of $m(\tilde{\chi}^{0}_{1}) = 50\ GeV$ and omitted for other neutralino masses for clarity. The predicted cross section for $m(\tilde{q}) = 350\ GeV$ is 50 pb, and falls outside the y-axis range.

The 95% CL upper limits on $\sigma(pp \rightarrow \tilde{q}\bar{\tilde{q}})B(\tilde{q} \rightarrow q\tilde{\chi}^{0}_{1})$ as a function of $c\tau(\tilde{\chi}^{0}_{1})$ in the RPV SUSY model, for $B(\tilde{\chi}^{0}_{1} \rightarrow \mu^{+}\mu^{-}\nu) = 0.5$ and $m(\tilde{q}) = 700\ GeV$. The observed limits for various $m(\tilde{\chi}^{0}_{1})$ indicated in the legends are shown as solid curves. The median expected limits and their 68 and 95% quantiles are shown, respectively, as dashed black curves and green and yellow bands for the case of $m(\tilde{\chi}^{0}_{1}) = 50\ GeV$ and omitted for other neutralino masses for clarity. The gray horizontal line indicates the theoretical value of the squark-antisquark production cross section with the uncertainties shown as the gray shaded band.

The 95% CL upper limits on $\sigma(pp \rightarrow \tilde{q}\bar{\tilde{q}})B(\tilde{q} \rightarrow q\tilde{\chi}^{0}_{1})$ as a function of $c\tau(\tilde{\chi}^{0}_{1})$ in the RPV SUSY model, for $B(\tilde{\chi}^{0}_{1} \rightarrow \mu^{+}\mu^{-}\nu) = 0.5$ and $m(\tilde{q}) = 1150\ GeV$. The observed limits for various $m(\tilde{\chi}^{0}_{1})$ indicated in the legends are shown as solid curves. The median expected limits and their 68 and 95% quantiles are shown, respectively, as dashed black curves and green and yellow bands for the case of $m(\tilde{\chi}^{0}_{1}) = 50\ GeV$ and omitted for other neutralino masses for clarity. The gray horizontal line indicates the theoretical value of the squark-antisquark production cross section with the uncertainties shown as the gray shaded band.

The 95% CL upper limits on $\sigma(pp \rightarrow \tilde{q}\bar{\tilde{q}})B(\tilde{q} \rightarrow q\tilde{\chi}^{0}_{1})$ as a function of $c\tau(\tilde{\chi}^{0}_{1})$ in the RPV SUSY model, for $B(\tilde{\chi}^{0}_{1} \rightarrow \mu^{+}\mu^{-}\nu) = 0.5$ and $m(\tilde{q}) = 1600\ GeV$. The observed limits for various $m(\tilde{\chi}^{0}_{1})$ indicated in the legends are shown as solid curves. The median expected limits and their 68 and 95% quantiles are shown, respectively, as dashed black curves and green and yellow bands for the case of $m(\tilde{\chi}^{0}_{1}) = 50\ GeV$ and omitted for other neutralino masses for clarity. The gray horizontal line indicates the theoretical value of the squark-antisquark production cross section with the uncertainties shown as the gray shaded band.

Fractions of signal events with zero (green), one (blue), and two (red) STA muons matched to TMS muons by the STA to TMS association procedure, as a function of generated $L_{xy}$, in all HAHM signal samples combined.

Efficiencies of the Run 2 and Run 3 displaced dimuon triggers as a function of $c\tau$ for the HAHM signal events with $m(Z_D) = 50\ GeV$. The efficiency is defined as the fraction of simulated events that satisfy the requirements of the following sets of trigger paths: the Run 2 (2018) triggers (dashed black); the Run 3 (2022, L3) triggers (blue); the Run 3 (2022, L2) triggers (red); and the OR of all these triggers (Run 3 (2022), black). The lower panel shows the ratio of the overall Run 3 (2022) efficiency to the Run 2 (2018) efficiency.

Efficiencies of the Run 2 (2018) (red) and Run 3 (2022) (black) sets of displaced dimuon triggers as a function of $m(Z_D)$ for the HAHM signal events with $c\tau = 1\ cm$. The efficiency is defined as the fraction of simulated events that satisfy the detector acceptance and the requirements of the indicated set of trigger paths. The lower panel shows the ratio of the Run 3 (2022) efficiency to the Run 2 (2018) efficiency.

Efficiencies of the Run 2 (2018) (red) and Run 3 (2022) (black) sets of displaced dimuon triggers as a function of $m(Z_D)$ for the HAHM signal events with $c\tau = 10\ m$. The efficiency is defined as the fraction of simulated events that satisfy the detector acceptance and the requirements of the indicated set of trigger paths. The lower panel shows the ratio of the Run 3 (2022) efficiency to the Run 2 (2018) efficiency.

