The observed and predicted event yields in the eight BRT1 bins, as defined in Table 2. The signal yields expected in the maximally mixed scenario for a few representative sets of $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ values are overlaid: (100, 50), (100, 100), (200, 50), and (200, 100).

The observed and predicted event yields in the eight SR bins as defined in Table 2. The signal yields expected in the maximally mixed scenario for a few representative sets of $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ values are overlaid: (100, 10), (100, 50), (100, 100), (200, 10), (200, 50), (200, 100), (300, 10), (300, 50), and (300, 100). In bins where the observed yield is zero, the Garwood interval at 68% CL is shown as a positive uncertainty. The predicted yields and uncertainties are before the maximum likelihood fit to data under the background-only hypothesis, as described in Section 8.

The observed and predicted event yields in the eight SR bins as defined in Table 2. The signal yields expected in the maximally mixed scenario for a few representative sets of $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ values are overlaid: (100, 10), (100, 50), (100, 100), (200, 10), (200, 50), (200, 100), (300, 10), (300, 50), and (300, 100). In bins where the observed yield is zero, the Garwood interval at 68% CL is shown as a positive uncertainty. The predicted yields and uncertainties are after the maximum likelihood fit to data under the background-only hypothesis, as described in Section 8.

The observed upper limits in the $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ plane, for the maximally mixed scenario.

The set of $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ points lying on the observed exclusion contour, for the maximally mixed scenario.

The set of $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ points lying on the observed$+1\sigma$ exclusion contour, for the maximally mixed scenario.

The set of $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ points lying on the observed$-1\sigma$ exclusion contour, for the maximally mixed scenario.

The set of $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ points lying on the expected exclusion contour, for the maximally mixed scenario.

The set of $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ points lying on the expected$+1\sigma$ exclusion contour, for the maximally mixed scenario.

The set of $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ points lying on the expected$-1\sigma$ exclusion contour, for the maximally mixed scenario.

The set of $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ points lying on the expected$-2\sigma$ exclusion contour, for the maximally mixed scenario.

The observed upper limits in the $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ plane, for the mass-degenerate scenario.

The set of $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ points lying on the observed exclusion contour, for the mass-degenerate scenario.

The set of $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ points lying on the observed$+1\sigma$ exclusion contour, for the mass-degenerate scenario.

The set of $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ points lying on the observed$-1\sigma$ exclusion contour, for the mass-degenerate scenario.

The set of $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ points lying on the expected exclusion contour, for the mass-degenerate scenario.

The set of $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ points lying on the expected$+1\sigma$ exclusion contour, for the mass-degenerate scenario.

The set of $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ points lying on the expected$-1\sigma$ exclusion contour, for the mass-degenerate scenario.

The set of $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ points lying on the expected$+2\sigma$ exclusion contour, for the mass-degenerate scenario.

The set of $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ points lying on the expected$-2\sigma$ exclusion contour, for the mass-degenerate scenario.

Cross section upper limits at 95% CL for the pair production of long-lived staus in the maximally mixed scenario, as a function of $m_{\tilde{\tau}}$, for $c\tau_{0}=10$ mm.

Cross section upper limits at 95% CL for the pair production of long-lived staus in the maximally mixed scenario, as a function of $m_{\tilde{\tau}}$, for $c\tau_{0}=30$ mm.

Cross section upper limits at 95% CL for the pair production of long-lived staus in the maximally mixed scenario, as a function of $m_{\tilde{\tau}}$, for $c\tau_{0}=50$ mm.

Cross section upper limits at 95% CL for the pair production of long-lived staus in the maximally mixed scenario, as a function of $m_{\tilde{\tau}}$, for $c\tau_{0}=100$ mm.

Cross section upper limits at 95% CL for the pair production of long-lived staus in the maximally mixed scenario, as a function of $m_{\tilde{\tau}}$, for $c\tau_{0}=200$ mm.

Cross section upper limits at 95% CL for the pair production of long-lived staus in the maximally mixed scenario, as a function of $m_{\tilde{\tau}}$, for $c\tau_{0}=300$ mm.

Cross section upper limits at 95% CL for the pair production of long-lived staus in the mass-degenerate scenario, as a function of $m_{\tilde{\tau}}$, for $c\tau_{0}=10$ mm.

Cross section upper limits at 95% CL for the pair production of long-lived staus in the mass-degenerate scenario, as a function of $m_{\tilde{\tau}}$, for $c\tau_{0}=30$ mm.

Cross section upper limits at 95% CL for the pair production of long-lived staus in the mass-degenerate scenario, as a function of $m_{\tilde{\tau}}$, for $c\tau_{0}=50$ mm.

Cross section upper limits at 95% CL for the pair production of long-lived staus in the mass-degenerate scenario, as a function of $m_{\tilde{\tau}}$, for $c\tau_{0}=100$ mm.

Cross section upper limits at 95% CL for the pair production of long-lived staus in the mass-degenerate scenario, as a function of $m_{\tilde{\tau}}$, for $c\tau_{0}=200$ mm.

Cross section upper limits at 95% CL for the pair production of long-lived staus in the mass-degenerate scenario, as a function of $m_{\tilde{\tau}}$, for $c\tau_{0}=300$ mm.

Theoretical cross sections at NLO+NLL accuracy for stau pair production.

Signal yields in the maximally mixed scenario for the BR selections, for a few representative sets of $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ values

Comparison of L1T+HLT efficiencies of the MET+IsoTrk trigger calculated with 2022 data (black), 2023 data (blue), and $W \rightarrow l \nu$ simulation (red), as a function of offline reconstructed PF $p_{T}^{miss, \mu \hspace{-0.15cm} /}$ (right). The data follow the typical rise in efficiency, but the efficiency does not reach 100% because of the isolated track leg of the algorithm.

Efficiency of the L1T+HLT $p_{T}^{miss}$ leg as a function of offline reconstructed PF $p_{T}^{miss, \mu \hspace{-0.15cm} /}$ in 2022 data (black), 2023 data (blue), and $W \rightarrow l \nu$ simulation (red).

Efficiency of the full HLT path, taking into account only events that already passed through the $p_{T}^{miss}$ leg, as a function of the selected muon $p_{T}$ in 2022 data (black), 2023 data (blue), and $W \rightarrow l \nu$ simulation (red).

The L1T+HLT efficiency of the displaced $\tau_\mathrm{h}$ trigger, for simulated $\mathrm{p}\mathrm{p} \to \tilde{\tau}\tilde{\tau},(\tilde{\tau} \to \tau\tilde{\chi}^{0}_{1})$ events, where the $\tilde{\tau}$ has $c\tau = 10$ cm and each $\tau$ decays hadronically. The efficiency is shown for the displaced di-$\tau_\mathrm{h}$ trigger path (blue filled triangles), the previously available $\mathrm{p_{T}^{miss}}$-based paths (orange open circles), the previously available prompt di-$\tau_\mathrm{h}$ paths (purple open squares), the combination of the $\mathrm{p_{T}^{miss}}$-based and prompt di-$\tau_\mathrm{h}$ paths (gray open triangles), and the combination of the $\mathrm{p_{T}^{miss}}$-based, prompt di-$\tau_\mathrm{h}$, and displaced di-$\tau_\mathrm{h}$ paths (red filled circles), using 2022 data-taking conditions. The efficiency is evaluated with respect to generator-level quantities. Efficiency of the highest $\mathrm{p_{T}}$ $\tau$ lepton in the event as a function of the $d_{0}$ (left). Efficiency as a function of $\mathrm{p_{T}^{miss}}$ (right). A selection on the visible component of the generator-level $\tau$ lepton $\mathrm{p_{T}} >$ 30 GeV and its pseudorapidity $|{\eta}| < 2.1$ is applied. The lower panels show the ratio (improvement in \%) of the trigger efficiency given by the combination of the displaced di-$\tau_\mathrm{h}$ trigger path with the $\mathrm{p_{T}^{miss}}$-based and prompt di-$\tau_\mathrm{h}$ paths to that of the combination of the previously available $\mathrm{p_{T}^{miss}}$-based and prompt di-$\tau_\mathrm{h}$ paths.

