been misidentified as a hadronic $\tau$, and these are estimated using
either data-driven methods or simulated events. In the
$Z\rightarrow \tau\tau$ enriched region the background from
misidentified jets come from QCD or $W$+jets processes, while in
the $t\bar{t}$ enriched region the background comes from QCD or
semi-leptonic $t\bar{t}$ decay events. Other minor background sources
are due to diboson or $Z\rightarrow ee$ events where an electron is
mis-reconstructed as a hadronic $\tau$.  Figure <ref> shows
the comparison between data and MC simulation of the tau  in the
one-prong case for the $Z\rightarrow \tau\tau$ and $t\bar{t}$
selections obtained with the electron tag and tau probe trigger.

Distributions for data and MC simulation of the  of
one-prong taus in (left) the $Z\rightarrow \tau\tau$ and (right)
the $t\bar{t}$ signal regions (SRs). The data set
was recorded with the $e-\tau$ tag-and-probe trigger.
The bottom panels show the ratio
between data and the signal-plus-background prediction. Only
statistical uncertainties are shown.

The tau trigger efficiency is calculated with respect to the reconstructed offline tau candidates and is separated between one-prong and three-prong tau cases. Figure <ref> shows the resulting efficiency as a function of the offline tau  for one-prong and three-prong tau candidates using 2022 data recorded
with a combined electron tag and tau probe trigger.

Tau trigger efficiencies as a function of offline tau
for (left) the one-prong and (right) three-prong tau
candidates. The legacy isolated L1 tau trigger with $\et>12$  defined in Ref. <cit.> is used as the seed.
The measurement is performed using a combination of
$Z\rightarrow \tau\tau$ and $t\bar{t}$ selections <cit.> in events
recorded with the $e-\tau$ tag-and-probe trigger. The efficiency from the sum
of the $Z\rightarrow \tau\tau$ and $t\bar{t}$ signal MC processes
is shown with open markers, while the background-subtracted data
efficiency is shown with filled markers. The bottom panels show the
ratio between background-subtracted data and signal MC
efficiencies. Only statistical uncertainties are shown.

In the one-prong selection, the resulting efficiency of the tau
trigger reaches a plateau slightly below 95% for tau candidates with
$\pT>40\,$, while it is about 90% for the three-prong
case. The small differences between the data and MC signal prediction observed in Figure <ref>
are used to derive scale factors to correct other MC simulation samples used in data analyses.

§.§ Jets

§.§.§ Jet trigger reconstruction

A detailed description of jet triggers in can be found in Ref. <cit.>. At the HLT, small- and
large-radius jets are reconstructed using the algorithm <cit.> with a radius parameter
of $R=0.4$ and $R=1.0$, respectively. While jet triggers in employed only calorimeter topo-clusters
as input, triggers are able to rely on PFO
thanks to the extended tracking capabilities offered by the HLT in .

Despite the large reductions in tracking time at the HLT, the CPU time usage of jet chains is still
high due to full scan tracking, as discussed in Section <ref>.
For high-jet chains such as single- and multi-jet chains, the large gap between L1 and HLT thresholds allows for an early reduction in event rate via the application of a calorimeter-only jet selection (calorimeter preselection) before any kind of tracking is executed. It is based on topo-cluster jets,
described in Section <ref>. Minimal HLT jet requirements are adjusted to obtain the maximal CPU-time reduction which does not impact trigger efficiencies.
The preselection stage is found to reduce the output rates of HLT jet trigger chains by less than 2%.
Table <ref> shows the impact of different preselections on the event rates of various jet triggers.

Impact of calorimeter preselections on the event rates of jet triggers in which tracking reconstruction is performed.
The percentage of events passing the preselection step is estimated with respect to the original L1 trigger rate from a reprocessing of Enhanced-bias data <cit.>.
The HLT selection column shows the lowest jet trigger threshold which this preselection is applied for.

L1 selection     Preselection     HLT selection         Events passing preselection

1 jet, $\pt>100\,$     1 jet, $\pt>225\,$     1 jet, $\pt>275\,$      23%

3 jets, $\pt>50\,$     4 jets, $\pt>85\,$      4 jets, $\pt>115\,$      15%

4 jets, $\pt>15\,$      5 jets, $\pt>50\,$      5 jets, $\pt>70\,$      7%

4 jets, $\pt>15\,$      6 jets, $\pt>40\,$     6 jets, $\pt>55\,$      6%

Even though this strategy works well for baseline jet triggers, it is not optimal for triggers
whose HLT jet thresholds are very close to the L1 thresholds. One example of such triggers is the $b$-jet triggers,
where a more complex preselection step
detailed in Sections <ref> and <ref> is included in the HLT reconstruction.

After the preselection step, fast full scan tracking is executed as detailed in Section <ref>
and the resulting tracks are extrapolated to the calorimeter. The PFO formation starts by matching
full scan tracks and topo-clusters taking into account the extrapolated track position and topo-cluster location.
The topo-clusters which are not matched to any track are referred to as neutral PFOs.
The matched topo-clusters have their energy removed according to the expected calorimeter energy
deposited by the matched track. The tracks are considered as charged PFOs. Any topo-cluster surviving
the energy subtraction procedure becomes a neutral PFO. Charged PFOs not matched to the primary
vertex are discarded,
which is the dominant means of pile-up suppression.
Outside the geometrical acceptance of the tracker, only the calorimeter information is available. Hence, in the forward region
the topo-clusters alone are used as inputs to the PFlow jet reconstruction.

After reconstruction, small-$R$ jets are calibrated through a procedure similar to that used
offline <cit.>. A correction accounting for pile-up contamination is applied on
an event-by-event basis to the jets. This is followed by another correction, compensating for
the energy response of the calorimeter. Finally, a sequence of calibrations is applied to
PFlow triggers to correct for the residual discrepancies between reconstructed and simulated
jets and accounts, for example, for energy differences resulting from the different showering of quarks and gluons.

For , large-$R$ jet triggers are also extended
to use PFOs as inputs.
In addition, the Constituent Subtraction <cit.> and SoftKiller <cit.>
algorithms are applied to neutral PFOs to subtract energy contamination originating from pile-up interactions.
After this step,
Soft Drop grooming <cit.> with parameters $\beta=1.0$ and $z_\text{cut} =0.1$ is
applied to mitigate the contamination from initial state radiation and underlying event.
Finally, a calibration similar to small-$R$ jets is used to correct for the energy response of
the ATLAS calorimeter and adjust the reconstructed mass of the large-$R$ jet.

§.§.§ Jet trigger menu

Jet triggers are used for a wide set of measurements, ranging from precision physics measurements to detector performance studies.
The inclusive jet, di-jet and multi-jet production measurements rely on the events selected
by small-$R$ single- and multi-jet triggers. Events selected by these triggers are also employed for the calibrations of the jet
energy scale and resolution, as well as for new physics searches such as supersymmetry. Another important class of jet
triggers is represented by large-$R$ triggers, selecting final states with boosted weak vector bosons (W/Z) or Higgs bosons. These triggers
are generally employed by analyses searching for heavy resonances predicted, for example, by theories of extra-dimensions and the two-Higgs-doublet model.

The jet trigger chains are initiated by L1 algorithms selecting single jets, multi-jets, or, for very low- HLT thresholds,
a random trigger at L1.
The primary, unprescaled jet chain applies a threshold of 420  and has a rate of 42 Hz (at $1.8\times\lumi{e34}$).
Small-$R$ single jet chains with  thresholds below 420  are prescaled to provide a complete jet  spectrum, with a constant rate per chain ranging from 1 to 4 Hz; large-$R$ single jets with thresholds between 110  and 460  are also collected using prescaled triggers at a rate range between 2 and 3 Hz per chain.
Trigger chains, which select events based on the scalar sum of the transverse momentum of all jets (), contribute with a rate of 34 Hz.
Topo-cluster-based jet triggers are also available in as a backup for PFlow jet triggers.

Efficiency of the legacy L1 single jet triggers in the (left) central
and (right) forward
regions. The efficiency is computed using the bootstrap method with respect to events taken by an independent trigger, shown in brackets, that is 100% efficient in the relevant region.
Only statistical uncertainties are shown.

Efficiency of single jet trigger selection by the HLT in the (left) central
and (right) forward
regions. Central PFlow jet triggers exploit the particle flow reconstruction with calorimeter clusters and tracks,
while forward PFlow jet triggers rely on the topo-cluster-based reconstruction
to trigger events outside the ID acceptance ($|\eta| < 2.5$). The efficiency is computed using the bootstrap method with respect to events taken by an independent trigger, shown in brackets, that is 100% efficient in the relevant region.
Only statistical uncertainties are shown.

Multi-jet trigger efficiency as a function of the offline reconstructed $N^\text{th}$ jet (left) at L1
and (right) in the HLT. The efficiency is computed using the bootstrap method with respect to events taken by an independent single jet trigger,
shown in brackets, that is 100% efficient in the relevant region. Only statistical uncertainties are shown.

L1 and HLT efficiencies are shown for
single large-$R$ jet triggers as a function of (top left) the leading offline large-$R$ jet and (top right) highest mass offline large-$R$ jet mass (m), (bottom left) large-$R$ single jet triggers with a mass cut as a function of leading offline large-$R$ jet  and (bottom right)  triggers as a function of offline .
The efficiency of triggers is computed using the bootstrap method with respect to events taken by an independent trigger, shown in brackets,
that is 100% efficient in the relevant region.
Only statistical uncertainties are shown.

§.§.§ Jet trigger performance

The efficiency of jet triggers is primarily a function of the  of the leading jet in the event, and is measured using the bootstrap method.
In addition to the selection criteria specified in the following figures, the offline jets are required to satisfy a timing cut of less than
12.5 ns to minimise the contamination from out-of-time pile-up jets.

The efficiencies of L1 and HLT single jet triggers as a function of offline reconstructed jet  are shown in Figures <ref> and <ref>, respectively. A steep rise in efficiency near the nominal thresholds reflects the compatibility of energy scales for jets reconstructed in the trigger and offline.

The efficiency of a multi-jet trigger requiring \(N\) jets depends mostly on the  of the \(N^\text{th}\) -ranked jet. The relevant efficiency measurements are shown in Figure <ref> as a function of the offline reconstructed \(N^\text{th}\) jet  for the primary L1 and HLT multi-jet triggers.
Lower efficiency at high  in the L1 four-jet trigger is due to the merging of the close-by jets at L1, which should be improved in the upgraded L1Calo system.

Efficiencies of the large-$R$ jets as a function of the leading offline jet  are shown in Figure <ref> (top left), for both HLT and L1 trigger chains.
Figures <ref> (top right) and (bottom left) present the efficiencies as a function of the offline jet mass and , respectively, for two main HLT chains with mass cuts.
The L1 seed is shown not to have an impact on the efficiency of these triggers due to the large gap between L1 and HLT thresholds.
The triggers shown are fully efficient at high jet and mass values, and the steep rise in efficiency near the nominal thresholds reflects a good energy resolution.

The \(H_T\) trigger efficiency as a function of offline  is presented in Figure <ref> (bottom right) for both L1 and HLT triggers,
which also rises sharply. The observed data/MC differences will be corrected later-on in physics analyses by dedicated scale factors applied to MC simulation samples.

§.§.§ Trigger level analysis with jets

HLT topo-cluster-based and PFlow jets with transverse momentum larger than 20  are saved to the TLA stream described in Section <ref>.
To remain within the CPU constraints of the HLT farm, full scan tracking and PFO reconstruction are executed only
if the event passes the calorimeter preselection step.

In 2022, jet chains populating the TLA stream were seeded by two L1Calo legacy triggers, L1 jet $\pt>100\,$ (which reaches 50% efficiency at around 160 ) and
with a total rate of approximately 4 kHz.
This allows for the recording of orders of magnitude more events containing lower-jets with respect to standard ATLAS jet triggers, extending the sensitivity of hadronic searches to resonance masses as low as 400  <cit.>.