Overall selection efficiencies as a function of $c\tau(Z_D)$ for the HAHM signal with $m(Z_D) = 20\ GeV$ in different years of data taking. Efficiencies are computed as the ratios of the number of simulated signal events in which at least one dimuon candidate passes all 2016 (dashed green), 2018 (dashed red), and 2022 (solid black) trigger and offline selection criteria to the total number of simulated signal events. The lower panel shows the ratio of the 2022 efficiency to the 2018 efficiency (dashed red) and to the 2016 efficiency (dashed green).

Overall selection efficiencies as a function of $c\tau(Z_D)$ for the HAHM signal with $m(Z_D) = 50\ GeV$ in different years of data taking. Efficiencies are computed as the ratios of the number of simulated signal events in which at least one dimuon candidate passes all 2016 (dashed green), 2018 (dashed red), and 2022 (solid black) trigger and offline selection criteria to the total number of simulated signal events. The lower panel shows the ratio of the 2022 efficiency to the 2018 efficiency (dashed red) and to the 2016 efficiency (dashed green).

Overall selection efficiencies as a function of $c\tau(Z_D)$ for the HAHM model with $m(Z_D) = 10\ GeV$. The plot shows efficiencies of the two dimuon categories, TMS-TMS (dashed red) and STA-STA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the data-to-simulation scale factors described in the paper.

Overall selection efficiencies as a function of $c\tau(Z_D)$ for the HAHM model with $m(Z_D) = 20\ GeV$. The plot shows efficiencies of the two dimuon categories, TMS-TMS (dashed red) and STA-STA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the data-to-simulation scale factors described in the paper.

Overall selection efficiencies as a function of $c\tau(Z_D)$ for the HAHM model with $m(Z_D) = 30\ GeV$. The plot shows efficiencies of the two dimuon categories, TMS-TMS (dashed red) and STA-STA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the data-to-simulation scale factors described in the paper.

Overall selection efficiencies as a function of $c\tau(Z_D)$ for the HAHM model with $m(Z_D) = 40\ GeV$. The plot shows efficiencies of the two dimuon categories, TMS-TMS (dashed red) and STA-STA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the data-to-simulation scale factors described in the paper.

Overall selection efficiencies as a function of $c\tau(Z_D)$ for the HAHM model with $m(Z_D) = 50\ GeV$. The plot shows efficiencies of the two dimuon categories, TMS-TMS (dashed red) and STA-STA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the data-to-simulation scale factors described in the paper.

Overall selection efficiencies as a function of $c\tau(Z_D)$ for the HAHM model with $m(Z_D) = 60\ GeV$. The plot shows efficiencies of the two dimuon categories, TMS-TMS (dashed red) and STA-STA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the data-to-simulation scale factors described in the paper.

Overall selection efficiencies as a function of $c\tau(\tilde{\chi}^{0}_{1})$ for the RPV SUSY model, for events with $m(\tilde{q}) = 125\ GeV$ and $m(\tilde{\chi}^{0}_{1}) = 50\ GeV$. The plot shows efficiencies of the two dimuon categories, TMS-TMS (dashed red) and STA-STA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the data-to-simulation scale factors described in the paper.

Overall selection efficiencies as a function of $c\tau(\tilde{\chi}^{0}_{1})$ for the RPV SUSY model, for events with $m(\tilde{q}) = 200\ GeV$ and $m(\tilde{\chi}^{0}_{1}) = 50\ GeV$. The plot shows efficiencies of the two dimuon categories, TMS-TMS (dashed red) and STA-STA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the data-to-simulation scale factors described in the paper.

Overall selection efficiencies as a function of $c\tau(\tilde{\chi}^{0}_{1})$ for the RPV SUSY model, for events with $m(\tilde{q}) = 350\ GeV$ and $m(\tilde{\chi}^{0}_{1}) = 50\ GeV$. The plot shows efficiencies of the two dimuon categories, TMS-TMS (dashed red) and STA-STA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the data-to-simulation scale factors described in the paper.

Overall selection efficiencies as a function of $c\tau(\tilde{\chi}^{0}_{1})$ for the RPV SUSY model, for events with $m(\tilde{q}) = 700\ GeV$ and $m(\tilde{\chi}^{0}_{1}) = 50\ GeV$. The plot shows efficiencies of the two dimuon categories, TMS-TMS (dashed red) and STA-STA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the data-to-simulation scale factors described in the paper.