The L1T+HLT efficiency of the displaced $\tau_\mathrm{h}$ trigger, for simulated $\mathrm{p}\mathrm{p} \to \tilde{\tau}\tilde{\tau},(\tilde{\tau} \to \tau\tilde{\chi}^{0}_{1})$ events, where the $\tilde{\tau}$ has $c\tau = 10$ cm and each $\tau$ decays hadronically. The efficiency is shown for the displaced di-$\tau_\mathrm{h}$ trigger path (blue filled triangles), the previously available $\mathrm{p_{T}^{miss}}$-based paths (orange open circles), the previously available prompt di-$\tau_\mathrm{h}$ paths (purple open squares), the combination of the $\mathrm{p_{T}^{miss}}$-based and prompt di-$\tau_\mathrm{h}$ paths (gray open triangles), and the combination of the $\mathrm{p_{T}^{miss}}$-based, prompt di-$\tau_\mathrm{h}$, and displaced di-$\tau_\mathrm{h}$ paths (red filled circles), using 2022 data-taking conditions. The efficiency is evaluated with respect to generator-level quantities. Efficiency of the highest $\mathrm{p_{T}}$ $\tau$ lepton in the event as a function of the $d_{0}$ (left). Efficiency as a function of $\mathrm{p_{T}^{miss}}$ (right). A selection on the visible component of the generator-level $\tau$ lepton $\mathrm{p_{T}} >$ 30 GeV and its pseudorapidity $|{\eta}| < 2.1$ is applied. The lower panels show the ratio (improvement in \%) of the trigger efficiency given by the combination of the displaced di-$\tau_\mathrm{h}$ trigger path with the $\mathrm{p_{T}^{miss}}$-based and prompt di-$\tau_\mathrm{h}$ paths to that of the combination of the previously available $\mathrm{p_{T}^{miss}}$-based and prompt di-$\tau_\mathrm{h}$ paths.

Total rate of the displaced $\tau_\mathrm{h}$ trigger for a few representative runs in 2022 data, as a function of PU.

Total rate of the displaced $\tau_\mathrm{h}$ trigger for a few representative runs in 2023 data, as a function of PU.

The HLT efficiency for a given event passing the main displaced-jet trigger to satisfy HLT calorimeter $H_{\mathrm{T}}>430~\mathrm{GeV}$ as a function of the offline calorimeter $H_{\mathrm{T}}$. For this trigger, the minimum calorimeter $H_{\mathrm{T}} threshold was 430 GeV in 2022. The measurements are performed in data collected in 2022 (green circles), in 2023 before an update of the HCAL gain values and energy response corrections (black squares), and in 2023 after the update (blue triangles).

The HLT efficiency for a given event passing the main displaced-jet trigger to satisfy HLT calorimeter $H_{\mathrm{T}}>390~\mathrm{GeV}$ as a function of the offline calorimeter $H_{\mathrm{T}}$. For this trigger, the minimum calorimeter $H_{\mathrm{T}} threshold was 390 GeV in 2023 and later. The measurements are performed in data collected in 2022 (green circles), in 2023 before an update of the HCAL gain values and energy response corrections (black squares), and in 2023 after the update (blue triangles).

The HLT efficiency of the main displaced-jet trigger: Efficiency of an offline calorimeter jet to pass the online $\mathrm{p_T}$ requirement in the displaced-jet triggers. In the this plot, the HLT calorimeter jets must have $\mathrm{p_T}>40$ GeV. The efficiency is shown for data collected in 2022 (green squares), in 2023 before an update of the HCAL gains and energy response corrections (black filled circles), and in 2023 after the update (blue open circles). The efficiencies measured with QCD multijet simulations are also shown, for 2022 (red triangles) and 2023 (purple triangles) conditions. These measurements are performed using events collected with a prescaled trigger that requires $\mathrm{H_T} >425$ GeV at the HLT. An offline $\mathrm{H_T} >450$ GeV selection is also applied to ensure the prescaled trigger reaches its plateau. The efficiency is $> 96\%$ when the offline jet has $\mathrm{p_T}>40$ GeV. The efficiency threshold is lower for the later 2023 data following updates to the HCAL energy corrections and readout gains, although the $\mathrm{p_T}$ value at the start of the plateau is unchanged.

The HLT efficiency of the main displaced-jet trigger: Efficiency of an offline calorimeter jet to have at most one HLT prompt track. The efficiency in this plot is shown for 2022 conditions, as a function of the number of offline prompt tracks, in simulated $\mathrm{H} \to \mathrm{SS}$, $\mathrm{S} \to \mathrm{b\overline{b}}$ signal events where $m_{H}=125$ GeV and $m_{S}=40$ GeV. Two proper decay lengths of the S particle are shown: $c\tau=10$ mm (green circles) and $c\tau=100$ mm (blue squares). For jets in signal events, when the number of offline prompt tracks is $<4$, the tagging efficiency is larger than 70%.

The HLT efficiency of the main displaced-jet trigger for 2022 conditions, for $\mathrm{H} \to \mathrm{S}\mathrm{S}$ signal events where $m_{H}=125$ GeV and $m_{S}=40$ GeV. The per-parton (quark or lepton) HLT displaced-jet tagging efficiency as a function of the generator-level $L_{xy}$ of the parton is shown for displaced b quarks (blue circles), d quarks (purple triangels), and $\tau$ leptons (green squares) with $p_{\mathrm{T}}>40~\mathrm{GeV}$ and $|\eta|<2.0$. Events are required to satisfy the HLT $H_{T} > 430$ GeV requirement.

The ratio between the Run 3 displaced-jet trigger efficiency and the Run 2 displaced jet trigger efficiency as a function of LLP $c\tau$, in simulated $\mathrm{H}\to\mathrm{SS}$, $\mathrm{S}\to\mathrm{b\overline{b}}$ signal events where $m_{\mathrm{H}}=125~\mathrm{GeV}$ and $m_{\mathrm{S}}=15$ (blue triangles), 40 (green squares), or 55 (red circles)$\mathrm{GeV}$. The Run 3 displaced trigger efficiencies are measured for 2022 conditions.

The L1T HCAL trigger tower efficiency of the delayed timing towers in 2023 HCAL timing-scan data, with efficiencies split by trigger towers centered at $\eta\approx 0$ (blue circles), 0.65 (red squares), 1.26 (black triangles), and with width $\Delta \eta = 0.087$. The sharp rise in efficiency between timing delays of 0-6 ns is expected, as the prompt timing range includes pulses up to and including those recorded at a 6 ns arrival time (reported in half-ns steps by the TDC), demonstrating the timing trigger performance. The delayed timing towers must have at least one delayed cell, no prompt cells, and energy ${>} 4$ GeV. The efficiency is calculated relative to towers with any valid timing code, meaning the tower contains at least one cell with energy ${>} 4$ GeV and a TDC code of prompt, slightly delayed, or very delayed. Multiple delayed or displaced towers are required for the HCAL-based displaced- and delayed-jet L1T to pass, and this shows the efficiency at a per-tower level relative to incoming pulse timing.

The L1T efficiency of the LLP jet trigger in 2023 HCAL timing-scan data. The HCAL LLP-flagged L1T trigger delayed jet fraction versus jet $E_T$ during the 2023 HCAL phase scan demonstrates that the delayed jet fraction approaches unity as the timing shift increases. The results are inclusive in pseudorapidity for the HCAL barrel, corresponding to $|{\eta}| < 1.35$. The fraction of LLP-flagged L1 jets is compared to all L1 jets from a data set of events enriched with jets or $p_T^{\text{miss}}$. No explicit selection criterion is applied on the jet $E_T$, though the implicit requirement for a jet to have at least two cells with $E_T > 4$ GeV shapes the resulting jet trigger efficiency curve.

The L1T efficiency of the HCAL-based LLP jet triggers, as a function of event $H_T$, for $H \to SS \to b\bar{b}b\bar{b}$ events with $m_{H}=350$ GeV, $m_{S}=80$ GeV, and $c\tau_{S}=0.5$ m (light blue circles) and $m_{H}=125$ GeV, $m_{S}=50$ GeV, and $c\tau_{S}=3$ m (purple triangles), for 2023 conditions. The trigger efficiency is evaluated for LLPs decaying in HB depths 3 or 4, corresponding to $214.2< R<295$ cm and $|{\eta}|< 1.26$. These LLPs are also required to be matched to an offline jet in HB.

The L1T efficiency of the HCAL-based LLP jet triggers, as a function of jet $p_T$, for $H \to SS \to b\bar{b}b\bar{b}$ events with $m_{H}=350$ GeV, $m_{S}=80$ GeV, and $c\tau_{S}=0.5$ m (light blue circles) and $m_{H}=125$ GeV, $m_{S}=50$ GeV, and $c\tau_{S}=3$ m (purple triangles), for 2023 conditions. The trigger efficiency is evaluated for LLPs decaying in HB depths 3 or 4, corresponding to $214.2< R<295$ cm and $|{\eta}|< 1.26$. These LLPs are also required to be matched to an offline jet in HB.

