Observed profile likelihood scans of $\kappa_\lambda$. The scans are performed by varying only the coupling modifier of interest, while all other relevant coupling modifiers are fixed to unity.

Expected profile likelihood scans of $\kappa_\lambda$. The scans are performed by varying only the coupling modifier of interest, while all other relevant coupling modifiers are fixed to unity.

Observed profile likelihood scans of $\kappa_{2V}$. The scans are performed by varying only the coupling modifier of interest, while all other relevant coupling modifiers are fixed to unity.

Expected profile likelihood scans of $\kappa_{2V}$. The scans are performed by varying only the coupling modifier of interest, while all other relevant coupling modifiers are fixed to unity.

Confidence level contours at 68% (solid line) and 95% (dashed line) in the $(\kappa_\lambda, \kappa_{2V})$ parameter space, when all other coupling modifiers are fixed to their SM predictions. The corresponding expected contours are shown by the inner and outer shaded regions The SM prediction is indicated by the star, while the best-fit value is denoted by the cross.

Confidence level contours at 68% (solid line) and 95% (dashed line) in the $(\kappa_\lambda, \kappa_{2V})$ parameter space, when all other coupling modifiers are fixed to their SM predictions. The corresponding expected contours are shown by the inner and outer shaded regions The SM prediction is indicated by the star, while the best-fit value is denoted by the cross.

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 2. 3he lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

The expected number of events (estimated by using simulation) from the SM HH signals and single Higgs boson production, and the expected number of events from the continuum background, evaluated in the 120 GeV < $m_{\gamma\gamma}$ < 130 GeV window in Run 3 for the different low-mass (LM) and high-mass (HM) categories. For comparison, the number of data events is also shown. The uncertainties in the HH signals and single Higgs boson backgrounds include the systematic uncertainties discussed in Section 6. Asymmetric uncertainties arise primarily from the theory calculation of the SM ggF HH cross section and the large uncertainty in the yield of single Higgs bosons produced in ggF events in association with heavy-flavour jets. The uncertainty in the continuum background is given by the sum in quadrature of the statistical uncertainty from the fit to the data and the spurious signal uncertainty.

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-ej and (c, d) SR-2L-ej of the e+light-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_de) = (2.0&nbsp;TeV, 1.0) and S&#771;₁ (m, y_de) = (3.0&nbsp;TeV, 1.0), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-&mu;j and (c, d) SR-2L-&mu;j of the &mu;+light-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_s&mu;) = (2.0&nbsp;TeV, 1.5) and S&#771;₁ (m, y_s&mu;) = (3.0&nbsp;TeV, 1.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-&mu;j and (c, d) SR-2L-&mu;j of the &mu;+light-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_s&mu;) = (2.0&nbsp;TeV, 1.5) and S&#771;₁ (m, y_s&mu;) = (3.0&nbsp;TeV, 1.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-&mu;j and (c, d) SR-2L-&mu;j of the &mu;+light-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_s&mu;) = (2.0&nbsp;TeV, 1.5) and S&#771;₁ (m, y_s&mu;) = (3.0&nbsp;TeV, 1.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-&mu;j and (c, d) SR-2L-&mu;j of the &mu;+light-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_s&mu;) = (2.0&nbsp;TeV, 1.5) and S&#771;₁ (m, y_s&mu;) = (3.0&nbsp;TeV, 1.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-eb and (c, d) SR-2L-eb of the e+b-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_be) = (1.5&nbsp;TeV, 2.5) and S&#771;₁ (m, y_be) = (2.0&nbsp;TeV, 2.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-eb and (c, d) SR-2L-eb of the e+b-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_be) = (1.5&nbsp;TeV, 2.5) and S&#771;₁ (m, y_be) = (2.0&nbsp;TeV, 2.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-eb and (c, d) SR-2L-eb of the e+b-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_be) = (1.5&nbsp;TeV, 2.5) and S&#771;₁ (m, y_be) = (2.0&nbsp;TeV, 2.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-eb and (c, d) SR-2L-eb of the e+b-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_be) = (1.5&nbsp;TeV, 2.5) and S&#771;₁ (m, y_be) = (2.0&nbsp;TeV, 2.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-&mu;b and (c, d) SR-2L-&mu;b of the &mu;+b-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_b&mu;) = (1.5&nbsp;TeV, 1.5) and S&#771;₁ (m, y_b&mu;) = (2.0&nbsp;TeV, 1.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-&mu;b and (c, d) SR-2L-&mu;b of the &mu;+b-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_b&mu;) = (1.5&nbsp;TeV, 1.5) and S&#771;₁ (m, y_b&mu;) = (2.0&nbsp;TeV, 1.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-&mu;b and (c, d) SR-2L-&mu;b of the &mu;+b-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_b&mu;) = (1.5&nbsp;TeV, 1.5) and S&#771;₁ (m, y_b&mu;) = (2.0&nbsp;TeV, 1.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-&mu;b and (c, d) SR-2L-&mu;b of the &mu;+b-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_b&mu;) = (1.5&nbsp;TeV, 1.5) and S&#771;₁ (m, y_b&mu;) = (2.0&nbsp;TeV, 1.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Exclusion limits for minimal models of S&#771;₁ production with only y_de being non-zero obtained from a simultaneous fit to SR-1L and SR-2L of the e+light-jet channel combining Run-2 and Run-3 data. All limits are computed at 95&percnt; CL and the observed (red solid lines) and expected (black dashed lines) exclusion limits are shown in the m(S&#771;₁) &ndash; y_de plane. The observed exclusion should be interpreted as the region above the red line. The yellow inner (green outer) shaded band around the expected limits corresponds to the &plusmn;1 &sigma; (&plusmn;2 &sigma;) variations of the expected limit, accounting for all uncertainties. The observed limit obtained from ATLAS searches for LQ pair production is also shown as dark blue line [13]. Constraints from weak charge measurements of protons and nuclei on y_de couplings derived by Ref. [10] are shown as light magenta line.

