1 Trigger and Data Acquisition

1.1 General Remarks

In the latest and most powerful collider, the Large Hadron Collider (LHC), bunches of protons collide with a nominal frequency of 40 MHz, i.e., every 25 ns. Due to gaps in the beams, at most 2556 bunches are actually present [1]. As the bunch revolution frequency equals 11,245 Hz, the average bunch crossing rate is about 28.7 MHz. The average number of individual proton collisions per bunch crossing, called the pile-up , depends on the luminosity. In the CMS experiment, it varied between about five and slightly more than 60 in 2018 [2], so that bunch crossings without collisions are extremely unlikely in CMS and likewise in ATLAS. The result of a bunch crossing with at least one collision is called an event. In CMS and ATLAS, the event rate is virtually the same as the bunch crossing rate. In the LHCb experiment, however, not all events are actually visible in the detector, so that the effective event rate is lower than the bunch crossing rate; see Sect. 2.1.3.

The most frequent value of pile-up observed by CMS in 2018 was around 30, corresponding to nearly 900 million individual collisions per second. Clearly, it is neither possible nor desirable for the experiment to record all of the event data produced during data taking. A selection mechanism is therefore required that tags the physically interesting events and activates the recording mechanism, called data acquisition (DAQ). Such a selection mechanism is called a trigger.

Triggers have been deployed for many decades, ever since bubble chambers were superseded by experiments with electronic tracking detectors and calorimeters. Triggers are needed both in fixed target and in colliding beam experiments because of limitations in data rates, storage capacity and computing resources. In order to deal with the high event rates typical for electronic experiments, it is important to minimize the dead time of the trigger, i.e., the time after an event during which the system is not able to process another event. Triggers are therefore implemented in several stages or levels, with increasing computational complexity and decision time or latency. The principle and possible implementations are best demonstrated on examples. In the following the trigger/DAQ systems of the CMS and the LHCb experiments will be described in somewhat more detail.

1.2 The CMS Trigger System

CMS [3] is one of the two general purpose experiments at the LHC; see Sect. 1.6.1.3. Its trigger has two levels, the Level-1 Trigger (L1, [4]) and the High-Level Trigger (HLT, [5, 6]). During data taking virtually every bunch crossing results in at least one collision of protons, and the average primary event rate equals the average bunch crossing rate of 28.7 MHz. The trigger, however, must be able to process events separated by only 25 ns.

The task of the L1 trigger is to reduce the primary event rate to less than 100 kHz . This is achieved using high-speed customized hardware running up to 128 different algorithms. Its inputs come from the calorimeters, the muon detectors , and the beam monitors. Its latency is 3.2 µs, including data collection, decision making, and propagation back to the detector front-ends. A block diagram of the L1 trigger is shown in Fig. 2.1.

Fig. 2.1
figure 1

Block diagram of the CMS L1 trigger. The details are explained in the text. (From [4], by permission of Elsevier)

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The input to the muon trigger (MT) comes from three different detector types. The local MTs find track segments, the regional MTs find tracks, and the global MT combines the information from all regional MTs, selects the best four muon candidates, and provides their momenta and directions.

The calorimeter trigger (CT) uses information from the both the electromagnetic and the hadronic calorimeter. The local CTs compute energy deposits, the regional CTs find candidates for electrons, photons, jets, isolated hadrons, and compute transverse energy sums. The transverse energy vector E T is defined as:

$$\displaystyle \begin{gathered} {{\boldsymbol{E}}_{\mathrm{T}}}=E\cdot\begin{pmatrix}\cos\phi\cos\lambda\\\sin\phi\cos\lambda\end{pmatrix}, \end{gathered} $$
(2.1)

where ϕ is the azimuth angle and λ = π∕2 − θ is the dip angle of the particle or jet direction. The global CT sorts the candidates in all categories, computes total and missing transverse energy sums, and computes jet multiplicities for different thresholds.

Finally, the global trigger makes the final decision which is passed on to the detector front-end electronics and the DAQ.

The HLT is designed to reduce the L1 output rate of 100 kHz to the final recording rate of O(100) Hz . It is implemented purely in software which runs on a farm of commercial processors, using the full event data and performing the reconstruction and selection of physics objects such as electrons, photons, muons, τ leptons, hadronic jets, and missing energy; see Sect. 2.4.

1.3 The LHCb Trigger System

Although the intersection point of LHCb is tuned to lower luminosity than the one of CMS and ATLAS, the number of produced \({b\bar {b}}\) pairs is still of the order of 1011 per year. An efficient, robust and flexible trigger is required in order to cope with the harsh hadronic environment. It must be sensitive to many different final states.

While the average bunch crossing rate is 28.7 MHz, the frequency of events actually visible in the detector is about 13 MHz [7]. This must be reduced to about 1 MHz, the frequency at which the detector can be read out. As in CMS, the trigger is organized in two levels, Level-0 (L0) and HLT (see Fig. 2.2).