The L1T efficiency of the HCAL-based LLP jet triggers as a function of LLP decay radial position $R$ for $H \to SS \to b\bar{b}b\bar{b}$ events with $m_{H}=350$ GeV, $m_{S}=80$ GeV, and $c\tau_{S}=0.5$ m (light blue circles) and $m_{H}=125$ GeV, $m_{S}=50$ GeV, and $c\tau_{S}=3$ m (purple triangles), for 2023 conditions. The trigger efficiency is evaluated for LLPs within $|{\eta}| <1.26$ where either the LLP or its decay products are matched to an offline jet in HB with $p_T>100$ GeV.

The HLT efficiency of the CalRatio trigger as a function of the leading PF jet NHEF in 2024 data, measured with respect to a logical OR of the HCAL-based LLP L1 jet triggers (left). Events are required to have $H_{\mathrm{T}} > 200 \,\mathrm{GeV}$ and the leading jet is required to have $p_{\mathrm{T}} > 60 \,\mathrm{GeV}$ and $|\eta| < 1.5$, which are equivalent to the respective HLT jet object selections. The signal distributions additionally require the leading jet to be matched to an LLP decaying anywhere inside the barrel calorimeter volume ($129 < R < 295 \,\mathrm{cm}$).

Distribution of the leading PF jet NHEF (right) in 2024 data (black circles), W$\to l\nu$ background simulation for 2024 conditions (red squares), and $H \to SS \to b\bar{b}b\bar{b}$ signal simulation for 2023 conditions (blue and purple triangles). Events are required to have $H_{\mathrm{T}} > 200\,\mathrm{GeV}$ and the leading jet is required to have $p_{\mathrm{T}} > 60\,\mathrm{GeV}$ and $|\eta| < 1.5$, which are equivalent to the respective HLT jet object selections. The signal distributions additionally require the leading jet to be matched to an LLP decaying anywhere inside the barrel calorimeter volume ($129 < R < 295\,\mathrm{cm}$). The clear separation between the displaced signal and the prompt background in the plot motivates the development of the CalRatio trigger.

The L1T+HLT efficiency of the inclusive and trackless delayed-jet triggers introduced in Run 3, shown as red squares and blue triangles, for 2022 conditions, and of the $H_T$ trigger (black circles), which was the most appropriate path available in Run 2, for a $H \to X X \to b\bar{b}\,b\bar{b}$ signal with $m_H$ = 1000 GeV, $m_X$ = 450 GeV, and $c\tau = 10$ m. The addition of these delayed-jet triggers results in a significant improvement in the efficiency of the signal for $430 < H_T < 1050 GeV$.

The L1T+HLT efficiency of the $H_T$-seeded delayed jet trigger, the $H_T$-seeded delayed trackless jet trigger, the tau-seeded delayed jet trigger, and the tau-seeded delayed trackless jet trigger, as functions of $H_T$, for a $H \to X X \to 4b$ signal. The addition of the delayed-jet triggers results in a significant improvement in the efficiency of the signal in the intermediate $H_T$ range.

The L1T+HLT efficiency of the $H_T$-seeded delayed jet trigger, the $H_T$-seeded delayed trackless jet trigger, the tau-seeded delayed jet trigger, and the tau-seeded delayed trackless jet trigger, as functions of $H_T$, for a $H \to X X \to 4\tau$ signal. The addition of the delayed-jet triggers results in a significant improvement in the efficiency of the signal in the intermediate $H_T$ range.

The L1T+HLT efficiency of the delayed-jet triggers as a function of jet timing for 2022 and 2023 data-taking periods. A clear rise in efficiency is evident around the threshold values. The plots include events that pass the $E_T^{\text{miss}} > 200\,\mathrm{GeV}$ trigger and have at least one barrel jet with $p_T > 50\,\mathrm{GeV}$, number of ECAL cells $> 8$, and ECAL energy $ > 25\,\mathrm{GeV}$. The $H_T$ is calculated using the scalar sum of jets with offline $p_T > 40 GeV$, and this is different from the $H_T$ calculation used at the HLT level, which can cause trigger inefficiencies. The maximum jet time accepted by the trigger is $12.5\,\mathrm{ns}$.

The L1T+HLT efficiency of the delayed-jet triggers as a function of jet timing for 2022 and 2023 data-taking periods. A clear rise in efficiency is evident around the threshold values. The plots include events that pass the $E_T^{\text{miss}} > 200\,\mathrm{GeV}$ trigger and have at least one barrel jet with $p_T > 50\,\mathrm{GeV}$, number of ECAL cells $> 8$, and ECAL energy $ > 25\,\mathrm{GeV}$. The $H_T$ is calculated using the scalar sum of jets with offline $p_T > 40 GeV$, and this is different from the $H_T$ calculation used at the HLT level, which can cause trigger inefficiencies. The maximum jet time accepted by the trigger is $12.5\,\mathrm{ns}$.

The ECAL time delay of the $\mathrm{e/\gamma}$ L1 seeds in the barrel. The distributions are shown for $\mathrm{Z\ \rightarrow\ ee}$ simulation and $\mathrm{\chi^{0}\ c\tau}$ values of $\mathrm{3\ cm,\ 30\ cm}$ and $\mathrm{3\ m}$, assuming the singlet-triplet Higgs dark portal model ($\mathrm{\chi^{\pm}\ \rightarrow\ \chi^{0} \ell^{\pm} \nu}$, where the $\mathrm{\chi^{\pm}}$ has a mass of $\mathrm{220\ GeV}$ and the $\mathrm{\chi^{0}}$ has a mass of $\mathrm{200\ GeV}$), for 2023 conditions. The distributions are normalized to unity.

The ECAL time delay of the $\mathrm{e/\gamma}$ L1 seeds in the endcap. The distributions are shown for $\mathrm{Z\ \rightarrow\ ee}$ simulation and $\mathrm{\chi^{0}\ c\tau}$ values of $\mathrm{3\ cm,\ 30\ cm}$ and $\mathrm{3\ m}$, assuming the singlet-triplet Higgs dark portal model ($\mathrm{\chi^{\pm}\ \rightarrow\ \chi^{0} \ell^{\pm} \nu}$, where the $\mathrm{\chi^{\pm}}$ has a mass of $\mathrm{220\ GeV}$ GeV and the $\mathrm{\chi^{0}}$ has a mass of $\mathrm{200\ GeV}$ GeV), for 2023 conditions. The distributions are normalized to unity.

The HLT rate (blue points) of the delayed-diphoton trigger for a few representative runs in the first data collected in 2023, corresponding to an integrated luminosity of $\mathrm{4.2\ fb^{-1}}$, compared with the PU during the same data-taking period (red points), as a function of integrated luminosity. The rate decreases nonlinearly during a single fill as a result of the increasing crystal opacity. It recovers by the start of the next fill with $\mathrm{<\ 1\%}$ reduction in rate between the fills. The rate generally increased throughout the year because of periodic online calibrations to mitigate the loss in trigger efficiency, which was produced as a result of the ECAL crystal radiation damage. For display purposes in this HepData record, the PU value is scaled by 1/9.04.

The delayed-diphoton trigger rate is shown as a function of PU for fill 9573 in 2024 data, at an instantaneous luminosity of approximately $1.8\times10^34~cm^-2~s^-1$. The trigger rate displays a linear dependency on PU.

The delayed-diphoton trigger rate is shown as a function of PU for fill 9574 in 2024 data, at an instantaneous luminosity of approximately $1.8\times10^34~cm^-2~s^-1$. The trigger rate displays a linear dependency on PU.

The delayed-diphoton trigger rate is shown as a function of PU for fill 9575 in 2024 data, at an instantaneous luminosity of approximately $1.8\times10^34~cm^-2~s^-1$. The trigger rate displays a linear dependency on PU.

The delayed-diphoton trigger rate is shown as a function of PU for fill 9579 in 2024 data, at an instantaneous luminosity of approximately $1.8\times10^34~cm^-2~s^-1$. The trigger rate displays a linear dependency on PU.