Overall selection efficiencies as a function of $c\tau(\tilde{\chi}^{0}_{1})$ for the RPV SUSY model, for events with $m(\tilde{q}) = 1150\ GeV$ and $m(\tilde{\chi}^{0}_{1}) = 50\ GeV$. The plot shows efficiencies of the two dimuon categories, TMS-TMS (dashed red) and STA-STA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the data-to-simulation scale factors described in the paper.

Overall selection efficiencies as a function of $c\tau(\tilde{\chi}^{0}_{1})$ for the RPV SUSY model, for events with $m(\tilde{q}) = 1600\ GeV$ and $m(\tilde{\chi}^{0}_{1}) = 50\ GeV$. The plot shows efficiencies of the two dimuon categories, TMS-TMS (dashed red) and STA-STA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the data-to-simulation scale factors described in the paper.

Overall selection efficiencies as a function of $c\tau(\tilde{\chi}^{0}_{1})$ for the RPV SUSY model, for events with $m(\tilde{q}) = 700\ GeV$ and $m(\tilde{\chi}^{0}_{1}) = 500\ GeV$. The plot shows efficiencies of the two dimuon categories, TMS-TMS (dashed red) and STA-STA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the data-to-simulation scale factors described in the paper.

Overall selection efficiencies as a function of $c\tau(\tilde{\chi}^{0}_{1})$ for the RPV SUSY model, for events with $m(\tilde{q}) = 1150\ GeV$ and $m(\tilde{\chi}^{0}_{1}) = 500\ GeV$. The plot shows efficiencies of the two dimuon categories, TMS-TMS (dashed red) and STA-STA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the data-to-simulation scale factors described in the paper.

Overall selection efficiencies as a function of $c\tau(\tilde{\chi}^{0}_{1})$ for the RPV SUSY model, for events with $m(\tilde{q}) = 1600\ GeV$ and $m(\tilde{\chi}^{0}_{1}) = 500\ GeV$. The plot shows efficiencies of the two dimuon categories, TMS-TMS (dashed red) and STA-STA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the data-to-simulation scale factors described in the paper.

Signal efficiencies in the TMS-TMS dimuon category as a function of the smaller of the two values of generated muon $p_T$ and $d_0$ in dimuons with $L_{xy}^\mathrm{true}$ smaller than 20 cm in the HAHM signal model. The efficiency in each bin is computed as the ratio of the number of simulated signal dimuons in that bin that pass the trigger requirements and selection criteria to the total number of simulated signal dimuons in that bin and within the geometric acceptance. The geometric acceptance is defined as the generated longitudinal decay length $L_{z}$ smaller than $8\ m$ and $|\eta^\mathrm{true}|$ of both generated muons forming the dimuon smaller than 2.0. The efficiencies obtained from simulation were further corrected by the data-to-simulation scale factors described in the paper.

Signal efficiencies in the STA-STA dimuon category as a function of the smaller of the two values of generated muon $p_T$ and $d_0$ in dimuons with $L_{xy}^\mathrm{true}$ smaller than 20 cm in the HAHM signal model. The efficiency in each bin is computed as the ratio of the number of simulated signal dimuons in that bin that pass the trigger requirements and selection criteria to the total number of simulated signal dimuons in that bin and within the geometric acceptance. The geometric acceptance is defined as the generated longitudinal decay length $L_{z}$ smaller than $8\ m$ and $|\eta^\mathrm{true}|$ of both generated muons forming the dimuon smaller than 2.0. The efficiencies obtained from simulation were further corrected by the data-to-simulation scale factors described in the paper.

Signal efficiencies in the TMS-TMS dimuon category as a function of the smaller of the two values of generated muon $p_T$ and $d_0$ in dimuons with $L_{xy}^\mathrm{true}$ 20-70 cm in the HAHM signal model. The efficiency in each bin is computed as the ratio of the number of simulated signal dimuons in that bin that pass the trigger requirements and selection criteria to the total number of simulated signal dimuons in that bin and within the geometric acceptance. The geometric acceptance is defined as the generated longitudinal decay length $L_{z}$ smaller than $8\ m$ and $|\eta^\mathrm{true}|$ of both generated muons forming the dimuon smaller than 2.0. The efficiencies obtained from simulation were further corrected by the data-to-simulation scale factors described in the paper.

Signal efficiencies in the STA-STA dimuon category as a function of the smaller of the two values of generated muon $p_T$ and $d_0$ in dimuons with $L_{xy}^\mathrm{true}$ 20-70 cm in the HAHM signal model. The efficiency in each bin is computed as the ratio of the number of simulated signal dimuons in that bin that pass the trigger requirements and selection criteria to the total number of simulated signal dimuons in that bin and within the geometric acceptance. The geometric acceptance is defined as the generated longitudinal decay length $L_{z}$ smaller than $8\ m$ and $|\eta^\mathrm{true}|$ of both generated muons forming the dimuon smaller than 2.0. The efficiencies obtained from simulation were further corrected by the data-to-simulation scale factors described in the paper.