Fig. 2.2
figure 2

Scheme of the LHCb trigger system. (From [8], reproduced under License CC-BY-4.0)

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The L0 trigger is implemented in field-programmable gate arrays (FPGAs) with a fixed latency of 4 µs [8]. It has two components: the calorimeter trigger, which looks for particles (electrons, photons, neutral pions, hadrons) with large transverse energies; and the muon trigger which uses the tracks reconstructed in the muon chambers and selects the two muons with the highest transverse momentum for each quadrant of the muon detector.

The HLT is implemented purely in software running on the nodes of the event filter farm [8]. It is subdivided in two stages, HLT1 and HLT2; see Sect. 10.4. HLT1 does a partial event reconstruction. Its output, at a rate of about 100 kHz, is directed to HLT2, which performs the full event reconstruction and writes the results to mass storage. For more details on track and vertex reconstruction, see Sect. 10.4.

2 Track Reconstruction

Track reconstruction is a central task in the analysis of the event data. Its aim is to provide estimates of the track parameters, i.e., the position, the direction, and the momentum of charged particles at one or several specific points or surfaces. For an excellent review of track reconstruction, see [9].

Only the tracks of stable or sufficiently long-lived charged particles—for instance electrons, protons, muons and charged pions—are visible in the tracking detectors. Short-lived particles, for instance B hadrons or J∕ψ mesons, are reconstructed from their decay products. The reconstruction of charged particles can be divided into the following steps:

A. Hit generation

The recorded signals are converted to spatial coordinates, either 2D or 3D, using the detector-specific calibration constants. The coordinates will be called “measurements”, “observations” or “hits” in the following. For some examples, see Sects. 1.2 and 1.3.

B. Local track reconstruction

First, tracks are reconstructed in each tracking system. This can again be divided into two or three steps.

  1. 1.

    Track segment reconstruction. This step is relevant only for tracking systems that are in turn composed of several independent devices capable of giving at least the position and the direction of the particle and possibly the momentum. A typical example is the barrel muon system of the CMS experiment which consists of four muon stations, each with up to 12 layers of drift tubes. Although a muon station is not considered a fully-fledged tracking system in the context of track reconstruction, it provides enough hits to estimate the parameters of a straight line track segment [10].

  2. 2.

    Track finding. In this step, hits or track segments are clustered to track candidates, i.e., collections of hits, such that ideally all hits or segments in a collection are produced by the same particle. Track finding can be done iteratively, especially in the very-high multiplicity events recorded by the LHC experiments. In this approach, “easy” tracks with high momentum and small material effects are found first, while more difficult tracks are found in the subsequent passes (see Sect. 10.3). Algorithms for track finding are discussed in detail in Chap. 5. Specific solutions by experiments are discussed in Chaps. 10 and 11.

  3. 3.

    Track fitting. For each track candidate, the track model is fitted to the hits in order to get the best estimates of the track parameters. This is the topic of Chap. 6. The track fit also gives an indication of the quality of the fit, usually in the form of a chi-square statistic χ 2 . An abnormally large value of the chi-square statistic indicates either a random combination of hits, i.e., a “fake” or “ghost” track, or the presence of outliers in the track candidate . Outliers can either be removed from the track or down-weighted by employing a robust estimator ; see Sects. 6.2 and 6.4.2.

C. Global track reconstruction

After the local track reconstruction, the tracks found in the individual tracking systems have to be combined to global track candidates. To this end, the track candidates accepted by the track fit in the main tracking system are extrapolated to the other tracking systems and checked for compatibility with the tracks reconstructed there. As the estimated track parameters in different tracking systems are stochastically independent, the test for compatibility is usually based on the chi-square statistic of their weighted mean, but more sophisticated machine learning methods can be applied as well [11]. The successful combination of local tracks to a global candidate is normally followed by a track fit of the latter.

Some tracking systems do not have enough redundancy to allow stand-alone local track reconstruction, for instance a pixel vertex detector with only two layers. In this case, the tracks found in the global track reconstruction are extrapolated and used to find compatible hits, which are then attached to the track; see Sect. 5.1.7.

D. Assessment of track quality

Not every track candidate generated by the track finding is a valid track. Testing the track hypothesis and assessing the track quality after the track fit is therefore mandatory. This is the topic of Sect. 6.4.

Given a careful calibration of the tracking devices (Sects. 1.2 and 1.3) the chi-square statistic of the track fit is used to reject fake tracks (Sect. 6.4.1) and to trigger the search for outliers (Sect. 6.4.2) or kinks (Sect. 6.4.3) . Another important ingredient to the assessment of track quality is the track length or the effective number of hits attached to the track after removal or down-weighting of outliers; see Sect. 6.4.1. Checking the compatibility with the collision or production region can also be used to reject fake tracks.