As shown in Figure <ref>, the response of trigger jets with the default calibration is already within 2% of offline jets across the momentum range of interest to TLA studies.
For , a custom residual energy scale calibration is to be derived and applied at the analysis level in order to further improve the response and resolution of TLA jets.
In order to derive such a calibration, an extensive set of jet variables, beyond the jet four-momentum, is saved in the TLA stream.
This includes the energy fraction deposited in
the EM and hadronic endcap calorimeters, the momentum density of soft radiation in the event, the number of primary vertices reconstructed at the HLT, the jet active area <cit.>,
and the number of constituents encompassing 90% of the jet transverse energy.

The response curve for HLT-level PFlow jets in the momentum range of interest for Run 3 TLA.
The online-to-offline response is evaluated at the final energy scale in the calibration sequence
of the jets. HLT-level jets are calibrated with the default sequence used at the HLT for the 2022 data taking.
Offline jets are corrected with the calibration available during 2022 data-taking. Events are required to pass the single
jet $p_{\text{T}} > 15\,$ (circle markers), $p_{\text{T}} > 25\,$ (triangle markers) or $p_{\text{T}} > 35\,$ (square markers) random-seeded triggers depending on the
$p_{\text{T}}$ of the leading reference jet. For each event, only HLT jets matched ($\Delta R < 0.3$) to the leading and
sub-leading offline jets reconstructed within $\left|\eta\right| < 2.4$ are considered. The overlaid heat map refers
to the number of events in the analyzed sample for each configuration of the reference jet momentum and response.

§.§.§ Jet triggers for heavy-ion collisions

Jets are direct probes of the quark–gluon plasma produced in HI collisions, and studying how they are
modified in such collisions compared to collisions provides insight into their interactions with this QCD medium.
The main challenge for triggering on jets in HI collisions is the presence of a large amount of UE.
The HLT jet algorithm uses the HI UE subtraction procedure described in Section <ref>
and selects events containing jets with transverse energies exceeding a threshold ranging from 60 to $85$ .
Jets are reconstructed at the HLT across the entire calorimeter using the anti-algorithm with distance parameter
$R = 0.4$, from projective towers of size $\Delta\eta \times \Delta\phi = 0.1 \times 0.1$ formed from the summation of calorimeter cell energies with UE subtraction applied.

§.§ Jets containing $b$-hadrons

§.§.§ $b$-jet trigger reconstruction and selection

Triggers based on jets containing $b$-hadrons, so-called $b$-jet triggers, are designed to allow for highly efficient recording of fully hadronic events
with predominantly heavy flavor content jets. The detailed description of the $b$-jet triggers in can be found in Ref. <cit.>, the changes for are discussed here.
The basic inputs to $b$-tagging are reconstructed jets, reconstructed tracks and the position of the
primary vertex.
The jet reconstruction is described in Section <ref>.
The primary vertex finding and $b$-jet track reconstruction are discussed in Sections <ref> and <ref>, respectively.

The main $b$-jet identification steps are as follows:

* A fast $b$-tagging algorithm is run on super-and uses the tracks inside them to provide the first $b$-jet preselection. To reduce the rate of the full scan tracking for $b$-jet triggers, the $b$-jet preselection stage is run with lower track  thresholds and
with a super-composed of wider regions around jets than were used for the vertex tracking in  <cit.>.
The details of the fast $b$-tagging algorithm used at this stage are provided in Ref. <cit.>.

* The final $b$-tagging algorithm, detailed below, uses precision tracking and primary vertex information.

The $b$-jet identification relies on the properties of $b$-hadrons: long lifetime (about 1.5 ps), hard fragmentation, a relatively large mass of about 5 ,
and a displaced (secondary) vertex (SV) formed a few millimeters away from the primary vertex.
Tracks associated with $b$-jets are characterised by larger transverse ($d_0$) and longitudinal ($z_0$) impact parameters.
In addition, $b$-hadrons decay semileptonically, either promptly, or via a subsequent $c$-hadron decay, to electrons or muons.
The branching ratio of these semileptonic decays is about 20% each and results in the presence of a low-lepton close to the $b$-jet.

The flavor tagging identification is done in two steps <cit.>.
Low-level algorithms reconstruct characteristic features of the heavy flavor jets
based on track properties, such as impact parameters, or combine those tracks to reconstruct the SV. The outputs of these low-level algorithms are then
combined into high-level algorithms, usually using some multivariate technique.

Low-level taggers used at the HLT are the IP2D algorithm, which utilises the signed transverse impact parameter significance of tracks,
and the IP3D algorithm, which uses, in addition, the longitudinal impact parameter significance <cit.>.

The secondary vertex algorithm, SV1, uses tracks associated with jets (after rejecting those compatible with $K_s$ or
$\Lambda$, photon conversions or interactions with detector material) to assign decay products from
$b$- or $c$-hadrons to a single common SV. Several discriminating variables associated with the SV are then used as inputs to the high-level tagger.
Finally, the JetFitter algorithm exploits the topology of weak $b$- and subsequent $c$-hadron decays inside a jet to reconstruct the full decay chain,
recreating the approximate $b$-hadron path from the primary vertex via bottom and charm vertices.

Another low-level algorithm is the Deep Impact Parameter Sets (DIPS) <cit.>, based on the Deep Sets architecture. It uses
impact parameter information, accounting for correlations between the track features, among other variables.
DIPS considers tracks in the jet as an unordered and variable-sized set, which is physically better motivated than the algorithm based
on recurrent neural network <cit.> used in , given that the $b$-hadron decay products do not exhibit any intrinsic sequential ordering.
The performance of the DIPS tagger is investigated using  MC events and 2022 data
collected with a calibration trigger with one electron, one muon and two jets.
The final DIPS discriminant distribution is shown in Figure <ref> (left).
In the case of SM $HH\to\bbbar\bbbar $, a key signature relying on $b$-jet triggers,
the $b$-jet preselection step lowers the input rate to the remaining HLT
by a factor of five at the cost of reducing the overall signal efficiency by roughly 2%.
More details about DIPS, its training and usage in $b$-jet triggers are given in Ref. <cit.>.

The newly developed algorithm based on deep feed-forward Neural Networks, the so-called DL1 series <cit.>, replaced
boosted-decision-tree based taggers utilised in  <cit.>.
The particular instance of the algorithm used in 2022 is called DL1d and takes as inputs the kinematic variables ( and $\eta$) of the jet
as well as final discriminants from lower-level taggers (IPxD, SV1, JetFitter and DIPS).

From 2023 the $b$-jet trigger relies on a novel algorithm GN1, which is based on Graph Neural Networks (GNNs) <cit.>.
Unlike the DIPS and DL1d, the GN1 utilises a single neural network
taking the tracks and jet information directly as inputs and is thus independent of
other flavor tagging algorithms. The GN1 combines a GNN
with the two auxiliary training objectives: the grouping of tracks originating from a common vertex
and the prediction of the underlying physics process from which each track originated.
This approach leads to a better understanding of the jet's internal structure and, thus, a better algorithm performance.

The expected trigger rate as a function of the $b$-tagging efficiency using the DL1d and GN1 algorithms is shown in Figure <ref> (right).
The expected light jet rejection as a function of the $b$-tagging efficiency for various $b$-taggers as well as their operating points
are shown in Figure <ref>. The GN1 tagger performance exceeds that of DL1d, which was the main tagger in 2022.

(left) Distribution of the $b$-jet discriminant score for the DIPS algorithm shown in data from selected runs and  MC events
collected with a calibration trigger with one electron, one muon and two jets.
Only statistical uncertainties are shown.
(right) Expected trigger rates as a function of $b$-tagging efficiency using the
DL1d and GN1 algorithms, while requiring at least four HLT PFlow jets, three of which are
required to be above the $b$-tagging threshold. Rates are estimated with
Enhanced Bias data, and the $b$-jet efficiencies are estimated for $t\bar{t}$
samples using PFlow jet. The relative errors on trigger rates are between 8(7)% and 18(20)% for DL1d (GN1).

The light jet rejection as a function of the $b$-tagging efficiency (ROC curve) for the DIPS algorithm used on topo-cluster jets for preselection stage (dash-dotted line), the DIPS algorithm used on PFlow jets for TLA triggers (dashed line), the DL1d algorithm used as the final tagger in 2022 (solid line) and the GN1 algorithm used as the final tagger from 2023 (dotted line) obtained on a  MC sample. Statistical uncertainties for each ROC curve are represented with shaded regions around the curves. The vertical dashed lines represent the operating points for $b$-tagging used at the HLT. The bottom panel displays the ratio of all the ROC curves with respect to the DL1d performance.

§.§.§ $b$-jet trigger menu

$b$-jet triggers are crucial for several precision measurements and searches for new particles such as resonant and
non-resonant $HH\to\bbbar\bbbar $ <cit.>, VBF $H\to\bbbar $ <cit.>,
$\ttbar H\to \ttbar \bbbar$ with both top quarks decaying hadronically <cit.>, $b\phi\to b\bbbar$ <cit.>,
third generation squarks <cit.>, low mass di-$b$-jet resonances <cit.>, etc.

The $b$-jet trigger menu consists of the following physics triggers: single-$b$-jet triggers,
multi-$b$-jet triggers and specialised $b$-jet triggers designed for specific physics processes which often occur in combination with other signatures.
Single-$b$-jet triggers and multi-$b$-jet triggers are seeded from dedicated single-jet or multi-jet L1 objects.
At the HLT various combinations of the $p_T$ thresholds and $b$-tagging operating points are employed.
In multi-$b$-jet triggers, between one and four jets are tagged, while other jets are not tagged.
An asymmetric chain requiring four jets with  greater than
80 , 55 , 28 , and 20  of which two are $b$-tagged (with efficiency of 77%) has a rate around 150 Hz,
the lowest unprescaled single $b$-jet trigger ($>225\,$) around 50 Hz and
one jet of $>150\,$ plus two $b$-jets with $>55\,$ and $b$-tagging
efficiency of 70% around 10 Hz at luminosity of $1.8\times\lumi{e34}$.

Flavor-tagging calibration triggers <cit.> include a single lepton (electron or muon)
with one or two jets with $>20$ , electron-plus-muon with one or
two jets with $>20$ , and muon-jet matched triggers,
that are also used for physics studies in HI collisions.
These latter triggers were seeded from either a single-muon or a muon-plus-jet trigger item at L1 in 2022.
New chains seeded from L1 objects which use topological information,
such as $\Delta R$, are planned to be introduced later in .
At the HLT, a muon is required to be matched to a jet by fulfilling a requirement of
$\Delta R(\mu,\mathrm{jet})<0.5$, with an additional requirement for collisions
$ \Delta z (\mu,\mathrm{jet})<2$ mm, where the $ z$-position of the jet is taken to be the primary vertex $z$-position.

§.§.§ Trigger level analysis with $b$-jets

The TLA HLT infrastructure allows for the full outcome of flavour tagging
algorithms to be written out in events triggered by TLA chains targeting $b$-jet signatures.
In every TLA event, each HLT-level jet (for which flavour tagging is performed) is linked to
the corresponding $b$-tagging object in which the values of low and high-level taggers are stored.
Furthermore, the value of the DIPS tagger is added to every PFlow jet saved to the TLA stream,
regardless of whether the triggering chain is configured to perform dedicated flavour tagging or not.
This setup allows for the recording of orders of magnitude more events containing lower-$b$-jets with respect to standard $b$-jet triggers, extending the sensitivity of low mass di-$b$-jet resonance searches to resonance masses
down to 100  .