Signal efficiencies in the STA-STA dimuon category as a function of the smaller of the two values of generated muon $p_T$ and $d_0$ in dimuons with $L_{xy}^\mathrm{true}$ 70-500 cm in the HAHM signal model. The efficiency in each bin is computed as the ratio of the number of simulated signal dimuons in that bin that pass the trigger requirements and selection criteria to the total number of simulated signal dimuons in that bin and within the geometric acceptance. The geometric acceptance is defined as the generated longitudinal decay length $L_{z}$ smaller than $8\ m$ and $|\eta^\mathrm{true}|$ of both generated muons forming the dimuon smaller than 2.0. The efficiencies obtained from simulation were further corrected by the data-to-simulation scale factors described in the paper.

Signal efficiencies in the TMS-TMS dimuon category as a function of the smaller of the two values of generated muon $p_T$ and $d_0$ in dimuons with $L_{xy}^\mathrm{true}$ smaller than 20 cm in the RPV SUSY signal model. The efficiency in each bin is computed as the ratio of the number of simulated signal dimuons in that bin that pass the trigger requirements and selection criteria to the total number of simulated signal dimuons in that bin and within the geometric acceptance. The geometric acceptance is defined as the generated longitudinal decay length $L_{z}$ smaller than $8\ m$ and $|\eta^\mathrm{true}|$ of both generated muons forming the dimuon smaller than 2.0. The efficiencies obtained from simulation were further corrected by the data-to-simulation scale factors described in the paper.

Signal efficiencies in the STA-STA dimuon category as a function of the smaller of the two values of generated muon $p_T$ and $d_0$ in dimuons with $L_{xy}^\mathrm{true}$ smaller than 20 cm in the RPV SUSY signal model. The efficiency in each bin is computed as the ratio of the number of simulated signal dimuons in that bin that pass the trigger requirements and selection criteria to the total number of simulated signal dimuons in that bin and within the geometric acceptance. The geometric acceptance is defined as the generated longitudinal decay length $L_{z}$ smaller than $8\ m$ and $|\eta^\mathrm{true}|$ of both generated muons forming the dimuon smaller than 2.0. The efficiencies obtained from simulation were further corrected by the data-to-simulation scale factors described in the paper.

Signal efficiencies in the TMS-TMS dimuon category as a function of the smaller of the two values of generated muon $p_T$ and $d_0$ in dimuons with $L_{xy}^\mathrm{true}$ 20-70 cm in the RPV SUSY signal model. The efficiency in each bin is computed as the ratio of the number of simulated signal dimuons in that bin that pass the trigger requirements and selection criteria to the total number of simulated signal dimuons in that bin and within the geometric acceptance. The geometric acceptance is defined as the generated longitudinal decay length $L_{z}$ smaller than $8\ m$ and $|\eta^\mathrm{true}|$ of both generated muons forming the dimuon smaller than 2.0. The efficiencies obtained from simulation were further corrected by the data-to-simulation scale factors described in the paper.

Signal efficiencies in the STA-STA dimuon category as a function of the smaller of the two values of generated muon $p_T$ and $d_0$ in dimuons with $L_{xy}^\mathrm{true}$ 20-70 cm in the RPV SUSY signal model. The efficiency in each bin is computed as the ratio of the number of simulated signal dimuons in that bin that pass the trigger requirements and selection criteria to the total number of simulated signal dimuons in that bin and within the geometric acceptance. The geometric acceptance is defined as the generated longitudinal decay length $L_{z}$ smaller than $8\ m$ and $|\eta^\mathrm{true}|$ of both generated muons forming the dimuon smaller than 2.0. The efficiencies obtained from simulation were further corrected by the data-to-simulation scale factors described in the paper.

Signal efficiencies in the STA-STA dimuon category as a function of the smaller of the two values of generated muon $p_T$ and $d_0$ in dimuons with $L_{xy}^\mathrm{true}$ 70-500 cm in the RPV SUSY signal model. The efficiency in each bin is computed as the ratio of the number of simulated signal dimuons in that bin that pass the trigger requirements and selection criteria to the total number of simulated signal dimuons in that bin and within the geometric acceptance. The geometric acceptance is defined as the generated longitudinal decay length $L_{z}$ smaller than $8\ m$ and $|\eta^\mathrm{true}|$ of both generated muons forming the dimuon smaller than 2.0. The efficiencies obtained from simulation were further corrected by the data-to-simulation scale factors described in the paper.