Exclusion limits for minimal models of S&#771;₁ production with only y_s&mu; being non-zero obtained from a simultaneous fit to SR-1L and SR-2L of the &mu;+light-jet channel combining Run-2 and Run-3 data. All limits are computed at 95&percnt; CL and the observed (red solid lines) and expected (black dashed lines) exclusion limits are shown in the m(S&#771;₁) &ndash; y_s&mu; plane. The observed exclusion should be interpreted as the region above the red line. The yellow inner (green outer) shaded band around the expected limits corresponds to the &plusmn;1 &sigma; (&plusmn;2 &sigma;) variations of the expected limit, accounting for all uncertainties. The observed limit obtained from ATLAS searches for LQ pair production is also shown as dark blue line [13].

Exclusion limits for minimal models of S&#771;₁ production with only y_be being non-zero obtained from a simultaneous fit to SR-1L and SR-2L of the e+b-jet channel combining Run-2 and Run-3 data. All limits are computed at 95&percnt; CL and the observed (red solid lines) and expected (black dashed lines) exclusion limits are shown in the m(S&#771;₁) &ndash; y_be plane. The observed exclusion should be interpreted as the region above the red line. The yellow inner (green outer) shaded band around the expected limits corresponds to the &plusmn;1 &sigma; (&plusmn;2 &sigma;) variations of the expected limit, accounting for all uncertainties. The observed limit obtained from ATLAS searches for LQ pair production is also shown as dark blue line [13].

Exclusion limits for minimal models of S&#771;₁ production with only y_b&mu; being non-zero obtained from a simultaneous fit to SR-1L and SR-2L of the &mu;+b-jet channel combining Run-2 and Run-3 data. All limits are computed at 95&percnt; CL and the observed (red solid lines) and expected (black dashed lines) exclusion limits are shown in the m(S&#771;₁) &ndash; y_b&mu; plane. The observed exclusion should be interpreted as the region above the red line. The yellow inner (green outer) shaded band around the expected limits corresponds to the &plusmn;1 &sigma; (&plusmn;2 &sigma;) variations of the expected limit, accounting for all uncertainties. The observed limit obtained from ATLAS searches for LQ pair production is also shown as dark blue line [13].

Exclusion limits for minimal models of S&#771;₁ production obtained from a fit to SR-1L, SR-2L and their combination of (a) the e+light-jet, (b) the &mu;+light-jet, (c) the e+b-jet and (d) the &mu;+b-jet channel using Run-2 and Run-3 data. All limits are computed at 95&percnt; CL and the observed (solid lines) and expected (dashed lines) exclusion limits are shown in the m(S&#771;₁) &ndash; y plane. The observed exclusion regions should be interpreted as the region above the solid lines. Constraints from weak charge measurements of protons and nuclei&nbsp; and ATLAS searches for LQ pair production&nbsp; are shown as light magenta and dark blue areas, respectively.