The L1T+HLT efficiency of the delayed-diphoton trigger as a function of the subleading probe electron ($\mathrm{e_2}$) supercluster seed time, measured with data collected in 2023. At the HLT, the subleading $\mathrm{e/\gamma}$ supercluster ($\mathrm{e/\gamma_2}$) is required to have $\mathrm{E_T\ >\ 12\ GeV}$, $\mathrm{|\eta|\ <\ 2.1}$, and a seed time $\mathrm{>\ 1\ ns}$. The trigger is fully efficient above $\mathrm{1\ ns}$.

The L1T+HLT efficiency of the delayed-diphoton trigger as a function of subleading probe electron ($\mathrm{e_2}$) $\mathrm{p_T}$, measured with data collected in 2023. At the HLT, the subleading $\mathrm{e/\gamma}$ supercluster ($\mathrm{e/\gamma_2}$) is required to have $\mathrm{E_T\ >\ 12\ GeV}$, $\mathrm{|\eta|\ <\ 2.1}$, and a seed time $\mathrm{>\ 1\ ns}$. The efficiency rises sharply for $\mathrm{p_T\ >\ 12\ GeV}$ and plateaus for $\mathrm{p_T\ >\ 35\ GeV}$. The slow rise in between is from additional L1 $\mathrm{H_T}$ requirements.

The L1T+HLT efficiency of the delayed-diphoton trigger as a function of subleading probe electron ($\mathrm{e_2}$) $\eta$, measured with data collected in 2023. At the HLT, the subleading $\mathrm{e/\gamma}$ supercluster ($\mathrm{e/\gamma_2}$) is required to have $\mathrm{E_T\ >\ 12\ GeV}$, $\mathrm{|\eta|\ <\ 2.1}$, and a seed time $\mathrm{>\ 1\ ns}$. The trigger is efficient in the region $\mathrm{|\eta|\ <\ 2.1}$.

Total rate of the displaced-photon + $H_\mathrm{T}$ HLT path for a few representative runs in 2022 data, at an instantaneous luminosity of approximately $1.8\times10^{34}~cm^{-2}~s^{-1}$, as a function of PU. The rate vs PU behavior was nonlinear in 2022 and fixed in time for 2023 data taking.

Total rate of the displaced-photon + $H_\mathrm{T}$ HLT path for a few representative runs in 2023 data, at an instantaneous luminosity of approximately $2.0\times10^{34}~cm^{-2}~s^{-1}$, as a function of PU. The rate vs PU behavior was nonlinear in 2022 and fixed in time for 2023 data taking.

The BMTF L1T efficiencies for beamspot-constrained and beamspot-unconstrained $\mathrm{p_{T}}$ assignment algorithms for L1T $\mathrm{p_{T}} > 10\mathrm{GeV}$ with respect to generator-level muon track $\mathrm{d_{0}}$, obtained using a sample which produces LLPs that decay to dimuons. The L1T algorithms and data-taking conditions correspond to 2024. A selection on the generator-level muon track $\mathrm{p_{T}} > 15\mathrm{GeV}$ is applied to show the performance at the efficiency plateau. The generator-level muon tracks are extrapolated to the second muon station to determine the $\eta^{\mathrm{gen}}_{\mathrm{st2}}$ values that are used in the plot. The solid markers show the new vertex-unconstrained algorithm performance, while the hollow markers show the default beamspot-constrained algorithm performance.

The OMTF L1T efficiencies for beamspot-constrained and beamspot-unconstrained $\mathrm{p_{T}}$ assignment algorithms for L1T $\mathrm{p_{T}} > 10\mathrm{GeV}$ with respect to generator-level muon track $\mathrm{d_{0}}$, obtained using a sample which produces LLPs that decay to dimuons. The L1T algorithms and data-taking conditions correspond to 2024. A selection on the generator-level muon track $\mathrm{p_{T}} > 15\mathrm{GeV}$ is applied to show the performance at the efficiency plateau. The generator-level muon tracks are extrapolated to the second muon station to determine the $\eta^{\mathrm{gen}}_{\mathrm{st2}}$ values that are used in the plot. The solid markers show the new vertex-unconstrained algorithm performance, while the hollow markers show the default beamspot-constrained algorithm performance.

The EMTF L1T efficiencies for beamspot-constrained and beamspot-unconstrained $\mathrm{p_{T}}$ assignment algorithms for L1T $\mathrm{p_{T}} > 10\mathrm{GeV}$ with respect to generator-level muon track $\mathrm{d_{0}}$, obtained using a sample which produces LLPs that decay to dimuons. The L1T algorithms and data-taking conditions correspond to 2024. A selection on the generator-level muon track $\mathrm{p_{T}} > 15\mathrm{GeV}$ is applied to show the performance at the efficiency plateau. The generator-level muon tracks are extrapolated to the second muon station to determine the $\eta^{\mathrm{gen}}_{\mathrm{st2}}$ values that are used in the plot. The solid markers show the new vertex-unconstrained algorithm performance, while the hollow markers show the default beamspot-constrained algorithm performance. In the EMTF plot, the different colors show different $|\eta|$ regions: $1.24 < \eta^{\mathrm{gen}}_{\mathrm{st2}} < 1.6$ (blue), $1.6 < \eta^{\mathrm{gen}}_{\mathrm{st2}} < 2.0$ (red).

The L1T+HLT efficiencies of the various displaced-dimuon triggers and their logical OR as a function of $c\tau$ for the HAHM signal events with $m_H = 125\ GeV$ and $m_{Z_D} = 20\ GeV$, for 2022 conditions. The efficiency is defined as the fraction of simulated events that satisfy the detector acceptance and the requirements of the following sets of triggers: the Run 2 (2018) triggers (dashed black); the Run 3 (2022, L3) triggers (blue); the Run 3 (2022, L2) triggers (red); and the logical OR of all these triggers (Run 3 (2022), solid black). The lower panel shows the ratio of the overall Run 3 (2022) efficiency to the Run 2 (2018) efficiency.

The HLT efficiency, defined as the fraction of events recorded by the Run 2 (2018) triggers that also satisfied the requirements of the Run 3 (2022, L2) triggers, as a function of offline-reconstructed min($d_0$) of the two muons forming STA-STA dimuons in events enriched in cosmic ray muons. The data represent efficiencies during the 2022 and 2023 data-taking periods. For displaced muons, the efficiency of the online min($d_0$) requirement is larger than 95% in all data-taking periods.

The invariant mass distribution for TMS-TMS dimuons in events recorded by the Run 2 (2018) triggers in the combined 2022 and 2023 data set, and in the subset of events also selected by the Run 3 (2022, L2) triggers, illustrating the prompt muon rejection of the Run 3 (2022, L2) triggers.

The L1T+HLT efficiency of the Run 3 (2022, L3) triggers in 2022 data (black), 2023 data (red), and simulation (green) as a function of min($p_T$) of the two muons forming TMS-TMS dimuons in events enriched in J/ψ → μμ events. The efficiency in data is the fraction of J/ψ → μμ events recorded by the triggers based on the information from jets and $p_T^{miss}$ that also satisfy the requirements of the Run 3 (2022, L3) triggers. It is compared to the efficiency of the Run 3 (2022, L3) triggers in a combination of simulated samples of J/ψ → μμ events produced in various b hadron decays. The lower panels show the ratio of the data to simulated events.

The L1T+HLT efficiency of the Run 3 (2022, L3) triggers in 2022 data (black), 2023 data (red), and simulation (green) as a function of max($p_T$) of the two muons forming TMS-TMS dimuons in events enriched in J/ψ → μμ events. Efficiency in data is the fraction of J/ψ → μμ events recorded by the triggers based on the information from jets and $p_T^{miss}$ that also satisfy the requirements of the Run 3 (2022, L3) triggers. It is compared to the efficiency of the Run 3 (2022, L3) triggers in a combination of simulated samples of J/ψ → μμ events produced in various b hadron decays. The lower panels show the ratio of the data to simulated events.

The L1T+HLT efficiency of the Run 3 (2022, L3) triggers in 2022 data (black), 2023 data (red), and simulation (green) as a function of min($d_0$) of the two muons forming TMS-TMS dimuons in events enriched in J/ψ → μμ events. Efficiency in data is the fraction of J/ψ → μμ events recorded by the triggers based on the information from jets and $p_T^{miss}$ that also satisfy the requirements of the Run 3 (2022, L3) triggers. It is compared to the efficiency of the Run 3 (2022, L3) triggers in a combination of simulated samples of J/ψ → μμ events produced in various b hadron decays. The lower panels show the ratio of the data to simulated events.