§.§ Missing transverse momentum

§.§.§ trigger reconstruction

The missing transverse momentum () trigger is used to identify events with
particles that do not interact with the ID or calorimeters because of the absence
of strong or electromagnetic interactions and that have lifetimes large enough to leave the detector without decaying into detectable particles.
Examples of such processes include SM Z boson decays to neutrinos <cit.>, as well as searches
for beyond SM decays involving dark matter <cit.> or supersymmetric <cit.> particles.

The can be computed from the magnitude of the vector sum of constituents, c:

$$\met = \left| \sum_c \Vec{p}_{T,c} \right|.$$

In addition to the , the scalar sum of the constituents is also computed. The main variations in how is computed in the trigger involve details of which constituents to utilise in the sum in the equation above.

The following HLT algorithms are available in Run 3:

* : The is formed from a sum over all calorimeter cells passing the selection $E_i>-5\sigma_i$, $|E_i|>2\sigma_i$, where $\sigma_i$ is the estimated noise in that cell.
This is to protect against spurious large negative energy signals[The LAr calorimeter electronics are designed such that signals from pile-up in earlier bunch crossings appear as negative energy.]. The cell energy magnitude must be greater than $2\sigma_\textrm{cell}$ to reduce the effect of noise from electronics and pile-up.

* :
The is formed using topo-clusters
as inputs,
which are combined in $\eta-\phi$ patches with dimensions of approximately $0.7\times 0.7$ (roughly the size of an $R=0.5$ jet).
The energy contribution from pile-up to these patches is estimated by a fit over them, requiring that pile-up events have
no true and are approximately evenly distributed over the calorimeter <cit.>.
The estimated pile-up contribution to each patch is subtracted, and the remaining patch
transverse momenta are summed to obtain the . The full algorithm is described in Appendix A of Ref. <cit.>.

* : The is formed over all jets passing a Jet Vertex Tagger (JVT) selection <cit.> where applicable.
The vector sum of the  of tracks from the primary vertex that are not associated with a passing jet
defines a track soft term which is added into the calculation.

* : The  algorithm uses the same techniques as ,
but the input topo-clusters are modified to use PFO tracks <cit.>.
As well as the improved momentum resolution of the PFOs,
the vertex information provided by the charged PFOs is used to improve the categorisation
of deposits into hard-scatter and pile-up.

* : The is formed from a sum over jets passing a JVT selection <cit.>.
A similar technique to  is used to correct these jets for the impact of pile-up.
Two variants are used:  uses PFOs and jets formed from them
to estimate the pile-up contributions,  uses jets formed from
EM scale topo-clusters and the hadronic scale topo-clusters to estimate the pile-up contributions.

* : The is formed from a sum over the PFOs in the event.
Two variants exist: in  the PFOs have their energies reduced according to their
Voronoi areas <cit.>, whereas in  the constituent
subtraction method <cit.> is used instead.
In both cases, the SoftKiller algorithm <cit.> is used to remove PFOs from
low-energy areas of the calorimeter.

In 2022, the primary L1 item for was the L1Calo legacy trigger with $>50\,$ <cit.>.
Before any kind of tracking is executed, an early reduction of rate at HLT is achieved by a calorimeter preselection requirement
that the cell-based  is greater than 65 .
The choice of default algorithm is made based on the performance in terms of background rejection versus signal efficiency and is discussed in the following paragraphs.

§.§.§ trigger performance and menu

Since muons are treated as invisible by the  trigger algorithms described above,
events with a boosted  can be used for the performance studies with
\(p_T(\mu\mu)\) serving as a proxy for .
A background acceptance vs. trigger efficiency curve is shown in Figure <ref> (left) comparing the performance of all algorithms considered for .
The efficiencies are calculated as the fraction of events passing a given  requirement for data events with
an actual number of interactions per bunch crossing of at least 38, and a  event selection passing
a single muon trigger, with \(76<M(\mu\mu)<106\)  and \(p_T(\mu\mu)>175\) .
The background rate is obtained from an offline trigger reprocessing of the 2022 data collected with zero-bias triggers described in section <ref>.
The new  default pfopufit trigger shows the best ability to retain signal, whilst rejecting background. The  default tcpufit
trigger is maintained as backup and for analyses where the primary vertex may not match the online primary vertex.
These triggers had unprescaled HLT thresholds of 90  and 115  in 2022 and rates of about 70 Hz and 30 Hz
at luminosity of $1.8\times\lumi{e34}$, respectively.
Requiring the presence of additional objects in the event, allows for decreased thresholds for triggers, as discussed in Section <ref>.

A signal efficiency curve is shown in Figure <ref> (right) comparing the performance of the primary L1 trigger alone to the default HLT  trigger chains used in and .
The efficiencies are calculated as the fraction of events passing a given \(p_T(\mu\mu)\) requirement for data events with a  event selection passing a single muon trigger, with \(76<M(\mu\mu)<106\) . The 2018 L1 efficiency matches that of 2022 within a few percent, so it is not shown.
The improved efficiency seen for the  pfopufit-based chain compared to the  chain reflects the pfopufit algorithm's enhanced momentum resolution and hard-scatter/pile-up categorisation.

(left) Background acceptance vs. trigger efficiency curves for the   trigger algorithms.
(right) Trigger efficiency as a function of \(p_T(\mu\mu)\) for the primary L1 trigger and the full trigger chain, with specific thresholds listed.
The trigger rates for the HLT chains shown are approximately the same rate (to within 10%).
The data are presented in comparison to 2018 efficiency.
Only statistical uncertainties are shown.

§.§ $B$-physics and light states

The trigger selection of events for $B$-physics analyses is primarily based on the identification of $b$-hadrons through decays with a muon pair in the final state. However, one or more muons or electrons could also be present in specific selections. Examples are decays with charmonium, $B\rightarrow (\Jpsi$ or $\psi')X \rightarrow \mu\mu X$, rare decays $B^0_{(s)}\rightarrow \mu\mu$, and semileptonic $B \rightarrow \mu\mu X$ decays. Decays of prompt charmonium and bottomonium are also identified through their di-muon decays, and are therefore similar to $B$-meson decays, apart from the lack of measurable displacement from the $pp$ interaction point. As the BLS topologies are significantly different from the majority of the ATLAS physics triggers, they are recorded to a separate BLS stream, as discussed in Section <ref>. In 2022 this stream collected data with an average rate of approximately 240 Hz.

Invariant mass distribution of offline-selected di-muon candidates passing the lowest thresholds of di-muon $B$-physics triggers. Triggers targeting different invariant mass ranges are illustrated with different colours, and the differing thresholds are shown with different shadings. No accounting for overlaps between triggers is made, and the distributions are shown overlaid, and not stacked.

As $B$-mesons are light, the resulting muon momenta are rather soft.
To control the input rate to the HLT, most of the $B$-physics triggers require two muons at L1. Their rate is substantially reduced compared to single-muon L1 triggers. Depending on the mass of the resonance this can result in the muons being within a single or in separate . At the HLT, muons are reconstructed using the same algorithms as described in Section <ref> with the additional requirement that the combined muons have opposite charges and form a good vertex (where a fit is performed using the ID track parameters) within a certain invariant mass window. For example, the mass range of the bJpsimumu is between 2.5 and 4.3  while bUpsi is between 8 and 12 . Examples of these mass spectra can be seen in Figure <ref>.

Di-muon trigger rate restrictions at L1 define the lowest muon transverse momentum thresholds for primary $B$-physics triggers. HLT triggers based on two L1 muons passing a 3  threshold need to be prescaled for most data-taking luminosities.
The prescales are adjusted to maximise the recorded number of low-di-muon events while remaining within operational constraints of the ATLAS TDAQ system as discussed in Section <ref>.
Higher threshold HLT triggers seeded from two muons passing 5  or 8  thresholds at L1
are unprescaled when the L1 and HLT bandwidths allow it.

Additional primary and supporting triggers are also implemented. Triggers requiring three muons at L1 help to maintain the lowest muon thresholds for certain event signatures with a likely presence of a third muon. For semileptonic decays, such as $B^0 \rightarrow \mu\mu K^{*0} \left(\rightarrow K^+\pi^- \right)$, searches for additional ID tracks and a combined vertex fit are performed, assuming a few exclusive decay hypotheses. For the start of Run 3 a so-called bBmuX selection is implemented to perform the partial reconstruction of the B-hadron decay final state $D^{*+} \mu^- X$ with the $D^{*+}$ reconstructed through the cascade hadronic decay chain $D^{*+} \to \pi^+ D^0(\to K^-\pi^+)$.

To validate the selection of the bBmumux the mass spectra of the selected (left) $B_d \rightarrow J/\psi K^*$ and (right) $B_s \rightarrow J/\psi \phi$ events from the BLS Delayed stream are plotted along with the spectra for a variety of bJpsimumu and bBmumux trigger decisions.
Only statistical uncertainties are shown.

To evaluate the $B$-meson selection at the HLT, supporting triggers without vertex or charge requirements are used.
The mass spectra of various bBmumux trigger decisions are plotted and fitted using events from the BphysDelayed stream. The consistency of the mass peaks in Figure <ref> with PDG averages and previous measurements <cit.> demonstrate the validity of the HLT reconstruction and selection.

§.§ Minimum-bias and forward signatures

To study diffraction, soft-QCD and similar topics, highly efficient triggers are necessary to select inelastic, diffractive and scattering interactions with
the least possible trigger bias. These data also serve as references for heavy-ion measurements.

Depending on the number of collisions per bunch crossing, $\mu$, the minimum-bias triggers play various roles.
At very low values of $\mu$ ($\mu \ll 1$) the triggers require one or two signals on any side of the Minimum Bias Trigger Scintilator (MBTS) detector to select actual collision events and to ensure that
the data sample is not dominated by empty events with no interactions. The MBTS detector was replaced for , as discussed in Ref. <cit.>.
It is a two-armed large-area plastic scintillator with a very high light yield covering $2.0<|\eta|<4.0$.
On each side, the scintillator is divided into two concentric rings, each consisting of 8 octants covering the full azimuth.
Altogether, the MBTS deliver 32 signals to the CTP, which can be used independently or combined.
Further event selection is possible at the HLT by requiring matching timing between MBTS signals or the reconstruction of tracks in the ID.
As a side benefit, reconstructing the MBTS signals at the HLT allows for the monitoring of the timing and energies of individual channels.

At $\mu$ values close to unity the need for MBTS as a source for the hardware trigger is less relevant and the minimum bias sample can be collected by a random trigger at L1
followed by the requirement of a track reconstructed at the HLT.

At $\mu\sim1-3$, every bunch crossing contains an inelastic collision and the L1 random trigger is sufficient for minimum bias triggering.
In these conditions, the focus shifts to collecting events with high multiplicity tracks (HMT) or events with a high momentum track
for analyses like Bose-Einstein correlations or azimuthal correlations similar to what is done in HI physics <cit.>.
The possibility of using a trigger with the total (transverse) energy deposit in the calorimeter is also planned.

In the track reconstruction for minimum-bias trigger is based on offline algorithms.
As a consequence, the performance is very close to that of offline tracking.
To ensure that there is no inefficiency the following study is performed.
At the start of 2022 data taking no track selection was applied at the HLT. This allows for the comparison in performance of the minimum-bias tracking selection in offline versus the trigger.
A comparison of transverse momentum, and $\eta$ for online tracks and offline tracks undergoing
dedicated minimum-bias analysis selection is shown in Figure <ref>.
The minimum-bias tracks are required to have above 0.1  and to have $|\eta|<2.5$, $|d_0|<1$ mm, $|z_0\sin\theta|<1.5$ mm,
have a measurement in the IBL if it is expected, and at least one pixel measurement on track. The number of measurements in the SCT is dependent
and is required to be above 2, 4, and 6 for tracks of above 0.1, 0.3, and 0.4   respectively.