Exclusion limits for minimal models of S&#771;₁ production obtained from a fit to SR-1L, SR-2L and their combination of (a) the e+light-jet, (b) the &mu;+light-jet, (c) the e+b-jet and (d) the &mu;+b-jet channel using Run-2 and Run-3 data. All limits are computed at 95&percnt; CL and the observed (solid lines) and expected (dashed lines) exclusion limits are shown in the m(S&#771;₁) &ndash; y plane. The observed exclusion regions should be interpreted as the region above the solid lines. Constraints from weak charge measurements of protons and nuclei&nbsp; and ATLAS searches for LQ pair production&nbsp; are shown as light magenta and dark blue areas, respectively.

Exclusion limits for minimal models of S&#771;₁ production obtained from a fit to SR-1L, SR-2L and their combination of (a) the e+light-jet, (b) the &mu;+light-jet, (c) the e+b-jet and (d) the &mu;+b-jet channel using Run-2 and Run-3 data. All limits are computed at 95&percnt; CL and the observed (solid lines) and expected (dashed lines) exclusion limits are shown in the m(S&#771;₁) &ndash; y plane. The observed exclusion regions should be interpreted as the region above the solid lines. Constraints from weak charge measurements of protons and nuclei&nbsp; and ATLAS searches for LQ pair production&nbsp; are shown as light magenta and dark blue areas, respectively.