The HLT efficiency, defined as the fraction of events recorded by the Run 2 (2018) triggers that also satisfied the requirements of the Run 3 (2022, L3) triggers, as a function of offline-reconstructed min($d_0$) of the two muons forming TMS-TMS dimuons in events enriched in J/ψ → μμ. The data represent efficiencies during the 2022 and 2023 data-taking periods. For dimuons with offline min($d_0$) > 0.012 cm, the combined efficiency of the L3 muon reconstruction and the online min($d_0$) requirement is larger than 90% in all data-taking periods.

The HLT efficiency of the Run 3 (2022, L3) triggers and the Run 3 (2022, L3 dTks) triggers for J/ψ → μμ events in the 2022 and 2023 data set as a function of offline-reconstructed min($d_0$) of the two muons forming TMS-TMS dimuons in events enriched in J/ψ → μμ.

Invariant mass distribution for TMS-TMS dimuons in events recorded by the Run 2 (2018) triggers in the combined 2022 and 2023 data set, and in the subset of events also selected by the Run 3 (2022, L3) trigger and Run 3 (2022, L3 dTks) trigger, illustrating the prompt muon rejection of the L3 triggers.

The L1T+HLT efficiency of the double displaced L3 muon trigger as a function of min($\mathrm{p_{T}}$) of the two global or tracker muons in the event. The efficiency is plotted for HAHM signal events for 2022 conditions with $m_{Z_D} = 50$ GeV and $\epsilon = 4 \times 10^{-9}$ (black triangles), $m_{Z_D} = 60$ GeV and $\epsilon = 2 \times 10^{-9}$ (red triangles), and $m_H=125$ GeV in both cases. The events are required to have at least two good global or tracker muons with $\mathrm{p_T}>23$ GeV.

The L1T+HLT efficiency of the double displaced L3 muon trigger in 2022, as a function of min($\mathrm{d_{0}}$) of the two global or tracker muons in the event. The efficiency is plotted for MC-simulated $J/\psi o \mu\mu$ events produced in various b hadron decays (green squares) and data enriched in $J/\psi o \mu\mu$ events recorded by jet- and $\mathrm{p_T^miss}$-based triggers (black points). The events are required to have at least two good global or tracker muons compatible with the $J/\psi$ meson mass and with $\mathrm{p_T}>45$ GeV.

The L1T+HLT efficiency of the double displaced L3 muon trigger in 2022, as a function of min($\mathrm{p_{T}}$) of the two global or tracker muons in the event. The efficiency is plotted for MC-simulated $J/\psi o \mu\mu$ events produced in various b hadron decays (green squares) and data enriched in $J/\psi o \mu\mu$ events recorded by jet- and $\mathrm{p_T^miss}$-based triggers (black points). The events are required to have at least two good global or tracker muons compatible with the $J/\psi$ meson mass and with $\mathrm{p_T}>23$ GeV.

L1T+HLT efficiency of the dimuon scouting trigger as a function of the subleading muon $p_{T}$, for 2024 data. The efficiency of the L1T dimuon seeds (pink squares) and the HLT dimuon scouting trigger with the vertex-unconstrained reconstruction algorithm (blue triangles) is shown. The events in the denominator are required to have at least two vertex-unconstrained muons ($N_{\mu(\text{no-vtx})} > 2$) and additionally have $\chi^2/N_{\text{dof}} < 3$ and $\Delta R > 0.1$.

L1T+HLT efficiency of the dimuon scouting trigger as a function of the generator-level $L_{xy}$, for HAHM signal events, for 2024 conditions. The efficiency is shown for $m_{Z_D} = 14$ GeV and $c\tau = 100$ mm (pink squares) and $m_{Z_D} = 2.5$ GeV and $c\tau = 100$ mm (blue triangles). The muons are required to have $p_{T} > 15$ GeV and $|\eta| < 2.4$ at the generator level.

L1T+HLT efficiency of the dimuon scouting trigger as a function of the generator-level subleading muon $\mathrm{p_{T}}$, for HAHM signal events for 2024 conditions. The efficiency is shown for a $m_{Z_D}$ mass of 2.5 GeV, and $c\tau$ values of 1 (purple squares), 10 (blue triangles), and 100 mm (pink circles). The muons are required to have $|\eta|<2.4$ at the generator level.

L1T+HLT efficiency of the dimuon scouting trigger as a function of the generator-level subleading muon $\mathrm{p_{T}}$, for HAHM signal events for 2024 conditions. The efficiency is shown for a $m_{Z_D}$ mass of 14 GeV, and $c\tau$ values of 1 (purple squares), 10 (blue triangles), and 100 mm (pink circles). The muons are required to have $|\eta|<2.4$ at the generator level.

Scouting muon reconstruction efficiency of the vertex-constrained (pink circles) and vertex-unconstrained (blue triangles) algorithms as a function of the generator-level $L_{xy}$, for HAHM signal events for 2024 conditions. This efficiency is representative of the reconstruction efficiency of the L2 and L3 HLT muon reconstruction employed in scouting data. The efficiency is shown for $m_{Z_D} = 2.5$ GeV and $c\tau = 100$ mm. The muons are required to have $p_{T} > 15$ GeV and $|\eta| < 2.4$ at the generator level.

Scouting muon reconstruction efficiency of the vertex-constrained (pink circles) and vertex-unconstrained (blue triangles) algorithms as a function of the generator-level $L_{xy}$, for HAHM signal events for 2024 conditions. This efficiency is representative of the reconstruction efficiency of the L2 and L3 HLT muon reconstruction employed in scouting data. The efficiency is shown for $m_{Z_D} = 14$ GeV and $c\tau = 100$ mm. The muons are required to have $p_{T} > 15$ GeV and $|\eta| < 2.4$ at the generator level.

The $p_{T}$ resolution of scouting muons with respect to offline muons, as a function of the scouting muon $p_{T}$, for 2024 data events. The root mean square (RMS) of the difference of the scouting muon $p_{T}$ and the offline muon $p_{T}$, divided by the offline muon $p_{T}$, is plotted. The dimuon $\Delta R$ is required to be greater than 0.2, and the scouting muon $p_{T}$ is required to be greater than 3 GeV. The resolution is shown for muons in the barrel (blue filled points) and the endcaps (purple filled triangles) that are reconstructed with both the vertex-unconstrained reconstruction algorithm, as well as for muons in the barrel (red filled squares) and the endcaps (orange unfilled squares) that are reconstructed with the vertex-constrained reconstruction algorithm. A special monitoring data set is used that collects events triggered by a mixture of HLT paths (both scouting and standard triggers) with a very high prescale, in which all information about the muon objects is stored from the offline and scouting reconstruction.

The HLT efficiency of the DT MDS triggers as a function of $p_T^{miss}$, for simulated $H \to S S \to b\bar{{b}}\,b\bar{{b}}$ events with $m_{H}=125$ GeV, $m_{S}=40$ GeV, and $c\tau_{S}=1$ m, for 2023 conditions. Events are required to have at least one cluster with more than 50 hits.

The HLT efficiency of the DT MDS triggers as a function of cluster size, for simulated $H \to S S \to b\bar{{b}}\,b\bar{{b}}$ events with $m_{H}=125$ GeV, $m_{S}=40$ GeV, and $c\tau_{S}=1$ m, for 2023 conditions. Events are required to have $p_T^{miss}>250$ GeV.

Rate of the main muon No-BPTX HLT path as a function of the number of colliding bunches, for 2016.

Rate of the main muon No-BPTX HLT path as a function of the number of colliding bunches, for 2017.

Rate of the main muon No-BPTX HLT path as a function of the number of colliding bunches, for 2018.

Rate of the main muon No-BPTX HLT path as a function of the number of colliding bunches, for 2022.

Rate of the main muon No-BPTX HLT path as a function of the number of colliding bunches, for 2023.