Comparison of (left)  spectra and (right) $\eta$ of tracks reconstructed offline and passing
minimum-bias quality selection and tracks reconstructed by the HLT online during low pile-up run in 2022.

(left) Efficiency of triggering for events with at least two tracks of $\pt>0.1\,$ and
passing minimum-bias quality track criteria (see text) by single track trigger and MBTS triggers requiring single (MBTS 1) or two hits (MBTS 2) in the scintillator.
(right) Efficiency of triggering for events with at least one track of $\pt > 0.5\,$ passing minimum-bias
track quality criteria by the same triggers as shown on the left panel. The efficiency is measured as a function of the number of offline tracks, $N_\mathrm{trk}$,
with respect to the fully efficient trigger requiring only two clusters in the pixels detector and three space-points in SCT seeded from random bunch crossing at L1.
Efficiencies of the MBTS single and two hit triggers are measured with respect to the single track trigger. Only statistical uncertainties are shown.
These triggers were active during low pile-up runs in 2022.

Triggers with track reconstruction include a preselection step based on the count of pixel clusters and SCT space-points (coinciding pairs of hits on both sides of an SCT module).
In particular, the single-track trigger preselection requires two-pixel clusters and three SCT space points.
This preselection step reduces the input rate prior to execution of the tracking algorithms without any efficiency loss.
Random-seeded triggers with only the preselection step and no further HLT requirements are used to collect unbiased samples for performance studies.
Figure <ref> shows the efficiency of HLT tracking selection and the L1 MBTS trigger as a function of the number of tracks reconstructed offline passing minimum-bias selection,
as obtained with a data set collected with the random-seeded trigger at L1.
The HLT tracking selection is nearly fully efficient if at least two tracks in the event are present (a required minimum multiplicity for the $\pt > 0.1\,$ working point).
The inefficiency of the MBTS triggers is attributed to disabled modules (one on each side) and only a partial geometric overlap between the MBTS and the inner tracking volume.
For track above 0.5 , the track trigger is again fully efficient and the MBTS trigger performance mostly recovered.
This is because the presence of at least one track of this momentum is usually correlated with additional activity resulting in signals in a few MBTS counters and thus corresponding triggers.

For HMT triggers the requirement on pixel clusters is removed and only the SCT space-points are counted and subject to a threshold requirement, optimised to have full efficiency at a given number of tracks.
For HMT triggers at moderate values of $\mu$, an additional pile-up mitigation strategy is required. This is because
the counting of all tracks in the event instead of only tracks belonging to the highest multiplicity vertex impacts the purity of this type of trigger.
In addition, performing tracking in the full volume of the ID becomes more time-consuming with rising $\mu$, and so any preselection is beneficial.
An algorithm to approximate the vertex position along $z$ and the count of tracks originating from it was developed and optimised for expected data-taking conditions.
It uses the triplets of clusters from the Pixel detector that are used to construct a linear extrapolation to the luminous region.
Extrapolated positions are histogrammed along $z$ with the binning optimised so that the coincidental combinations form a negligible background and real vertices form a well-pronounced peak.
The threshold cut is applied on the count in the peak in the step preceding the tracking step.
Because of the availability of the vertex $z$ position, the tracks in HMT triggers with pile-up suppression are counted only if they are within 10 mm along $z$ from the approximate vertex position.
The impact of the additional pile-up suppression procedure on the efficiency of HMT triggers is shown in Figure <ref>, here again the offline tracks are required to pass a minimum-bias selection and the triggers are seeded from the random L1 trigger.
At moderate $\mu$ values, these chains are planned to be seeded by a trigger summing up all energy in calorimeters. At the time of the 2022 low-$\mu$ runs these were not yet commissioned.

Efficiencies of high multiplicity triggers targeting selection of events with 40, 60, and 80 tracks as
a function of number of tracks passing minimum-bias selection quality, $N_\mathrm{trk}$.
For each requirement the performance of the pile-up suppression (PU SUPP) variant of the trigger, designed to be robust in higher values of pile-up, is shown.
Only statistical uncertainties are shown.
These triggers were active during low pile-up runs in 2022.

In addition to the minimum bias triggers above, a diverse set of triggers aims to record events with elastic, diffractive or central-exclusive interactions. Their usage depends on the data-taking conditions such as pile-up or LHC beam optics <cit.>. The latter is usually defined by the value of the betatron function at the collision point, $\beta^*$ <cit.>.
During the high-$\beta^*$ runs the focus is on elastic scattering events triggered solely by the ALFA detector, although there are also some triggers
combining ALFA detector information with that of other ATLAS subdetectors which target the soft diffractive events. A detailed description of ALFA triggers can be found in Ref. <cit.>.
During low-$\beta^*$ (`standard') runs triggers are based on signals from various stations of the AFP detectors with or without coincidence with standard signatures from the central detector.
A detailed description of AFP can be found in Refs. <cit.>.
The AFP can deliver trigger signals from two of its detector systems: the Silicon Trackers (SiT) and the Time of Flight (ToF) detectors. SiT trigger signals are expected to be more efficient (98-99% per station) than the signals from the ToF system (about 80% per side),
but are also known to suffer from a 400 ns dead time after each hit <cit.>, causing the efficiency to significantly decrease
for the later bunches in a bunch train when the pile-up exceeds one.
As the SiT trigger dead time depends on the beam intensity and train structure, the following logic is used:

* During high-$\mu$ runs, when the presence of protons in AFP is expected to be in every second bunch crossing[In the first approximation this depends on pile-up. E.g. for $\mu = 50$ and a probability of registering pile-up proton originating from a single interaction of 2%, the chance of observing a proton in AFP is $1 - (1-0.02)^{50} \approx 64\%$.], the trigger items are based on ToF,

* during low-$\mu$ runs, when the probability of observing a proton in consecutive bunch crossings is small, the trigger items are based on SiT.

During high-$\mu$ data taking, the physics programme using proton tagging is focused on the measurements of exclusive and two-photon exchange processes, typically in conjunction with high-$p_T$ object(s) produced in the ATLAS detector to keep the rate low. An example of such a process is exclusive jet production when un-prescaled jets with $p_T$ of about 150  are required.
In order to trigger such events, the presence of a jet with a minimum threshold of 50  and a proton(s) in AFP (ToF trigger) is required at L1. At the HLT, matching is required between the kinematics of the centrally reconstructed di-jet system and the scattered protons as reconstructed using the SiT. Depending on the settings of
the algorithm selection criteria, the efficiency is expected to be $60-85\%$. In addition, the match between the di-jet vertex and the vertex $z$ location reconstructed using the ToF data can be applied.
Such trigger chains may obtain a rate reduction of a factor of 100 when compared to a nominal jet trigger with a similar $p_T$ threshold.

The composition of the trigger menu for low-$\mu$ runs depends on the exact data-taking conditions. The number of colliding bunches, pile-up and beam optics <cit.> play a key role in the expected event rate.
Studies of soft diffractive processes are usually realised using the least biased triggers.
For AFP, this translates into the requirement of a proton to be detected in both stations on the same side of ATLAS (single tagged events) or all four
AFP stations (both ATLAS sides; double-tagged events). AFP triggers can be combined with other ATLAS trigger objects.
For example, for diffractive charm meson production, in addition to the presence of protons in AFP, a track with a certain transverse momentum is additionally required.

§.§ Unconventional tracking signatures

LLPs are an important part of the  search program as they appear in many motivated scenarios of phenomena beyond the SM.
LLP which decay within the ID volume or pass entirely through it result in a variety of unconventional tracking signatures in the detector.
Several new triggers presented below were developed to target such unique signatures: long-lived charged particles, displaced jets, jets with displaced tracks and displaced leptons.
They make use of both standard tracking and LRT, described in Section <ref>.
The use of tracking for these signatures leads to lower background rates, which allows for lower particle momentum or requirements in the trigger, resulting in
large gains in sensitivity for  searches. Rates for the triggers discussed below are given in Table <ref>.

§.§.§ Long-lived charged particles that partially or fully traverse the inner detector

Three new triggers are developed targeting long-lived charged particles that partially or fully traverse the ID.
They make use of standard prompt full scan tracking executed after a calorimeter  or jet preselection is applied to reduce
the full scan tracking rate, as described in Section <ref>.
In , these searches generally relied on the  trigger <cit.>
to select events, which resulted in a low acceptance for models not producing large .

Isolated high trackHeavy charged particles (such as charginos, sleptons, and $R$-hadrons) with sufficiently long lifetimes can leave an isolated, high- track in the ID.
A new isolated high- track trigger
is introduced for to increase sensitivity to LLP signatures with low in the event.
It requires a tcpufit  threshold of 80 , 30  below the lowest unprescaled  trigger, to reduce the amount of CPU-time spent on full scan tracking.
The trigger uses tracks from the fast tracking step to
select events with at least one isolated track with $\pt>120$ that also passes additional track quality requirements. For the track to be isolated,
the scalar sum of the track  within $\Delta R<0.3$ must be less than 10 .
Figure <ref> shows
the expected performance of the isolated high- track trigger
with respect to the HLT calculated with  and  algorithms,
compared to the “or” of the lowest unprescaled  triggers based on  and  algorithms.
All of these algorithms are described in Section <ref>.
SUSY di-stau LLP MC simulation for a stau mass of 600  and a lifetime of 10 ns is used to evaluate the efficiency.
The new trigger increases the acceptance to signal-like events at lower values of .

Isolated high- track trigger expected efficiency using MC simulation of SUSY di-stau events with a mass of 600  and a lifetime of 10 ns
vs (left) the  and (right) the  algorithm .
The efficiency of the new trigger (circles) is compared with that of
a logical “or” of the lowest unprescaled  triggers based on  and  algorithms described in Section <ref> (squares).
Both of these are overlaid on the signal sample  distribution of fraction of events per bin (gray histogram), and include the L1 trigger efficiency.
Only statistical uncertainties are shown.

Large $dE/dx$ triggersNew heavy, charged particles, mentioned above, may also leave large energy deposits in the ID silicon layers compared to what is expected from a minimally ionizing particle.
The measurement of these large ionisation energy losses per unit pathlength, $dE/dx$, in the Pixel detector is a handle to identify tracks as signal candidates.
A new trigger targeting long-lived, heavy, charged particles <cit.>
uses the $dE/dx$ measurement capabilities of the ID for trigger decisions.
The same  triggers, as used for the isolated track trigger above, are required before running the full scan tracking.
The $dE/dx$ trigger selects events with at least one track with $\pt>50$ ,
an average $dE/dx>1.7\,$$/$cm, at least two hits with
$dE/dx>1.7\,$$/$cm, track $|d_{0}|<2.5$ mm, and $|\eta|<2.5$.
Figure <ref>  shows
the online $dE/dx$ distribution of tracks with $\pt>10\,$ in data collected during 2022 with
, single-jet, and multi-jet triggers where full scan tracking was run.
It also shows the correlation of the online $dE/dx$ measurement to the offline measurement.

(left) Distribution of $dE/dx$ for tracks reconstructed in the trigger used for monitoring the dE/dx-based trigger.
(right) Correlation of online vs offline $dE/dx$ for offline tracks with $\pt>12~\GeV$.

Disappearing track triggersCharged particles with slightly shorter lifetimes than the signatures above can decay part way through the ID and leave a short tracklet of a few hits.
These tracklets are referred to as disappearing tracks when the charged particle decays into invisible and low- particles that are not reconstructed.
As in the previous two cases, the disappearing track trigger
makes use of full scan tracking
executed after the same  trigger requirements, which are lower than the lowest unprescaled  trigger.
The fast tracking algorithm is modified to save tracklets with four hits in the inner layers of the ID that fail to become tracks.
In order to reduce the large background to this signature,
a BDT based on the track parameters, quality of fit, and number
of hits in the Pixel and SCT detectors is used to separate signal-like tracklets from background.
The disappearing track trigger selects events with at least one tracklet with $\pt>20$  that passes a stringent requirement on the BDT score.
Figure <ref> shows the expected performance of the trigger compared to that of the  trigger with
a 110  threshold, which was used in , for a model with long-lived charginos <cit.>.
The acceptance of the trigger to events with chargino momentum below 150  is greatly improved.