Exclusion limits for minimal models of S&#771;₁ production obtained from a fit to SR-1L, SR-2L and their combination of (a) the e+light-jet, (b) the &mu;+light-jet, (c) the e+b-jet and (d) the &mu;+b-jet channel using Run-2 and Run-3 data. All limits are computed at 95&percnt; CL and the observed (solid lines) and expected (dashed lines) exclusion limits are shown in the m(S&#771;₁) &ndash; y plane. The observed exclusion regions should be interpreted as the region above the solid lines. Constraints from weak charge measurements of protons and nuclei&nbsp; and ATLAS searches for LQ pair production&nbsp; are shown as light magenta and dark blue areas, respectively.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$ej$ and (b) Run 2 SR-2L-$ej$ and (c) Run 3 SR-1-$ej$ and (d) Run 3 SR-2-$ej$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$ej$ and (b) Run 2 SR-2L-$ej$ and (c) Run 3 SR-1-$ej$ and (d) Run 3 SR-2-$ej$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$ej$ and (b) Run 2 SR-2L-$ej$ and (c) Run 3 SR-1-$ej$ and (d) Run 3 SR-2-$ej$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$ej$ and (b) Run 2 SR-2L-$ej$ and (c) Run 3 SR-1-$ej$ and (d) Run 3 SR-2-$ej$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$ej$ and (b) Run 2 SR-2L-$ej$ and (c) Run 3 SR-1-$ej$ and (d) Run 3 SR-2-$ej$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$ej$ and (b) Run 2 SR-2L-$ej$ and (c) Run 3 SR-1-$ej$ and (d) Run 3 SR-2-$ej$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$ej$ and (b) Run 2 SR-2L-$ej$ and (c) Run 3 SR-1-$ej$ and (d) Run 3 SR-2-$ej$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$ej$ and (b) Run 2 SR-2L-$ej$ and (c) Run 3 SR-1-$ej$ and (d) Run 3 SR-2-$ej$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu j$ and (b) Run 2 SR-2L-$\mu j$ and (c) Run 3 SR-1L-$\mu j$ and (d) Run 3 SR-2L-$\mu j$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu j$ and (b) Run 2 SR-2L-$\mu j$ and (c) Run 3 SR-1L-$\mu j$ and (d) Run 3 SR-2L-$\mu j$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu j$ and (b) Run 2 SR-2L-$\mu j$ and (c) Run 3 SR-1L-$\mu j$ and (d) Run 3 SR-2L-$\mu j$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu j$ and (b) Run 2 SR-2L-$\mu j$ and (c) Run 3 SR-1L-$\mu j$ and (d) Run 3 SR-2L-$\mu j$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu j$ and (b) Run 2 SR-2L-$\mu j$ and (c) Run 3 SR-1L-$\mu j$ and (d) Run 3 SR-2L-$\mu j$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu j$ and (b) Run 2 SR-2L-$\mu j$ and (c) Run 3 SR-1L-$\mu j$ and (d) Run 3 SR-2L-$\mu j$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu j$ and (b) Run 2 SR-2L-$\mu j$ and (c) Run 3 SR-1L-$\mu j$ and (d) Run 3 SR-2L-$\mu j$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu j$ and (b) Run 2 SR-2L-$\mu j$ and (c) Run 3 SR-1L-$\mu j$ and (d) Run 3 SR-2L-$\mu j$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$eb$ and (b) Run 2 SR-2L-$eb$ and (c) Run 3 SR-1L-$eb$ and (d) Run 3 SR-2L-$eb$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$eb$ and (b) Run 2 SR-2L-$eb$ and (c) Run 3 SR-1L-$eb$ and (d) Run 3 SR-2L-$eb$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$eb$ and (b) Run 2 SR-2L-$eb$ and (c) Run 3 SR-1L-$eb$ and (d) Run 3 SR-2L-$eb$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$eb$ and (b) Run 2 SR-2L-$eb$ and (c) Run 3 SR-1L-$eb$ and (d) Run 3 SR-2L-$eb$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP of $\tilde{S}$ in (a) Run 2 SR-1L-$eb$ and (b) Run 2 SR-2L-$eb$ and (c) Run 3 SR-1L-$eb$ and (d) Run 3 SR-2L-$eb$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP of $\tilde{S}$ in (a) Run 2 SR-1L-$eb$ and (b) Run 2 SR-2L-$eb$ and (c) Run 3 SR-1L-$eb$ and (d) Run 3 SR-2L-$eb$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP of $\tilde{S}$ in (a) Run 2 SR-1L-$eb$ and (b) Run 2 SR-2L-$eb$ and (c) Run 3 SR-1L-$eb$ and (d) Run 3 SR-2L-$eb$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP of $\tilde{S}$ in (a) Run 2 SR-1L-$eb$ and (b) Run 2 SR-2L-$eb$ and (c) Run 3 SR-1L-$eb$ and (d) Run 3 SR-2L-$eb$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu b$ and (b) Run 2 SR-2L-$\mu b$ and (c) Run 3 SR-1L-$\mu b$ and (d) Run 3 SR-2L-$\mu b$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu b$ and (b) Run 2 SR-2L-$\mu b$ and (c) Run 3 SR-1L-$\mu b$ and (d) Run 3 SR-2L-$\mu b$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu b$ and (b) Run 2 SR-2L-$\mu b$ and (c) Run 3 SR-1L-$\mu b$ and (d) Run 3 SR-2L-$\mu b$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu b$ and (b) Run 2 SR-2L-$\mu b$ and (c) Run 3 SR-1L-$\mu b$ and (d) Run 3 SR-2L-$\mu b$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu b$ and (b) Run 2 SR-2L-$\mu b$ and (c) Run 3 SR-1L-$\mu b$ and (d) Run 3 SR-2L-$\mu b$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu b$ and (b) Run 2 SR-2L-$\mu b$ and (c) Run 3 SR-1L-$\mu b$ and (d) Run 3 SR-2L-$\mu b$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu b$ and (b) Run 2 SR-2L-$\mu b$ and (c) Run 3 SR-1L-$\mu b$ and (d) Run 3 SR-2L-$\mu b$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu b$ and (b) Run 2 SR-2L-$\mu b$ and (c) Run 3 SR-1L-$\mu b$ and (d) Run 3 SR-2L-$\mu b$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Event selection cutflows of SR-1L-$eb$ for the signal sample with $m(\tilde{S}) = 2$ TeV and $y_{be} = 1.0$ individually for resonant production (RP) and combined Drell-Yan plus single production (DY+SP). The first number in the column for each mass points corresponds to the signal event yield after applying the associated cut while the second number in parentheses represents the efficiency with respect to the previous cut.

Event selection cutflows of SR-2L-$eb$ for the signal sample with $m(\tilde{S}) = 2$ TeV and $y_{be} = 1.0$ individually for resonant production (RP) and combined Drell-Yan plus single production (DY+SP). The first number in the column for each mass points corresponds to the signal event yield after applying the associated cut while the second number in parentheses represents the efficiency with respect to the previous cut.