Rate of the main muon No-BPTX HLT path as a function of the number of colliding bunches, for 2024.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay radial position, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=1000\,\mathrm{GeV}$ and $m_X=200\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay radial position, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=1000\,\mathrm{GeV}$ and $m_X=200\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay radial position, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=1000\,\mathrm{GeV}$ and $m_X=200\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay radial position, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=1000\,\mathrm{GeV}$ and $m_X=200\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay radial position, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=1000\,\mathrm{GeV}$ and $m_X=200\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay radial position, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=350\,\mathrm{GeV}$ and $m_X=80\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay radial position, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=350\,\mathrm{GeV}$ and $m_X=80\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay radial position, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=350\,\mathrm{GeV}$ and $m_X=80\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay radial position, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=350\,\mathrm{GeV}$ and $m_X=80\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay radial position, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=350\,\mathrm{GeV}$ and $m_X=80\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay radial position, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=350\,\mathrm{GeV}$ and $m_X=160\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay radial position, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=350\,\mathrm{GeV}$ and $m_X=160\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay radial position, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=350\,\mathrm{GeV}$ and $m_X=160\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay radial position, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=350\,\mathrm{GeV}$ and $m_X=160\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay radial position, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=350\,\mathrm{GeV}$ and $m_X=160\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay radial position, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=125\,\mathrm{GeV}$ and $m_X=25\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay radial position, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=125\,\mathrm{GeV}$ and $m_X=25\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay radial position, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=125\,\mathrm{GeV}$ and $m_X=25\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay radial position, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=125\,\mathrm{GeV}$ and $m_X=25\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay radial position, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=125\,\mathrm{GeV}$ and $m_X=25\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay position along the beam line, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=1000\,\mathrm{GeV}$ and $m_X=200\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay position along the beam line, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=1000\,\mathrm{GeV}$ and $m_X=200\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay position along the beam line, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=1000\,\mathrm{GeV}$ and $m_X=200\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay position along the beam line, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=1000\,\mathrm{GeV}$ and $m_X=200\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay position along the beam line, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=1000\,\mathrm{GeV}$ and $m_X=200\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay position along the beam line, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=350\,\mathrm{GeV}$ and $m_X=80\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay position along the beam line, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=350\,\mathrm{GeV}$ and $m_X=80\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay position along the beam line, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=350\,\mathrm{GeV}$ and $m_X=80\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay position along the beam line, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=350\,\mathrm{GeV}$ and $m_X=80\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay position along the beam line, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=350\,\mathrm{GeV}$ and $m_X=80\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay position along the beam line, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=350\,\mathrm{GeV}$ and $m_X=160\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay position along the beam line, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=350\,\mathrm{GeV}$ and $m_X=160\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay position along the beam line, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=350\,\mathrm{GeV}$ and $m_X=160\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay position along the beam line, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=350\,\mathrm{GeV}$ and $m_X=160\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay position along the beam line, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=350\,\mathrm{GeV}$ and $m_X=160\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay position along the beam line, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=125\,\mathrm{GeV}$ and $m_X=25\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay position along the beam line, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=125\,\mathrm{GeV}$ and $m_X=25\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay position along the beam line, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=125\,\mathrm{GeV}$ and $m_X=25\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay position along the beam line, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=125\,\mathrm{GeV}$ and $m_X=25\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

The L1T+HLT acceptances for various LLP triggers using different subdetectors, as functions of the LLP decay position along the beam line, for $H \to X X \to b\bar{b}\,b\bar{b}$ events for 2023 conditions with $m_H=125\,\mathrm{GeV}$ and $m_X=25\,\mathrm{GeV}$. The $c\tau$ is 0.1\,m for the displaced-jet triggers using the tracker and 1\,m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown.

Comparison of the acceptances in Run 2 and Run 3 for the CSC (left) and DT (right) MDS triggers at the L1T and HLT as functions of the LLP lifetime, for $H \to S S \to b\bar{{b}}\,b\bar{{b}}$ events with $m_{H}=125$ GeV and $m_{S}=40$ GeV, for 2023 conditions. The acceptance is defined as the fraction of events that pass the specified selection, given an LLP decay in the fiducial region of the CSCs (left) or DTs (right). The left plot compares the acceptance of the Run 2 strategy of triggering on $p_T^{miss}$ (blue circles), which corresponds to an offline requirement of $>200$ GeV, with that of the Run 3 strategy of triggering on the MDS signature in the CSCs, for both the L1T (L1T+HLT) acceptance is shown with orange squares (red triangles). The right plot compares the acceptance of the Run 2 strategy of triggering on $p_T^{miss}$ (blue circles) with the Run 3 strategy of triggering on the MDS signature in the DTs (red triangles), for L1T+HLT.

The L1T (blue circles) and L1T+HLT (orange squares) acceptances for the CSC MDS trigger as functions of the LLP decay positions in the $z$-direction, for $H \to S S \to b\bar{{b}}\,b\bar{{b}}$ events with $m_{H}=350$ GeV, $m_{S}=80$ GeV, and $c\tau_{S}=1$ m, for 2023 conditions.

The HLT (blue circles) and L1T+HLT (orange squares) acceptances for the DT MDS trigger as functions of the LLP decay positions in the radial direction, for $H \to S S \to b\bar{{b}}\,b\bar{{b}}$ events with $m_{H}=350$ GeV, $m_{S}=80$ GeV, and $c\tau_{S}=1$ m, for 2023 conditions.

The L1T acceptance for the CSC MDS trigger as functions of the LLP decay position, for $H \to S S \to b\bar{{b}}\,b\bar{{b}}$ events with $m_{H}=350$ GeV, $m_{S}=80$ GeV, and $c\tau_{S}=1$ m, for 2023 conditions.

The L1T+HLT acceptance for the CSC MDS trigger as functions of the LLP decay position, for $H \to S S \to b\bar{{b}}\,b\bar{{b}}$ events with $m_{H}=350$ GeV, $m_{S}=80$ GeV, and $c\tau_{S}=1$ m, for 2023 conditions.

The HLT acceptance for the DT MDS trigger as a function of the LLP decay position, for $H \to S S \to b\bar{{b}}\,b\bar{{b}}$ events with $m_{H}=350$ GeV, $m_{S}=80$ GeV, and $c\tau_{S}=1$ m, for 2023 conditions. The L1T acceptance that is based on the $p_T^{miss}$ trigger is not included.

The L1T+HLT acceptance of the displaced $\tau_\mathrm{h}$ trigger, for simulated $\mathrm{p}\mathrm{p} \to \tilde{\tau}\tilde{\tau},(\tilde{\tau} \to \tau\tilde{\chi}^{0}_{1})$ events,where each $\tau$ decays hadronically and the $\tilde{\tau}$ has a simulated $c\tau$ of 10 cm. The acceptance is shown for the displaced di-$\tau_\mathrm{h}$ trigger path for 2022 data-taking conditions and is plotted with respect to the generator-level $\tau$ lepton decay vertex radial position. Selections on the visible component of the generator-level $\tau$ lepton $\mathrm{p_{T}}$ ($\mathrm{p_{T}}(\tau) > 30$ GeV), its pseudorapidity ($|\eta(\tau)| <$ 2.1), and its decay vertex radial position ($R < $115 cm) are applied.

Inverse HLT muon $p_\text{T}$ resolution ($(1/p_\text{T}^\text{HLT}-1/p_\text{T}^\text{gen})/(1/p_\text{T}^\text{gen})$) as a function of the generator-level muon $p_\text{T}$, for simulated HAHM signal events, where the dark Higgs boson ($\text{H}_\text{D}$) mixes with the SM Higgs boson ($\text{H}$) and decays to a pair of long-lived dark photons ($\text{Z}_\text{D}$), for various values of $m_{\text{Z}_\text{D}}$ and $\epsilon$. Conditions for 2022 data-taking are shown. The muons must have $p_\text{T}>10\text{ GeV}$, and the L2 and L3 muons are geometrically matched to the generator-level muons.

Inverse HLT muon $p_\text{T}$ resolution ($(1/p_\text{T}^\text{HLT}-1/p_\text{T}^\text{gen})/(1/p_\text{T}^\text{gen})$) as a function of the generator-level $L_{xy}$, for simulated HAHM signal events, where the dark Higgs boson ($\text{H}_\text{D}$) mixes with the SM Higgs boson ($\text{H}$) and decays to a pair of long-lived dark photons ($\text{Z}_\text{D}$), for various values of $m_{\text{Z}_\text{D}}$ and $\epsilon$. Conditions for 2022 data-taking are shown. The muons must have $p_\text{T}>10\text{ GeV}$, and the L2 and L3 muons are geometrically matched to the generator-level muons. The dashed vertical lines indicate the radial positions of the layers of the tracking detectors, with BPX, TIB, and TOB denoting the barrel pixel, tracker inner barrel, and tracker outer barrel, respectively.

Expected and observed 95% CL upper limits on the V' boson production cross section as functions of the resonance mass mV' in the HVT model A.