Efficiency as a function of the chargino-pair system transverse momentum for the HLT  trigger (dotted line)
and a logical OR with the disappearing track trigger (solid line) with respect to the L1 $\met>50$  trigger.
Both triggers are based on tcpufit  algorithm. MC simulation with  conditions is used.
The events are taken from models with a chargino lifetime of 1 ns and the
chargino mass of either 91  or in the range 200–1000  with 100 spacing. Only events with $\met>60\,$ and at least one chargino decaying
between the pixel and SCT detectors (13–30 cm) in the central region, $|\eta|<1.8$,
are considered.

§.§.§ Long-lived particle decays into jets

A second set of three new triggers have been developed targeting long-lived particle decays into jets, which may be displaced themselves or contain displaced tracks.
The triggers make use of full scan tracking run after a  or jet requirement and in some cases use LRT as an additional handle to select events.

Hit-based displaced vertex triggersNeutral LLP may travel some distance into the detector before decaying, resulting in a displaced vertex (DV) or jet.
Previous searches relied on a variety of triggers looking for other objects in the final state.
Two hit-based DV triggers
make use of hits not associated to tracks after the standard full scan tracking is performed in events passing the L1 jet and  triggers, respectively.
Jets with a large number of remaining hits on the outer layers of the ID, and few on the inner layers, are indicative of DVs with displaced tracks that are not reconstructed.
Using this as an extra requirement allows for lower  and jet thresholds compared to the lowest unprescaled triggers.
A BDT trained on the fraction of hits in the layers of the ID is used to implement this selection on jets.
The first trigger seeded by the same 80   threshold as above selects events containing jets with $\pt>200\,$ and $|\eta|<1$.
Figure <ref> shows its expected performance versus the number of pile-up interactions
using MC simulation of a heavy Higgs boson decaying into two long-lived scalars, each subsequently decaying
into two $b$-jets compared to a background process of  with an all-hadronic final state.
The signal efficiency is around 70%, compared to a background efficiency of less than 5%, for high numbers of additional interactions.
No strong dependence on pile-up is expected.
The second trigger seeded by a L1 jet with $>100\,$ selects events containing  jets with $\pt>260\,$ and $|\eta|<1$.
It requires a jet with $\pt>180\,$ at the HLT calorimeter preselection step before running the tracking.

Another hit-based trigger under development is seeded by a L1 trigger with $>50\,$ and runs only the fast tracking step of LRT in a composite around the jets.
Tracks with $\pt>2~\GeV$ are then used to build vertices using a modified version of the offline secondary-vertexing algorithm <cit.>.
The algorithm is optimised to be faster by requiring track pairs to be consistent with an approximate vertex position and
by reducing the combinatorics of clustering by binning the vertex positions.

Expected performance of the hit-based displaced vertex trigger seeded by a tcpufit  threshold of 80  versus the average pile-up.
MC simulation is used for signal and background processes. The signal process is a heavy Higgs boson ($m_H=1\,\TeV$) decaying into two scalars ($m_S=50\,$) with a proper decay length of 9 mm,
which subsequently decay into two $b$-jets each.
The background process is  production with an all-hadronic final state.
Only statistical uncertainties are shown.

Emerging jet triggersIn the models of new phenomena with a dark sector, decays of particles into hadronically interacting particles may result in emerging jets with a large fraction of events possessing a DV and tracks with large $d_{0}$.
The fraction of momentum associated to prompt tracks in the jet relative to the total jet momentum is used to identify
those with a large fraction of displaced tracks, i.e. a low momentum fraction associated to prompt tracks.
This trigger is run in events that
contain a L1 jet with $\pt>100\,$ and an HLT jet with $\pt>200\,$ in order to reduce the rate of full scan tracking.
The  of tracks within $\Delta R<1.2$ of the leading large-R jet axis are summed.
Jets are only considered if within $|\eta|<1.8$ and the tracks must have $\pt>2~\GeV$, $|\eta|<2.4$, $|d_0|< 8$ mm, and $|d_{0}|<2.5\cdot \sigma_{d_{0}}$ mm, where the $d_0$ resolution $(\sigma_{d_0})$ is computed from $Z+$jets events in data.
The ratio of the sum of track  over the jet is computed, and events are selected if this ratio, PTF, is less than 0.08.
This extra requirement allows for a reduction of more than a factor of two of the jet  threshold as compared to that of the lowest unprescaled trigger (420  in 2022).

A second trigger of this type
is seeded by a 45  photon and selects events with two large-R jets with $|\eta|<2.0$, $\pt>55~\GeV$, and $\text{PTF}<0.1$.
Figure <ref> shows that the emerging jet trigger is efficient down to much lower jet  than the single large-R jet trigger.
A model of a 1.5 TeV $Z'$ decaying into two 20  dark pions with a proper decay length of 50 mm is used <cit.>.
The overall efficiency depends on the acceptance of the PTF requirement.

Efficiency of the new emerging jet trigger compared to a single large-radius jet trigger for a $Z'$
decaying into two dark pions with a proper decay length (c$\tau$) of 50 mm. The efficiency is calculated
as a function of the  of the leading offline anti-$k_t$ R=1.0 jet, reclustered from R=0.4 topocluster jets.
(right) Efficiency of the LRT-based displaced jets triggers plotted against the leading offline anti-$k_t$
R=0.4 jet  for a model of exotic decays of the Higgs boson into long-lived pseudoscalars $a$ with mass 55  and proper decay length of 100 mm.
Both studies use MC simulation with  conditions.
Only statistical uncertainties are shown.

Displaced jet triggersSimilar to the previous case, neutral LLP decaying into quarks or gluons may result in displaced jets.
Two new LRT-based triggers select such events with a jet from initial-state radiation and at least one or two displaced jets,
but with a lower  threshold than the lowest unprescaled single-jet trigger at 420 .
Tracks with $\pt>1$  and $|\eta|<2.4$ within $\Delta R<0.4$ of the jet are counted as prompt () or displaced () if they have $|d_{0}|<\text{or}>3~\text{mm}$, respectively.
After the standard tracking is run for the events that contain
a L1 jet with $\pt>100\,$ and an HLT jet with $\pt>180\,$,
jets are preselected by requiring $\ntrkprompt\leq2$.
LRT is then run on the remaining hits in around the three leading jets passing the preselection.
In addition to the leading jet $\pt>180~\GeV$ requirement, the displaced single-jet trigger
selects events with a $\pt>140~\GeV$ jet with $\ntrkdisp\geq3$ and $\ntrkprompt\leq1$.
Similarly, the displaced di-jet trigger
selects events with two $\pt>50~\GeV$ jets where at least one must satisfy $\ntrkdisp\geq3$ and $\ntrkprompt\leq2$, and the other may satisfy only $\ntrkdisp\geq0$ if $\ntrkprompt\leq1$.
Figure <ref> shows the expected performance of the displaced jets triggers based on MC simulation of a model with exotic Higgs decay into long-lived pseudoscalars $a$ in the jet  region below the primary single jet trigger. Details of the model can be found in Ref. <cit.>.

§.§.§ Long-lived particle decays into SM leptons

LLP may also decay into SM leptons resulting in displaced electrons, muons, and taus.
Three new sets of triggers target these decays using LRT, and also standard tracking in the case of taus.

To select such events in , searches generally relied on triggers without tracking information such as photon triggers to select displaced electrons and MS-only triggers to select muons <cit.>.
These triggers had high  thresholds of 50–120 , requiring two objects for the 50  threshold, and restrictions in $\eta$ in the case of muons.
New triggers for displaced electrons and muons directly trigger on these signatures allowing for lower thresholds with respect to those used in .
The displaced electron trigger
runs LRT in in events passing the same L1 threshold as the primary prompt electron chain, described in Section <ref>.
It selects events that have an electron with $\pt>30\,$ and $|d_{0}|>3\,$mm that passes a loose likelihood electron identification <cit.> without the use of $d_{0}$ or requirements on the number of hits in the Pixel detector.
The displaced muon trigger
runs LRT in in events passing the same L1 threshold as the primary prompt muon chain, described in Section <ref>.
It selects events that have a muon with $\pt>20$  and $|d_{0}|>2$ mm.
Figures <ref> and <ref> show the expected efficiency of the displaced
electron and muon HLT triggers with respect to their L1 seeds in terms of the offline reconstructed lepton transverse impact parameter ($d_0$)
and the production radius of offline reconstructed electrons and muons, respectively, using MC simulation of LLP di-stau production.
MC simulation of pair production of staus with a 1 ns lifetime is used, and
stau masses of 100–500  in 100  steps are merged.
The offline electrons are required to pass the same loose likelihood identification as used in the trigger and have $|d_0|>3$ mm.
The offline muons are required to pass the medium working point described in Ref. <cit.> without a cut on the number of pixel hits and have $|d_0|>2$ mm.
The acceptance of the LRT-based triggers extends out to the first layer of the SCT at 300 mm, where the layout of the detector no longer allows for eight hits on the track in most regions.
The standard tracking runs out to a $|d_0|$ of 5 and 10 mm for electrons and muons respectively, limiting the acceptance of the standard prompt lepton triggers.
The larger value for muon tracking increases the acceptance of $B$-meson decays.
Combining the standard and LRT light lepton triggers provides continuous acceptance from small to large displacements.

Displaced (left) electron and (right) muon trigger efficiencies with respect to their L1 seeds versus the offline lepton $d_0$ (LRT, open triangles).
The efficiencies for the isolated primary single electron and muon triggers (Standard), described in Sections <ref> and <ref>,
are shown as inverted triangles. MC simulation samples with  conditions are used.
Only statistical uncertainties are shown.

Displaced (left) electron and (right) muon trigger efficiencies with respect to their L1 seeds versus
the offline reconstructed lepton production radius (LRT, open triangles).
The efficiencies for the isolated primary single electron and muon triggers (Standard), described in Sections <ref> and <ref>,
are shown as inverted triangles. A logical OR between the LRT and standard triggers (Combination) is marked with open circles.
MC simulation samples with  conditions are used.
Only statistical uncertainties are shown.

Two dedicated triggers for displaced hadronically decaying taus are in development for . One is based on standard tracking and the other on LRT.
A search during  with this signature was not performed, but would have needed to use jet or  triggers with high thresholds.
The standard tau identification RNN is retrained to select displaced taus based on standard tracking.
The first tau LLP trigger
selects events containing a tau with $\pt>200\,$ passing the medium working point of this displaced tau identification.
This identification is also used in multi-object triggers looking for a tau+X, which allows for lower thresholds on the tau object.
Primary L1 di-tau, single muon, single isolated electron and triggers are used to seed them.
The second tau LLP trigger
runs LRT in an around the calorimeter tau seed and uses the same RNN-based tau identification as trained for the previous trigger.
Events are selected if they contain at least one tau passing the displaced tau identification.
The trigger is expected to have a requirement slightly lower than the lowest unprescaled single tau trigger, 160 .
Figure <ref> shows the expected performance of these triggers compared to the prompt tau trigger based on an MC simulation of 100 , 1 ns staus.
The efficiency is computed with respect to standard and large radius offline tau tracks that are truth-matched to signal tau decays.
Hence, multiple tracks from the same generated tau may be included in the computation.
New LLP and LLP LRT tau triggers significantly improve sensitivity to the displaced tau signals.