Event selection cutflows of SR-1L-$ej$ for the signal sample with $m(\tilde{S}) = 2$ TeV and $y_{de} = 1.0$ individually for resonant production (RP) and combined Drell-Yan plus single production (DY+SP). The first number in the column for each mass points corresponds to the signal event yield after applying the associated cut while the second number in parentheses represents the efficiency with respect to the previous cut.

Event selection cutflows of SR-2L-$ej$ for the signal sample with $m(\tilde{S}) = 2$ TeV and $y_{de} = 1.0$ individually for resonant production (RP) and combined Drell-Yan plus single production (DY+SP). The first number in the column for each mass points corresponds to the signal event yield after applying the associated cut while the second number in parentheses represents the efficiency with respect to the previous cut.

Event selection cutflows of SR-1L-$\mu b$ for the signal sample with $m(\tilde{S}) = 2$ TeV and $y_{b\mu} = 1.0$ individually for resonant production (RP) and combined Drell-Yan plus single production (DY+SP). The first number in the column for each mass points corresponds to the signal event yield after applying the associated cut while the second number in parentheses represents the efficiency with respect to the previous cut.

Event selection cutflows of SR-2L-$\mu b$ for the signal sample with $m(\tilde{S}) = 2$ TeV and $y_{b\mu} = 1.0$ individually for resonant production (RP) and combined Drell-Yan plus single production (DY+SP). The first number in the column for each mass points corresponds to the signal event yield after applying the associated cut while the second number in parentheses represents the efficiency with respect to the previous cut.

Event selection cutflows of SR-1L-$\mu j$ for the signal sample with $m(\tilde{S}) = 2$ TeV and $y_{s\mu} = 1.0$ individually for resonant production (RP) and combined Drell-Yan plus single production (DY+SP). The first number in the column for each mass points corresponds to the signal event yield after applying the associated cut while the second number in parentheses represents the efficiency with respect to the previous cut.

Event selection cutflows of SR-2L-$\mu j$ for the signal sample with $m(\tilde{S}) = 2$ TeV and $y_{s\mu} = 1.0$ individually for resonant production (RP) and combined Drell-Yan plus single production (DY+SP). The first number in the column for each mass points corresponds to the signal event yield after applying the associated cut while the second number in parentheses represents the efficiency with respect to the previous cut.

Observed 95% $\text{CL}_\text{S}$ upper limits on the production cross-section times acceptance times branching ratio to jets, $\sigma \cdot A \cdot \text{BR}$, of Gaussian-shaped signals of 5%, 10%, and 15% width relative to their peak mass, $m_G$. Also included are the corresponding expected upper limits predicted for the case the $m_{jj}$ distribution is observed to be identical to the background prediction in each bin and the $1\sigma$ and $2\sigma$ envelopes of outcomes expected for Poisson fluctuations around the background expectation. Limits are derived from the J100 signal region.

Observed 95% $\text{CL}_\text{S}$ upper limits on the the value of the coupling to quarks, $g_q$, of the $Z^\prime$ model as a function of the resonance mass $m_{Z^\prime}$. Also included are the corresponding expected upper limits predicted for the case the $m_{jj}$ distribution is observed to be identical to the background prediction in each bin and the $1\sigma$ and $2\sigma$ envelopes of outcomes expected for Poisson fluctuations around the background expectation. Limits are derived from the J50 signal region.

Observed 95% $\text{CL}_\text{S}$ upper limits on the the value of the coupling to quarks, $g_q$, of the $Z^\prime$ model as a function of the resonance mass $m_{Z^\prime}$. Also included are the corresponding expected upper limits predicted for the case the $m_{jj}$ distribution is observed to be identical to the background prediction in each bin and the $1\sigma$ and $2\sigma$ envelopes of outcomes expected for Poisson fluctuations around the background expectation. Limits are derived from the J100 signal region.

Acceptance of simulated $Z^\prime$ signal events given the analysis event selection as a function of $m_{Z^\prime}$. The solid black line corresponds to the acceptance without a lower $m_{jj}$ requirement applied, the solid blue line includes the $m_{jj} > 344$ GeV requirement of the J50 signal region, and the solid red line includes the $m_{jj} > 481$ GeV requirement of the J100 signal region.

Numbers of events in each of the two considered datasets after consecutively applying the analysis selections.