Expected and observed 95% CL upper limits on the V' boson production cross section as functions of the resonance mass mV' in the HVT model B.

Expected and observed 95% CL upper limits on the V' boson production cross section as functions of the resonance mass mV' in the HVT model C.

Expected and observed 95% CL exclusion contour in gF-gH parameter space for the DIQ channel at 3 TeV. Here, model A corresponds to (0.556, 0.562) and model B to (-2.928, 0.146)

Expected and observed 95% CL exclusion contour in gF-gH parameter space for the DIQ channel at 4 TeV.

Expected and observed 95% CL exclusion contour in gF-gH parameter space for the DIL channel at 3 TeV.

Expected and observed 95% CL exclusion contour in gF-gH parameter space for the DIL channel at 4 TeV.

Expected and observed 95% CL exclusion contour in gH-gF parameter space for the DIB channel at 3 TeV.

Expected and observed 95% CL exclusion contour in gH-gF parameter space for the DIB channel at 4 TeV.

Expected and observed 95% CL exclusion contour in gF-gH parameter space for the Full Combined channel at 3 TeV.

Expected and observed 95% CL exclusion contour in gF-gH parameter space for the Full Combined channel at 4 TeV.

Expected and observed 95% CL exclusion contour in g_q12-g_q3 parameter space at m_V' = 3 TeV. Uncertainty bands shown as separate contour lines. Channels not in combination are shown separately.

Expected and observed 95% CL exclusion contour in g_q12-g_q3 parameter space at m_V' = 4 TeV. Uncertainty bands shown as separate contour lines. Channels not in combination are shown separately.

Expected and observed 95% CL upper limits on the W' production cross section in the HVT Model A benchmark, compared with the theoretical prediction.

Expected and observed 95% CL upper limits on the W' production cross section in the HVT Model B benchmark, compared with the theoretical prediction.

Expected and observed 95% CL upper limits on the W' production cross section in the HVT Model C benchmark, compared with the theoretical prediction.

Expected and observed 95% CL upper limits on the Z' production cross section in the HVT Model A benchmark, compared with the theoretical prediction.

Expected and observed 95% CL upper limits on the Z' production cross section in the HVT Model B benchmark, compared with the theoretical prediction.

Expected and observed 95% CL upper limits on the Z' production cross section in the HVT Model C benchmark, compared with the theoretical prediction.

Observed (solid black line) and median expected (dashed black line) upper limits at 95% CL on the signal cross section times branching fraction $\sigma (\mathrm{pp} \to \mathrm{H})\,\mathcal{B}(\mathrm{H} \to \mathcal{A} \mathcal{A} \to 4 \gamma)$ at various $m_A$ mass points. The 68 and 95% confidence intervals around the median expected limit are shown as the green and yellow bands, respectively.

Relative cutflow fractions for representative signal samples, normalized to the number of events before any selection (All events = 1.0). The selections correspond to the trigger requirement, photon multiplicity and identification, kinematic requirements on the three-photon system, a selection on the angular separation (dR) of photons consistent with a merged topology, and a multivariate (MVA) discriminator and a charged-hadron isolation requirement applied to photon candidates used to suppress jet background. The final SR corresponds to the combination of the $m_H$ and $m_A$ signal regions used in the final fit.

The postfit pDNN distributions in the SR $\mu$ 3b3j assuming $m_{H^\pm} = 600$ GeV. Postfit signal for $m_{H^\pm} = 600$ GeV is also shown. Beneath plot the ratio of data to predictions is shown.

The postfit pDNN distributions in the SR e 2b2j assuming $m_{H^\pm} = 1$ TeV. The signal for $m_{H^\pm} = 1$ TeV is also shown before the fit, assuming a cross section of 1 pb.Beneath plot the ratio of data to predictions is shown.

The postfit pDNN distributions in the SR $\mu$ 2b2j assuming $m_{H^\pm} = 1$ TeV. The signal for $m_{H^\pm} = 1$ TeV is also shown before the fit, assuming a cross section of 1 pb.Beneath plot the ratio of data to predictions is shown.

The postfit pDNN distributions in the SR e 3b3j assuming $m_{H^\pm} = 1$ TeV. The signal for $m_{H^\pm} = 1$ TeV is also shown before the fit, assuming a cross section of 1 pb.Beneath plot the ratio of data to predictions is shown.

The postfit pDNN distributions in the SR $\mu$ 3b3j assuming $m_{H^\pm} = 1$ TeV. The signal for $m_{H^\pm} = 1$ TeV is also shown before the fit, assuming a cross section of 1 pb.Beneath plot the ratio of data to predictions is shown.

Observed and expected 95% CL limits on the cross section times branching ratio for different $H^{\pm}$ mass hypotheses with $ρ_{tc} = 0.4$, $ρ_{tt} = 0.6$ . The inner (green) band and the outer (yellow) band represent the regions containing 68% and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. Theoretical prediction with different $ρ_{tc}$ and $ρ_{tt}$ couplingsare shown with the grey bands representing the corresponding uncertainties due to the factorization and renormalization scales and the PDFs.

Observed excluded phase-space regions, based on 95% CL limits, as a function of $m_{H^{\pm}}$ and $ρ_{tc}$ for various assumed $ρ_{tt}$ values represented with different colors. The limits are extracted from the pDNN distributions based on g2HDM assuming all the extra Yukawa couplings except $ρ_{tt}$ and $ρ_{tc}$ are zero. The results are obtained from the 95% CL limits on the cross section times branching fraction in Fig 6.

Expected excluded phase-space regions, based on 95% CL limits, as a function of $m_{H^{\pm}}$ and $ρ_{tc}$ for various assumed $ρ_{tt}$ values represented with different colors. The limits are extracted from the pDNN distributions based on g2HDM assuming all the extra Yukawa couplings except $ρ_{tt}$ and $ρ_{tc}$ are zero. The results are obtained from the 95% CL limits on the cross section times branching fraction in Fig 6.

Observed excluded phase-space regions, based on 95% CL limits, as a function of $m_{H^{\pm}}$ and $ρ_{tc}$ for various assumed $ρ_{tt}$ values represented with different colors. The limits are extracted from the pDNN distributions based on g2HDM assuming all the extra Yukawa couplings except $ρ_{tt}$ and $ρ_{tc}$ are zero. The results are obtained from the 95% CL limits on the cross section times branching fraction in Fig 6.

Expected excluded phase-space regions, based on 95% CL limits, as a function of $m_{H^{\pm}}$ and $ρ_{tc}$ for various assumed $ρ_{tt}$ values represented with different colors. The limits are extracted from the pDNN distributions based on g2HDM assuming all the extra Yukawa couplings except $ρ_{tt}$ and $ρ_{tc}$ are zero. The results are obtained from the 95% CL limits on the cross section times branching fraction in Fig 6.

Observed excluded phase-space regions, based on 95% CL limits, as a function of $m_{H^{\pm}}$ and $ρ_{tc}$ for various assumed $ρ_{tt}$ values represented with different colors. The limits are extracted from the pDNN distributions based on g2HDM assuming all the extra Yukawa couplings except $ρ_{tt}$ and $ρ_{tc}$ are zero. The results are obtained from the 95% CL limits on the cross section times branching fraction in Fig 6.

Expected excluded phase-space regions, based on 95% CL limits, as a function of $m_{H^{\pm}}$ and $ρ_{tc}$ for various assumed $ρ_{tt}$ values represented with different colors. The limits are extracted from the pDNN distributions based on g2HDM assuming all the extra Yukawa couplings except $ρ_{tt}$ and $ρ_{tc}$ are zero. The results are obtained from the 95% CL limits on the cross section times branching fraction in Fig 6.

Observed excluded phase-space regions, based on 95% CL limits, as a function of $m_{H^{\pm}}$ and $ρ_{tc}$ for various assumed $ρ_{tt}$ values represented with different colors. The limits are extracted from the pDNN distributions based on g2HDM assuming all the extra Yukawa couplings except $ρ_{tt}$ and $ρ_{tc}$ are zero. The results are obtained from the 95% CL limits on the cross section times branching fraction in Fig 6.

Expected excluded phase-space regions, based on 95% CL limits, as a function of $m_{H^{\pm}}$ and $ρ_{tc}$ for various assumed $ρ_{tt}$ values represented with different colors. The limits are extracted from the pDNN distributions based on g2HDM assuming all the extra Yukawa couplings except $ρ_{tt}$ and $ρ_{tc}$ are zero. The results are obtained from the 95% CL limits on the cross section times branching fraction in Fig 6.