Displaced tau trigger efficiency as a function of truth signal tau (left)  and (right) decay radius of the tau.
MC simulation with conditions of staus with a mass of 100  and a 1 ns lifetime is used.
The efficiencies for the prompt tau trigger (inverted triangle), LLP tau trigger using standard tracking (square),
and LLP tau trigger using LRT (triangle) are overlaid by the logical OR of all three (circle).
The gray histogram shows the distribution of truth taus for this model.
Only statistical uncertainties are shown.

§ AUXILIARY TRIGGERS

§.§ Non-collision background

Non-collision backgrounds comprise detector signals which do not originate from the collisions of paired bunches at the ATLAS interaction point. They are categorised into beam-induced and cosmic-induced backgrounds.
Both beam-induced and cosmic-induced backgrounds are non-negligible background sources in searches for new phenomena targeting delayed or displaced detector signatures, like those discussed in Section <ref>. A number of dedicated triggers are used to select non-collision backgrounds for study.

§.§.§ Cosmic ray triggers

The cosmic-induced background results from the impact of extremely energetic cosmic muons on the detector,
which induce signals in the muon spectrometers or energy deposits in the calorimeters.
These events are collected either during LHC data taking (with L1 triggers in the empty bunch crossings which do not have collisions)
or during periods with no LHC data taking (e.g. for detector commissioning as described in Section <ref>).
The muon triggers are adapted to select muon tracks not pointing to the interaction point while no additional selection criteria are applied at
HLT for the calorimeter cosmic-induced background triggers.
Two data streams are used for cosmic-induced background data.

The IDCosmic stream is designed to have a total rate of about 20 Hz.
It consists of two single L1 muon triggers with thresholds of 3  and 8  at approximate rates of 8 Hz and 5 Hz respectively, the latter being unprescaled.
In the same stream, a dedicated TRT-based L1 trigger for cosmics data taking uses a fast readout path for groups
of channels in the detector <cit.>, running at a typical rate of around 10 Hz.

The CosmicCalo stream aims for a target rate of 5 Hz and includes legacy L1Calo EM triggers with $>3\,$ and 7 ,
a tau lepton trigger with $>8\,$
and jet triggers with $>12\,$ and 30
for $|\eta| < 3.1$ and $>30\,$
for $3.1 < |\eta| < 4.9$.

§.§.§ Beam-induced background triggers

Beam-induced background (BIB) <cit.> originates from (1) the inelastic interactions of protons with residual gas molecules upstream and nearby the detector, producing showers of secondary particles (beam-gas background), (2) protons with high transverse amplitude, or (3) from protons deflected in beam-gas scattering hitting the tertiary collimators resulting
in background/secondary particles entering the detector (beam halo).
The online monitoring of BIB is essential to track live information about the beam conditions, which is also provided to the LHC.
Further studies of BIB are essential to understand its origin and composition, and maintain and develop adequate monitoring.

Single jet triggers with L1 thresholds of 12  and 50  are used to record beam-induced background events in bunch crossings where a proton bunch is present in only one or in neither of the beams.
In addition, triggers based on hits in the Beam Conditions Monitor (BCM) <cit.> are used to record BIB events.
The BCM consists of two stations of detectors located symmetrically around the interaction point at $z = \pm$184 cm and $r=55\,$mm ($\eta\approx 4.2$).
Each station has four modules of two diamond sensors read out in parallel.
The implementation of the BCM hit-based trigger is based on a coincidence of an early hit on one side (A or C side) and one hit in-time with the bunch crossing on the other side (C or A side)
in unpaired bunch crossings, where only one of the two beams is filled with a proton bunch.
In order to be more independent of the presence of unpaired bunch crossings and to improve the purity of the selected events, a new logic is implemented
for which relies on two early hits on the same side (2A or 2C).
This allows for the triggering on paired bunch crossings while maintaining a similar rate to the AC/CA counterparts,
especially when triggering on the first colliding pair of bunches in a train which helps to mitigate against the impact of afterglow (increased cavern backgrounds following collisions at high $\mu$).
Furthermore, this allows for a measurement of the composition and fraction of BIB in paired bunch crossings, which was found to be different compared to unpaired bunch crossings.
The contribution of ghost collisions[Ghost collisions occur between protons from a filled bunch, which typically
has $>10^{11}$ protons, and protons in an unfilled (empty) bunch, which has $<10^8$ protons, due to diffusion from filled bunches which takes place at the interaction point.]
is eliminated and thus the purity of the recorded BIB events is increased.
A new bunch group with first paired bunch crossings in a train, containing all paired bunch crossings following a gap of at least 29 empty bunch crossings is defined.
In order to evaluate the performance of the new triggers, they are defined in different flavors, triggering on empty, unpaired, and the aforementioned first paired bunch crossings in a train. Figure <ref> shows the L1 rate of the old and new
BCM triggers as a function of a bunch crossing identification (BCID) value.
For each trigger the per-BCID rate is shown for five different bunch groups, paired colliding bunches,
the first colliding bunches in a train, empty bunch crossings, unpaired bunch crossings with either beam 1 or beam 2 filled with a proton bunch.
As expected the rate of the 2A/2C variants is much lower than the AC/CA variants in BCIDs with paired colliding bunches. Further, the rate in unpaired BCIDs is similar for both variations.

Per-BCID L1 rate of BCM hit-based triggers based on coincidence of (top left) AC
and (top right) 2A,
and (bottom left) CA and
and (bottom right) 2C.
The per-BCID rates are shown for paired colliding bunches, the first colliding bunches in a train, empty bunch crossings (orange), unpaired bunch crossings with either beam 1 or beam 2 filled with a proton bunch. The BCID range shown is restricted to the first 350 BCIDs.

§.§ Zero-bias trigger

The zero-bias data are collected using a dedicated trigger, which fires one LHC turn after a
L1 EM trigger with $\et>15\,$ fires. The triggered zero-bias data are proportional to the luminosity in each bunch crossing, but
are otherwise unbiased with respect to what happened in a collision.
This trigger was prescaled to a constant rate of about 10 Hz in 2022. Such triggers are used for detector studies as well as for
the MC simulation overlay method <cit.>, which relies on
the zero-bias data to account for the pile-up background, cavern background, and detector noise.

§.§ Triggers for tracking performance studies

There are dedicated triggers in the trigger menu to study lepton tracking performance, described in Section <ref>.
These idperf chains run the same selection as the corresponding triggers under study but do not apply any requirements on tracking.
This means that they are unbiased with respect to tracking and can be used for efficiency measurements.
For instance, if an electron candidate is formed from a track and a cluster, the idperf electron chain does not make any selection on the electron candidate, as this would include requirements on
track-cluster matching to define the candidate, as described in Section <ref>.

Two types of idperf triggers are employed in the trigger menu: di-lepton triggers and single lepton triggers.
The di-lepton idperf triggers target $Z$ boson or $J/\psi$ decays to leptons in order to study the performance with the tag-and-probe method.
These chains are based on primary single or di-object electron and muon triggers, described in Sections <ref> and <ref>,
and can run unprescaled at about 15-30 Hz not adding any unique rate.
These idperf triggers do not apply any requirements on tracking on the subleading trigger leg which can be an electron, muon or tau candidate.
The single object idperf triggers have thresholds of 5, 14, 20, 26 and 30  for electrons, 6, 20, 24 and 40  for muons
and 25, 35, 80 and 160 for taus. These are heavily prescaled to record events at 0.5 – 1 Hz.

There is at most one reference object (one track) per from the leptonic triggers. The purity of the muon triggers
is quite high. For the tau trigger, it is very low, and for the electron trigger, lower still.
There are very few real electrons in the sample accumulated by single electron idperf triggers,
so the dilepton idperf triggers are crucial to evaluate electron tracking performance.

§.§ Triggers for detector performance studies (calibration, noise)

Triggers used for detector performance studies often run at very high rates.
To compensate for this, only partial detector information is recorded through a strategy called Partial
Event Building (PEB), which has the potential to significantly reduce the event size and
thus overall bandwidth. These triggers operate either with a fixed subset of ROBs which are
to be included in events recorded to the PEB stream, or a list of ROBs can be derived dynamically on an event-by-event basis based on a set of .
A combination of both static and dynamic ROB lists is also possible.
These triggers are used for the calibration of muon subdetectors, low-offline muon
calibration and LAr calorimeter performance studies.

For example, a dedicated calibration trigger, called a laser trigger, is active during collisions runs to monitor the stability of the Tile calorimeter channels.
The LHC abort gap of about 3 $\mu$s is used to send and register laser pulses that are arbitrated,
timed and controlled with respect to the LHC signals <cit.>.
Laser pulses are sent to the Tile calorimeter at the increased rate of 12 Hz for and recorded for an analysis.
Laser events are used to track possible fast gain changes in the photomultiplier tubes and monitor the timing calibration.

Random events with PEB information for Pixel and SCT detectors are recorded in the unfilled LHC bunches into dedicated streams to identify noisy channels which need to be masked[Not used for the track reconstruction.] in these subdetectors.
These triggers typically run at about 10 Hz. A pixel with noise hit occupancy above $5\times 10^{-4}$ is classified as a noisy channel and masked in DAQ.

§.§.§ LArNoiseBurst algorithm

The LAr calorimeter has a small but luminosity-dependent probability of generating large noise signals
involving a considerable number of cells, as discussed in detail in Ref. <cit.>.
While this happens with milli-Hertz frequency,
high spurious values of energy are provided by these cells and it is therefore important
to veto affected events from the data quality monitoring and downstream of this from potentially affected physics analyses.
Veto windows occur across a much shorter timescale than that of a single luminosity block.
The detection and registration of LAr noise bursts is done via a LArNoiseBurst algorithm which runs in the HLT.

Noise bursts generate electrical pulses which do not correspond to physics objects and thus these have a bad quality of fit when energy reconstruction is attempted.
Offline tools examine the quality factor of the cell energy reconstruction procedure, counting the number of cells with a bad quality factor in a given event.
Given that many other factors could interfere with the cell quality factor (e.g. intense pile-up in a particular event),
a minimum of two events that are strongly correlated in time is required to declare a veto interval.

In the HLT, the offline algorithm is run for every accepted event that is written to certain streams, including the Main stream, the TLA, delayed streams and streams recording events with cosmic signatures in the calorimeter.
Events that are considered bad by the offline tool have their time stamp published online via an information
messaging system. A dedicated application then picks the time
stamps, performs a coincidence operation between them (a maximum time difference of 250 $\mu$s is
required) and declares the interval to a database used by the offline reconstruction.
The veto is then applied to reject events in the post-run analysis.
The computing resources taken by this algorithm are negligible due to very low rate of the Noise Bursts and large overlap with other calorimeter triggers.

§.§ Beam-spot algorithms

A dedicated system allows the HLT to continuously measure the position, size and orientation of the luminous region (also known as beam spot) at the ATLAS interaction point <cit.>.
Beam-spot parameters can change from fill to fill, and some, in particular the transverse position and size, show significant variation over the course of a fill as well.
Knowledge of the current beam-spot parameters is crucial for several HLT algorithms, most notably for the selection of events with $b$-jets, and for HLT tracking itself.
The parameters are also transmitted online to the LHC status display <cit.>.

The beam-spot parameters are continuously monitored and archived, determined bunch-by-bunch as well as fill average, and sampled over different intervals from one to many minutes depending on the required statistics.
One dedicated set that is used by the HLT is only updated whenever significant deviations from the currently used values are detected.
The process of obtaining the parameters, updating them and feeding them to the algorithms as condition parameters is referred to as beam-spot calibration.