If the track reconstruction proceeds iteratively, it is tempting to remove the hits used in an iteration from the hit pool to simplify the task of the subsequent iterations. It is, however, advisable to remove only those hits that are unambiguously attached to tracks of the highest quality.

3 Vertex Reconstruction

A point where particles are produced in a collision or a decay is called a vertex . The point of collision of two beam particles in a collider or of a beam particle with a target particle in a fixed-target experiment is called the primary vertex. In high-luminosity colliders, such as the LHC, many collisions occur in a single bunch crossing; consequently, there are many primary vertices. It is, however, statistically almost certain that at most one of the collisions generates a pattern recognized by the trigger as being of potential physical interest. The vertex of this collision is called the signal vertex.

Many of the particles produced at a primary vertex, including the signal vertex, are unstable and decay at a secondary vertex. The aim of of vertex reconstruction is to find sets of particles that have been produced at the same vertex, to estimate the vertex position, test whether the assignment of the particles to the vertex is correct, and improve the estimates of the track parameters by imposing the vertex constraint. Vertex finding and vertex fitting are the topics of Chaps. 7 and 8, respectively. For the various types of secondary vertices and how to find them, see Chap. 9. Examples of experimental strategies are given in Chaps. 10 and 11.

4 Physics Objects Reconstruction

Both the trigger and the physics analysis require not just tracks, but objects that represent physical entities such as electrons, photons, muons, τ leptons, jets, missing energy, etc. Object identification can be obtained by two complementary approaches: dedicated detectors for particle identification (PID), and combining information from different sub-detectors.

4.1 Particle ID by Dedicated Detectors

Charged particles can be identified by dedicated detectors in various ways [12].

Measurement of the velocity

Given the momentum as determined by the tracking system, the mass can be estimated. Velocity can be measured directly by time-of-flight detectors [13], or indirectly by measuring the emission angle of Cherenkov radiation in Cherenkov detectors [14] and time-of-propagation detectors [15].

Energy loss by ionization

In a large range of velocity, the expected energy loss by ionization is proportional to (m∕p)2, where m is the unknown mass and p is the momentum of the particle; see Sect. 4.5.2.1. In practice, the most probable energy loss is estimated from a number of measurements. In a silicon tracker, energy loss is measured in each sensor [16]; in a drift or time projection chamber, the energy loss is measured for each wire hit or for each cluster in the endplates, respectively [17].

Transition radiation

Transition radiation (TR) is electromagnetic radiation in the X-ray band. It is emitted when an ultra-relativistic particle crosses the boundary between two media with different dielectric constants. The radiator is combined with a gaseous sensing device that measures the TR signal and the position of the particle [13, 18].

4.2 Particle and Object ID by Tracking and Calorimetry

PID in dedicated detectors is complemented by combining information from the tracking systems and the calorimeters.

Electrons

Electrons and positrons are identified as such by the fact that they have a reconstructed track and a cluster in the electromagnetic calorimeter that matches the track in energy and position. For the special treatment of electrons in the track fitting, see Sects. 6.2.3, 10.2 and 10.3.

Photons

Clusters in the electromagnetic calorimeter that are not matched to a track or a cluster in the hadronic calorimeters are candidates for photons.

Muons

Global tracks with hits in both the central tracking system and the muon tracking system are candidates for muons.

Jets

Jets are narrow bundles of charged and neutral particles produced by the hadronization of a quark or a gluon. Jet reconstruction algorithms are based on clustering the charged tracks, but should also provide a good correspondence between the energy deposits in the calorimeters and the reconstructed tracks. This is the aim of the particle flow method, which originated in the ALEPH experiment at the LEP collider [19], and is now employed by LHC experiments as well [20, 21]. In this approach, the energy of a charged hadron is estimated by a weighted average of the track momentum and the associated calorimeter energy. The energy of the photons is measured by the electromagnetic calorimeter, and the energy of neutral hadrons is measured by the hadronic calorimeter.

Tau leptons

Tau leptons have to be reconstructed from their decay products (Sect. 9.2). In two thirds of the cases, τ leptons decay into hadrons, typically into one or three charged mesons (predominantly pions), often accompanied by neutral pions decaying into photons and an invisible neutrino. Therefore, the particle flow approach can be applied to τ leptons as well [22, 23].

Missing energy

Missing transverse energy is a signature for invisible particles such as neutrinos, dark matter, and neutral supersymmetric particles. In a typical collider experiment, it is a global quantity computed from the transverse momentum/energy components of all jets, electrons, photons, muons, and τ leptons in the event. In the LHC experiments, it has to be corrected for contributions from the pile-up collisions in the same bunch crossing; see for instance [24].