Observed excluded phase-space regions, based on 95% CL limits, as a function of $m_{H^{\pm}}$ and $ρ_{tc}$ for various assumed $ρ_{tt}$ values represented with different colors. The limits are extracted from the pDNN distributions based on g2HDM assuming all the extra Yukawa couplings except $ρ_{tt}$ and $ρ_{tc}$ are zero. The results are obtained from the 95% CL limits on the cross section times branching fraction in Fig 6.

Expected excluded phase-space regions, based on 95% CL limits, as a function of $m_{H^{\pm}}$ and $ρ_{tc}$ for various assumed $ρ_{tt}$ values represented with different colors. The limits are extracted from the pDNN distributions based on g2HDM assuming all the extra Yukawa couplings except $ρ_{tt}$ and $ρ_{tc}$ are zero. The results are obtained from the 95% CL limits on the cross section times branching fraction in Fig 6.

Two times the difference of the negative log-likelihood (NLL) as a function of σ(pp →(q$^{light}$)H$^{\pm}$) B(H$^{\pm}$ → tb, t → blν) and σ(pp → bH$^{\pm}$)B(H$^{\pm}$ → tb, t → blν) with the best fit point extracted from the pDNN distribution for the $H^{\pm}$ mass $m_{H^{\pm}} = 600$ GeV. The solid and dashed contours represent the observed and expected limits, respectively. The points along the contours represent 68% and 95% CL regions, extracted from the 2∆NLL values of 2.30 and 5.99, respectively. The g2HDM predictions are also shown. The points along the g2HDM prediction line represent different $ρ_{tt}$, $ρ_{tc}$ coupling sets, with all other extra Yukawa couplings assumed to be zero.

Two times the difference of the negative log-likelihood (NLL) as a function of σ(pp →(q$^{light}$)H$^{\pm}$) B(H$^{\pm}$ → tb, t → blν) and σ(pp → bH$^{\pm}$)B(H$^{\pm}$ → tb, t → blν) with the best fit point extracted from the pDNN distribution for the $H^{\pm}$ mass $m_{H^{\pm}} = 600$ GeV. The solid and dashed contours represent the observed and expected limits, respectively. The points along the contours represent 68% and 95% CL regions, extracted from the 2∆NLL values of 2.30 and 5.99, respectively. The g2HDM predictions are also shown. The points along the g2HDM prediction line represent different $ρ_{tt}$, $ρ_{tc}$ coupling sets, with all other extra Yukawa couplings assumed to be zero.

Two times the difference of the negative log-likelihood (NLL) as a function of σ(pp →(q$^{light}$)H$^{\pm}$) B(H$^{\pm}$ → tb, t → blν) and σ(pp → bH$^{\pm}$)B(H$^{\pm}$ → tb, t → blν) with the best fit point extracted from the pDNN distribution for the $H^{\pm}$ mass $m_{H^{\pm}} = 1000$ GeV. The solid and dashed contours represent the observed and expected limits, respectively. The points along the contours represent 68% and 95% CL regions, extracted from the 2∆NLL values of 2.30 and 5.99, respectively. The g2HDM predictions are also shown. The points along the g2HDM prediction line represent different $ρ_{tt}$, $ρ_{tc}$ coupling sets, with all other extra Yukawa couplings assumed to be zero.

Two times the difference of the negative log-likelihood (NLL) as a function of σ(pp →(q$^{light}$)H$^{\pm}$) B(H$^{\pm}$ → tb, t → blν) and σ(pp → bH$^{\pm}$)B(H$^{\pm}$ → tb, t → blν) with the best fit point extracted from the pDNN distribution for the $H^{\pm}$ mass $m_{H^{\pm}} = 1000$ GeV. The solid and dashed contours represent the observed and expected limits, respectively. The points along the contours represent 68% and 95% CL regions, extracted from the 2∆NLL values of 2.30 and 5.99, respectively. The g2HDM predictions are also shown. The points along the g2HDM prediction line represent different $ρ_{tt}$, $ρ_{tc}$ coupling sets, with all other extra Yukawa couplings assumed to be zero.

Covariance for spin correlation coefficients in beam basis for $p_{T}(t)$ vs. $|cos(\theta)|$ bins

Results for Eigenstate decomposition for $|\Phi^{+} \rangle$ in Helicity basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

Results for Eigenstate decomposition for $|\Phi^{-} \rangle$ in Helicity basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

Results for Eigenstate decomposition for $|\Psi^{+} \rangle$ in Helicity basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

Results for Eigenstate decomposition for $|\Psi^{-} \rangle$ in Helicity basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

Results for Eigenstate decomposition for $|\uparrow \uparrow \rangle$ in Beam basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

Results for Eigenstate decomposition for $|\downarrow \downarrow \rangle$ in Beam basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

Results for Eigenstate decomposition for $|\Psi^{+} \rangle$ in Beam basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

Results for Eigenstate decomposition for $|\Psi^{-} \rangle$ in Beam basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

Results for Purity in Helicity basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

Results for Purity in Beam basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

Results for Entropy in Helicity basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

Results for Entropy in Beam basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

Results for Entanglement in Helicity basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

Results for Entanglement in Beam basis in $m(t\bar{t})$ vs. $|cos(\theta)|$ bins

Results for Eigenstate decomposition for $|\Phi^{+} \rangle$ in Helicity basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

Results for Eigenstate decomposition for $|\Phi^{-} \rangle$ in Helicity basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

Results for Eigenstate decomposition for $|\Psi^{+} \rangle$ in Helicity basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

Results for Eigenstate decomposition for $|\Psi^{-} \rangle$ in Helicity basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

Results for Eigenstate decomposition for $|\uparrow \uparrow \rangle$ in Beam basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

Results for Eigenstate decomposition for $|\downarrow \downarrow \rangle$ in Beam basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

Results for Eigenstate decomposition for $|\Psi^{+} \rangle$ in Beam basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

Results for Eigenstate decomposition for $|\Psi^{-} \rangle$ in Beam basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

Results for Purity in Helicity basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

Results for Purity in Beam basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

Results for Entropy in Helicity basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

Results for Entropy in Beam basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

Results for Entanglement in Helicity basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

Results for Entanglement in Beam basis in $p_{T}(t)$ vs. $|cos(\theta)|$ bins

Measured and expected fiducial cross section for Z$\gamma$ production. Corresponding to Table 1 in the paper.

Data selection efficiency as a function of nuclear recoil energy

Data points used in analysis in log_10(S2)-S1 space

Normalized differential cross sections, compared with the SM predictions, as a function of the absolute value of pseudorapidity of the subleading jet in transverse momentum. The SM predictions are obtained using Madgraph5_aMC@NLO version 2.6.5 at NLO in QCD with PYTHIA version 8.240

Normalized differential cross sections, compared with the SM predictions, as a function of the invariant mass of the two jets. The SM predictions are obtained using Madgraph5_aMC@NLO version 2.6.5 at NLO in QCD with PYTHIA version 8.240

Normalized differential cross sections, compared with the SM predictions, as a function of the photon's transverse momentum. The SM predictions are obtained using Madgraph5_aMC@NLO version 2.6.5 at NLO in QCD with PYTHIA version 8.240

Normalized differential cross sections, compared with the SM predictions, as a function of the event centrality as defined in Ref.[13] of the paper. The SM predictions are obtained using Madgraph5_aMC@NLO version 2.6.5 at NLO in QCD with PYTHIA version 8.240

Normalized differential cross sections, compared with the SM predictions, as a function of the Zeppenfeld variable that is defined in Eq.(1) of the paper. The SM predictions are obtained using Madgraph5_aMC@NLO version 2.6.5 at NLO in QCD with PYTHIA version 8.240

Negative of twice in the difference in the log-likelihood as a function of $c_{\mathrm{W}}$, based on 138 $\mathrm{fb}^{-1}$ of CMS data at 13 TeV.

Negative of twice in the difference in the log-likelihood as a function of $c_{\mathrm{HWB}}$, based on 138 $\mathrm{fb}^{-1}$ of CMS data at 13 TeV.

Negative of twice in the difference in the log-likelihood as a function of $c_{\mathrm{HWB}}$ and $c_{\mathrm{W}}$, based on 138 $\mathrm{fb}^{-1}$ of CMS data at 13 TeV.

Predicted and measured EWK $\gamma\mathrm{jj}$ fiducial cross sections.