The calibration and update process is not trivial as it consists of multiple steps involving several cooperating sub-systems to synchronise the beam-spot parameters across the distributed HLT farm at the same time. This requires orchestrating a series of steps, primarily through the CTP:

* HLT algorithms extract tracking and vertexing information and publish their distributions in the form of histograms,

* histograms from all individual HLT instances are aggregated by a monitoring infrastructure referred to as the Gatherer,

* on each new luminosity block the merged histograms are processed and new estimates of the beam-spot parameters are calculated by an external application called the BeamspotTool,

* when the BeamspotTool determines that the new estimate constitutes a significant change with respect to the previous one, it sends these new parameters to the CTP process,

* the CTP process writes new beam-spot parameters to the conditions database with a validity interval starting with the next luminosity block and then notifies the HLT processes of the pending update via its event fragment,

* individual HLT processes read the new beam-spot parameters from the conditions database when they receive events from the next luminosity block, for which
the CoralServer and CoralProxy <cit.> infrastructure provides scalable access to the conditions database from the HLT farm.

The online beam-spot calibration received significant improvements in preparation for .

One long-standing issue with the online beam-spot calibration during was a small (5 – 15 $\mu m$) systematic difference observed in the transverse beam position with respect to the offline calibration.
During LS2 this was tracked down to an incorrect transverse position at the coordinate system origin being used for track clustering, which caused a systematic bias towards the origin.
The issue was resolved by using the current estimate of the transverse beam location for track clustering.
Reprocessing of the data with the fixed vertex finder showed the online calibration matching the offline measurement with excellent precision.
In 2022, there was still an observable difference in transverse position between offline and online due to different alignment constants, which makes a direct comparison difficult.

The original calibration used for and is based on optimised vertex finding and fitting algorithms.
The calibration introduces an additional algorithm based only on track information that does not involve vertexing.
The luminous region is narrower than the typical vertexing uncertainty, and an accurate estimation of the transverse widths requires precise knowledge of the vertexing resolution.
The resolution itself depends on detector and trigger conditions, and is therefore evaluated in real time through a split-vertex method that was introduced in .
However, the smaller beam-spot sizes of Run 2 required larger resolution corrections and the vertex method has shown limitations in case of low statistics. To study alternatives, a new method was developed for Run 3.
This method utilises information from reconstructed tracks only and determines beam-spot parameters by a likelihood fit to the observed set of $d_0$ and $\phi$ parameters of tracks.
In the ATLAS online environment the tracking information is local to each of the HLT processing nodes, and it is not possible to collect all track data at one location to perform fitting.
To support fitting of all available tracking data at a single location, the likelihood function is approximated to a sufficiently small set of additive terms.
These terms are calculated from the local set of tracks on each HLT node and merged for the final fit by utilizing the Gatherer infrastructure.
The new method demonstrated reasonable performance with the reprocessed data and a shorter ramp-up period between the start of data collection and calibration availability compared to the vertex-based method.
For both vertex-based and track-based algorithms are in use to further study their performance.
During the initial 2022 data-taking period the track-based algorithm was used preferentially due to its better robustness, lower demand on statistics and earlier availability of the beam spot. For high-luminosity running the vertex algorithm is still the preferred method for its accuracy over a wider range in beam sizes.

The multi-step calibration process outlined above introduces a delay in availability of the calibrated beam-spot position for HLT algorithms, with a typical latency of several luminosity blocks.
This is not an issue for the HLT during a run since the variations are small on that timescale.
However, at the start of each new fill this requires a short bootstrap period, during which certain HLT algorithms, such as those used for $b$-tagging, have to be held off until a first measurement of the beam spot has succeeded.
This results in a loss of a few luminosity blocks of data for the individual triggers: on average 4.5 luminosity blocks were missing beam-spot calibration at the start of each data-taking run in , which corresponds to approximately one percent of a duration of a typical run.

Improvements in the Gatherer infrastructure
helped to reduce the calibration bootstrap delay.
The calibration depends on histograms produced by the HLT and merged by the Gatherer.
Improvements in handling of histograms for each of the luminosity blocks in the Gatherer have reduced propagation delays for those types of histograms.
This results in a faster availability of those histograms for the BeamspotTool application and helps in shortening the inherent ramp-up delay, which has reduced to an average of 2.5 luminosity blocks in .

With the higher bunch intensities achieved by the injector upgrades, the LHC had for the first time begun $\beta^*$-levelling in order to limit pile-up in 2022.
This involves a large variation in spot sizes, in turn demanding more frequent updates of the HLT during the levelling phase between $\beta^*$ of 60 cm to 30 cm.
In 2023 the levelling range is extended to be between 120$\,$cm and 30 cm.

Another development begun in 2022 that can be applied in 2023 is to constrain HLT tracking to a 3$\sigma$ window around the longitudinal beam position which is projected to save a significant fraction of CPU time in the HLT.
This will involve yet another bootstrap procedure to settle on the beam spot at the start of each run.

Figure <ref> shows the time evolution of the vertical beam-spot position as measured, and subsequently applied, by the HLT over the course of
one LHC fill during November 2022 data taking.
An update of all parameters is performed whenever the position changes
by more than 10% of the width, or the width changes by more than 10%, or
the uncertainty on any of the parameters decreases by more than half.

Time evolution of the vertical beam-spot position over the course of one LHC fill.
The dots represent the monitored beam-spot position measured in luminosity blocks. The line represents the position currently
used by the HLT algorithms which is measured as an average over a
sliding window of a series of luminosity blocks. The band indicates a range corresponding
to 10% of the vertical beam-spot width that was measured at the same time.

§ TRIGGER SOFTWARE PERFORMANCE

§.§ Trigger software performance scaling

For Run 3 the same process forking architecture of the HLTMPPU was kept as in Run 2. However, due to the multithreaded event selection, each worker process can now contain multiple event slots, which are processed in parallel. In Run 2, each worker process handled one event, and the selection progressed sequentially. This allowed the HLTSV to assign new events directly to idle worker processes. In Run 3, the AthenaMT scheduler decides when an event slot is freed and when a new event can be read from the input source. The HLTSV, therefore, assigns events to an event queue for each HLTMPPU from which new events are pulled by the AthenaMT scheduler for each worker process.

In the system, the number of forked worker processes per HLTMPPU and the number of parallel event slots in each worker process are freely configurable. This allows for an adiabatic transition of a pure multi-process-based event selection like in Run 2 (i.e. many worker processes with one event slot each) to a pure multithreaded configuration with one worker process and many parallel event slots. Event throughput measurements are used to decide what configuration will be used.

Figure <ref> shows the trigger software performance scaling in terms of application throughput in events/s (left), CPU usage (middle), and memory usage (right) as a function of the number of events processed in parallel for AthenaMT executing trigger selection algorithms.
The measurements were performed in a standalone local environment using a machine identical to those used in the ATLAS HLT computing farm during data taking. It is a dual processor machine with 128 GB RAM using a NUMA memory architecture and two AMD EPYC 7302 CPUs, where each CPU has 16 real cores with two hyper-threads per core, giving the total number of 64 threads.
The data sample contains a mix of events representative of the real HLT input data and trigger selection configuration identical to one used during data taking. Four ways of achieving the parallelism are presented.
Data were taken in 2022 using a pure multi-process configuration with 48 forks as event throughput is the most critical metric for the HLT. Different constraints apply, however, to Grid <cit.> processing of MC simulated events. Here, available memory per core is significantly more restricted than on the dedicated HLT machines, and these tasks execute in in a pure multi-threaded configuration, the trigger simulation included. A typical Grid site in 2022 ran the multi-threaded configuration with eight event slots. As ATLAS' transition to multi-threading was new for , a number of components still make use of mutex locking to provide safe shared access to certain common resources. In aggregate, these bottlenecks severely limit event throughput at very high levels of multi-threaded execution, as seen in Figure <ref>. Work continues to refactor these components to minimise blocking behaviour in future software releases for both Run 3 and Run 4. In addition, the hybrid modes of operation continue to be studied as significant memory savings are made even in hybrid modes which use a small number of multi-threading event slots, hence minimising losses due to resource contention.

Application throughput in (left) events/s, (middle) CPU usage (CPU time divided by wall time) in percent and (right) memory usage in GB as a function of the number of events processed in parallel for AthenaMT executing trigger selection algorithms.  Blue squares represent a multi-processing approach.
Pink circles represent a multi-threading approach with a single process using a number of threads equal to the number of events requested to process in parallel.
Threads are not bound to events; instead, a pool of a number of threads ($N_{thread}$) is used to process an equivalent sized pool of events ($N_\text{event}=N_\text{thread}$). Green diamonds and orange triangles represent a hybrid approach where a number of processes, $N_\text{process} = N_\text{event} / N_\text{thread}$, forked after initialisation use a fixed number of threads each ($N_\text{thread} = 4$ and 8, respectively) to process an equivalent number of events in parallel. Differences between these approaches are discussed in Section <ref>.

Figure <ref> shows the calorimeter processing time dependency on the number of threads obtained
offline by concurrently processing various numbers of data events with different thread configurations.
In the Run 3 AthenaMT framework, the same block of cells cannot be requested by two different algorithms
(e.g. two overlapping or a full scan request at the same time as any ) as it may cause simultaneous reading and writing to a given memory area.
To avoid this, locks are added to the HLTCalo data preparation service, leading to a non-linear dependency between the processing time
and the number of parallel processing threads allocated for intra-event processing
as shown in Figure <ref>. Unpacking of the calorimeter cells and topological clustering algorithms do not show any dependence on the number of
threads, contrary to fast reconstruction, which exhibits turn-on-like dependence on the number of threads
the shape of which depends on the number of concurrently processed events.
Optimisations are planned to either employ a more fine-grained locking or through an updated processing model.
The time of the full scan calorimeter cell unpacking per call is slightly extended (mostly due to locks associated to ) with the
increased number of threads, but more linear scaling performance is achieved
through increasing the number of inter-event parallel processing slots.
This does not affect the HLTCalo algorithm's functional performance, such as cell and cluster parameters or reconstruction efficiency.

Average processing time per call of
(top left) the fast calorimeter reconstruction,
(top right) the unpacking of the full scan calorimeter cells and
(bottom) the full scan topo-clustering algorithm
as a function of the number of threads for various numbers of concurrently processed events.

§.§ HLT processing time

The event processing at the HLT is limited by the available resources of the HLT farm which depend on the rate of incoming events and the average processing time of an event at the HLT. The mean
time to process an event is a product of the trigger configuration arising from the trigger menu and prescales used during the run.
An example of the mean HLT processing time per event at different
instantaneous luminosity values throughout a run is presented in Figure <ref> (left).
The mean HLT processing time decreases with decreasing average pile-up due to a reduction in
event complexity.
The menu is adjusted based on the current rate of events in order to fully use available resources
while retaining a constant 5000 slot safety margin (about 6% of the final 2022 farm)
to protect against losing slots due to power glitches, technical problems, etc.
The slope of the distribution in Figure <ref> (left)
changes at the point where the additional trigger selections are enabled.
Additional event processing restrictions came from the delayed delivery of replacement ROS servers.
In 2022 the ROS (like in ) was able to supply full detector information at half of the maximum L1 rate (50 kHz). However, it is possible to reach the L1 rate of 100 kHz for a subset of detectors by re-configuring the readout, for example by increasing the number of ROS servers assigned to it.

In addition to the online monitoring of high-level HLT processing statistics, offline tools, such as Cost Monitoring <cit.>, are available to investigate the detailed performance of the
HLT (e.g. the average processing times of individual algorithms or whole trigger chains).
Data required for such studies is saved to a dedicated calibration stream which enables recording of this data for all events, not just those accepted. This stream contains information on algorithms' execution times and on any data requests they make to the ROSes.
By default, only the first 250 LBs are monitored in this way during physics data taking.
After the run has finished, the data from the stream undergo additional
post-processing and the performance details are available on a dedicated website.

The Cost Monitoring used during Runs 1 and 2 had to be adapted to the multi-threaded framework for . While the following figures and tables present data taken using the MP configuration in 2022, some changes and challenges which become more relevant in more MT-like configuration are pointed out in the following.
Upgraded monitoring includes a new MT-compatible algorithm gathering the data, a redesigned post-processing framework, and additional monitors (including thread monitoring).
Given that the new HLT runs under the AthenaMT scheduler, the analysis of the results is no longer as simple as in a sequential framework, therefore multiple metrics were prepared to provide an overview of the event processing time, for example, an event wall time or the sum of the execution times of all algorithms.
The wall time includes the framework operations/delays between scheduled algorithms.
A comparison between those values can be seen in Figure <ref> (right), which
shows the wall time which includes both algorithm execution time and time spent on framework operations (including algorithms scheduling, data traffic) as well as the total time of just the algorithms. These data were recorded in a MP-mode, where the scheduler was only tasked with processing a single event at a time using a single CPU core.

In the figure, three peaks can be identified, representing fast (approximately 30 ms), medium (approximately 300 ms), and
slow (approximately 2s) events. The last type of the event is the rarest due to the early rejection mechanism.
For faster events, when only fast algorithms are executed and most of the trigger chains are rejected,
the impact of steering operations from the underlying framework is observable as an overhead of about 10 ms.
For events with execution times much longer than 100 ms, when time-consuming algorithms, for example, tracking algorithms, are executed, it is negligible.
Table <ref> shows an example of collected Cost Monitoring metrics for a given period of time during a run, broken down into the main types of object reconstruction and the framework.
The Cost Monitoring data are used in an iterative process to identify areas
where optimisation of code and strategy can yield the greatest impact with zero or negligible physics impact.
The difference between the wall time and the total time of all algorithms per event can further diverge in different ways when running in MT mode. For the MP case, the total event wall time is always greater than the algorithm time, but with sufficient intra-event parallelism in an MT configuration, the total event wall time can be smaller than the algorithm time, as some of the event processing may occur simultaneously on multiple cores.

(left) Mean HLT wall time as a function of the average pile-up throughout a run.
A vertical line marks the instantaneous luminosity at which additional trigger selections are enabled.
Error bars denote the Gaussian width of the underlying per event measurements.
(right) HLT processing time distribution per event for an instantaneous luminosity of . Shown are the wall time spent per event as well as the sum of the algorithms only processing time. The difference between these two distributions is due to the time spent in framework operations.

Example of collected Cost Monitoring metrics for 50 LBs for an instantaneous luminosity of at pile-up of 51,
showing how the total time is distributed between the main types of object reconstruction and the framework software.
The fractional time consumption of algorithms is calculated based on the sum of the execution times of all algorithms.

Total time [%]

ID reconstruction     59

Muon reconstruction     14

Calorimeter reconstruction     11

Combined reconstruction and hypothesis algorithms     8

Trigger infrastructure     2

Other     6

At the peak instantaneous luminosity during the run, the HLT processing time of one event is approximately 600 ms (590 ms algorithm time), compared to 500 ms achieved during .
Out of this number about 59% of the total event time is spent on the ID tracking, despite the improvements discussed in Section <ref>.
This is due to the expanded use of the full scan tracking for the hadronic signatures in .
The HLT farm computing capacity has been increased for Run 3 by routine replacement of old servers, benefiting from the sustained industry trend of increasing processor performance. This has enabled the additional HLT processing for Run 3 that is described in this paper to support the physics goals of the experiment.
During , the HLT farm consisted of processors with a performance of 22.8 HS06/core <cit.> (0.8 MHS06 total farm performance). For , 60% of the farm was upgraded to 36.2 HS06/core (1.7 MHS06 total farm performance) for early 2022, rising to 100% by the end of 2022 (2.0 MHS06 available for the remainder of starting from 2023).

§ CONCLUSION

A large number of trigger upgrades and developments for the ATLAS experiment were made during the
second long shutdown of the LHC in preparation for the data taking. A summary of the various
updates as well as the first performance studies can be found in this paper.

Many changes in the L1 trigger system improve both its rejection of background events and
acceptance for interesting physics processes.
Upgrades in the L1 calorimeter trigger increased the granularity of information used by the trigger
and enable it to run more sophisticated algorithms to identify physics objects,
and to calculate missing transverse momentum in the event with higher precision.
The L1 muon system was enhanced through the addition of New Small Wheels, new resistive plate chambers
in the barrel/endcap transition region as well as upgraded electronics.
The topological trigger, installed during , has also undergone a hardware upgrade.
Its refined kinematic measurements of muons and other objects as well as new flexibility to
define multiplicity triggers allow for more sophisticated event selections at L1.

The underlying framework of the HLT was completely rewritten in order to execute trigger algorithms
within the multi-threaded software framework AthenaMT, sharing common features between the trigger
software and the software used for offline reconstruction. These changes help to optimise the use of the
HLT computing resources, both in terms of computing power and memory consumption.
New-and-improved selection algorithms and strategies further improve the reconstruction of objects at the trigger level, in the case of some of the hadronic signatures, at the expense of higher CPU time needs due to the expanded use of full scan tracking.

While maintaining a level of consistency with the trigger menu, the trigger menu
sets out to exploit the newly implemented detector features, more performant HLT hardware, and algorithmic advancements.
Trigger thresholds at L1 and HLT were generally kept the same as during , benefiting from improvements to reduce trigger rate.
The additional available HLT rate compared to is dedicated to expanding the physics menu in the physics and TLA streams, lowering trigger thresholds and including new triggers for previously unexplored phase space, which make extensive use of the various inner detector tracking algorithms in the HLT.

The ATLAS trigger system was successfully (re-)commissioned with the first data acquired at 13.6 ,
with some final commissioning steps for L1Calo and L1Muon to be completed during Run 3. First performance studies of the
different trigger signatures and trigger efficiencies with respect to the offline quantities are presented using
the 13.6  proton-proton collision data collected during 2022.

§ ACKNOWLEDGEMENTS

We thank CERN for the very successful operation of the LHC, as well as the
support staff from our institutions without whom ATLAS could not be
operated efficiently.

We acknowledge the support of
ANPCyT, Argentina;
YerPhI, Armenia;
ARC, Australia;
BMWFW and FWF, Austria;
ANAS, Azerbaijan;
CNPq and FAPESP, Brazil;
NSERC, NRC and CFI, Canada;
ANID, Chile;
CAS, MOST and NSFC, China;
Minciencias, Colombia;
MEYS CR, Czech Republic;
DNRF and DNSRC, Denmark;
IN2P3-CNRS and CEA-DRF/IRFU, France;
SRNSFG, Georgia;
BMBF, HGF and MPG, Germany;
GSRI, Greece;
RGC and Hong Kong SAR, China;
ISF and Benoziyo Center, Israel;
INFN, Italy;
MEXT and JSPS, Japan;
CNRST, Morocco;
NWO, Netherlands;
RCN, Norway;
MEiN, Poland;
FCT, Portugal;
MNE/IFA, Romania;
MESTD, Serbia;
MSSR, Slovakia;
ARRS and MIZŠ, Slovenia;
DSI/NRF, South Africa;
MICINN, Spain;
SRC and Wallenberg Foundation, Sweden;
SERI, SNSF and Cantons of Bern and Geneva, Switzerland;
MOST, Taipei;
TENMAK, Türkiye;
STFC, United Kingdom;
DOE and NSF, United States of America.
In addition, individual groups and members have received support from
BCKDF, CANARIE, CRC and DRAC, Canada;
PRIMUS 21/SCI/017 and UNCE SCI/013, Czech Republic;
COST, ERC, ERDF, Horizon 2020, ICSC-NextGenerationEU and Marie Skłodowska-Curie Actions, European Union;
Investissements d'Avenir Labex, Investissements d'Avenir Idex and ANR, France;
DFG and AvH Foundation, Germany;
Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the Greek NSRF, Greece;
BSF-NSF and MINERVA, Israel;
Norwegian Financial Mechanism 2014-2021, Norway;
NCN and NAWA, Poland;
La Caixa Banking Foundation, CERCA Programme Generalitat de Catalunya and PROMETEO and GenT Programmes Generalitat Valenciana, Spain;
Göran Gustafssons Stiftelse, Sweden;
The Royal Society and Leverhulme Trust, United Kingdom.

The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN, the ATLAS Tier-1 facilities at TRIUMF/SFU (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), RAL (UK) and BNL (USA), the Tier-2 facilities worldwide and large non-WLCG resource providers. Major contributors of computing resources are listed in Ref. <cit.>.

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[0000-0002-6665-4934]G. Aad$^\textrm{\scriptsize 102}$,
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[0000-0002-5888-2734]B. Abbott$^\textrm{\scriptsize 120}$,
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[0000-0003-2734-130X]F. Anulli$^\textrm{\scriptsize 75a}$,
[0000-0001-7498-0097]M. Aoki$^\textrm{\scriptsize 84}$,
[0000-0002-6618-5170]T. Aoki$^\textrm{\scriptsize 153}$,
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[0000-0001-8648-2896]C. Arcangeletti$^\textrm{\scriptsize 53}$,
[0000-0002-7255-0832]A.T.H. Arce$^\textrm{\scriptsize 51}$,
[0000-0001-5970-8677]E. Arena$^\textrm{\scriptsize 92}$,
[0000-0003-0229-3858]J-F. Arguin$^\textrm{\scriptsize 108}$,
[0000-0001-7748-1429]S. Argyropoulos$^\textrm{\scriptsize 54}$,
[0000-0002-1577-5090]J.-H. Arling$^\textrm{\scriptsize 48}$,
[0000-0002-6096-0893]O. Arnaez$^\textrm{\scriptsize 4}$,
[0000-0003-3578-2228]H. Arnold$^\textrm{\scriptsize 114}$,
[0000-0002-3477-4499]G. Artoni$^\textrm{\scriptsize 75a,75b}$,
[0000-0003-1420-4955]H. Asada$^\textrm{\scriptsize 111}$,
[0000-0002-3670-6908]K. Asai$^\textrm{\scriptsize 118}$,
[0000-0001-5279-2298]S. Asai$^\textrm{\scriptsize 153}$,
[0000-0001-8381-2255]N.A. Asbah$^\textrm{\scriptsize 61}$,
[0000-0002-4826-2662]K. Assamagan$^\textrm{\scriptsize 29}$,
[0000-0001-5095-605X]R. Astalos$^\textrm{\scriptsize 28a}$,
[0000-0002-3624-4475]S. Atashi$^\textrm{\scriptsize 159}$,
[0000-0002-1972-1006]R.J. Atkin$^\textrm{\scriptsize 33a}$,
M. Atkinson$^\textrm{\scriptsize 162}$,
H. Atmani$^\textrm{\scriptsize 35f}$,
[0000-0002-7639-9703]P.A. Atmasiddha$^\textrm{\scriptsize 128}$,
[0000-0001-8324-0576]K. Augsten$^\textrm{\scriptsize 132}$,
[0000-0001-7599-7712]S. Auricchio$^\textrm{\scriptsize 72a,72b}$,
[0000-0002-3623-1228]A.D. Auriol$^\textrm{\scriptsize 20}$,
[0000-0001-6918-9065]V.A. Austrup$^\textrm{\scriptsize 101}$,
[0000-0003-2664-3437]G. Avolio$^\textrm{\scriptsize 36}$,
[0000-0003-3664-8186]K. Axiotis$^\textrm{\scriptsize 56}$,
[0000-0003-4241-022X]G. Azuelos$^\textrm{\scriptsize 108,ag}$,
[0000-0001-7657-6004]D. Babal$^\textrm{\scriptsize 28b}$,
[0000-0002-2256-4515]H. Bachacou$^\textrm{\scriptsize 135}$,
[0000-0002-9047-6517]K. Bachas$^\textrm{\scriptsize 152,q}$,
[0000-0001-8599-024X]A. Bachiu$^\textrm{\scriptsize 34}$,
[0000-0001-7489-9184]F. Backman$^\textrm{\scriptsize 47a,47b}$,