Apparatus

Abstract

In this chapter, we present an overview of the apparatus used in high energy physics. First, we describe how the particle collisions with high energy are obtained, and then how the reaction of the particle collisions is recorded as the experimental data.

In this chapter, we present an overview of the apparatus used in high energy physics. First, we describe how the particle collisions with high energy are obtained, and then how the reaction of the particle collisions is recorded as the experimental data.

3.1 Particle Collisions at High Energies

The high energy particle physics (in short, the high energy physics) is the research to reveal the ultimate constituents of the universe and the rules obeyed by elementary particles by experimentally observing particle reactions. Since the size that can be probed is determined by the de Broglie wavelength, $\lambda = h/p$, the availability of the high energy particle is essential to investigate more microscopic worlds. At the same time, momentum transfer produced at particle-particle collisions can be used to generate another particle, which is different from the ones before the collision. This implies that the higher the momentum transfer, or the higher the collision energy, the heavier the particles that are generated. For these reasons, we have been using particles with high energy in the past and we will in the future. The increase of the collision energy is the history of the high energy physics.

In the ancient days of the high energy physics, only cathode rays or particles emitted from radioactive materials are available as a source of the particles for research. The naming convention of $\alpha$, $\beta$, $\gamma , \ldots ,$ reflects such history. As time went by, physicists discovered cosmic rays and started to use them as a source of particles. This is still widely used in modern high energy physics. Neutrino experiments underground are typical examples; there are so many facilities to detect and study cosmic, solar, and atmospheric neutrinos. In the meanwhile, physicists succeeded in building accelerators that allowed them to study artificially produced subatomic particles. Many new particles were discovered and investigated by accelerator experiments. The main subject of this book is, however, the accelerator experiments, or more specifically the collider experiments. Below, we concentrate on the topics of the collider experiments: accelerators and detectors.

3.2 Accelerator

There have been various types of accelerators in the world. Here, we describe a large hadron collider (LHC) [1] at CERN as an example of a large accelerator complex. LHC consists of several different accelerators shown in Fig. 3.1.

The LINAC is the first accelerator that accelerates protons or actually $H^{-}$ to 150 MeV. The electrons of $H^{-}$ are stripped off just before the injection to the Booster, and $H^{-}$ become the proton. The Booster accelerates protons to 1.4 GeV and sends them to proton synchrotron (PS) where the protons increase their energy until 25 GeV. The protons are further accelerated by super proton synchrotron (SPS) to 450 GeV, and then finally injected into LHC. The proton energy can be increased to 7 TeV in the design of LHC, but the largest achieved energy so far is 6.5 TeV as of writing this book (in 2021). As we have just seen LHC as an example, it is very common that the large collider complex consists of several accelerators.

Fig. 3.1

Reprinted under the Terms of Use from [2][2] © 2013-2022 CERN. All rights reserved

CERN accelerator complex [1].

The beam energy is one of the most important parameters in the collider experiments, which is related to the potential to generate heavy particles, the interaction cross section, and so on. It is a long-standing tradition that the physicists have been looking for something new in the particle reaction initiated by the highest energy collisions. In fact, the history of discoveries in the high energy physics is the history of the accelerators where the beam energy has been increased. Higher energy machines have enabled us to “see” the subatomic world with higher resolution, and generated heavier objects, such as the Higgs boson.

On top of that, the luminosity of the particle collisions is another key parameter of the experiment. The higher the luminosity, we can accumulate more data per unit time. This allows us to improve the precision in the view of statistical uncertainty, or to search for rarer events such as particle decays with small branching fractions.

Particles inside the synchrotron such as LHC are accelerated by radio frequency waves (RF) that are generated by a so-called RF cavity. Therefore, only the particles that are located in an appropriate phase of the RF can be accelerated. If not, they are decelerated and cannot be in the orbit of the accelerator. We call the cluster of particles spaced by the RF a “bunch”. LHC is operated with the 40 MHz bunch frequency, and hence the bunch crossing occurs every 25 ns if all the bunches are filled with protons.

While explaining above, we have paid careful attention, i.e. we have properly used two terms: the bunch crossing and the collision. The bunch crossing means that two clusters of particles cross at a small space region; some particles are interacted, which is the particle collision. In the LHC, that is, proton-proton collisions, if the number of protons in each bunch is small, or the proton beams are not squeezed enough, particle collisions would not occur so frequently, although the frequency of the bunch crossing is 40 MHz. Such a situation is said to be a “low luminosity”. There is a different story: the cross section in electron-positron collisions is much lower than that in proton-proton collisions, and hence the particle collisions may not occur at every bunch crossing even with the high luminosity electron-positron collider. This is true for the KEKB experiment, for example. In the LHC, however, the bunch crossing is almost identical to the proton-proton collisions. Let’s discuss a concrete example. Assuming the proton-proton collision cross section to be 80 mb and the instantaneous luminosity of $2\times 10^{34}~\textrm{cm}^{-2}\textrm{s}^{-1}$, the number of collisions or interactions per unit time is $16\times 10^8$. Let’s also assume that this luminosity is achieved with the 25 ns bunch spacing, which is close to the case in the actual LHC running in 2018. Based on these assumptions, the number of average interactions per bunch crossing is $16\times 10^8 \times 25 \times 10^{-9} = 40$. In reality, the number of protons are not uniformly spread across the bunches. Also, there is a statistical fluctuation from the average value. But one can imagine that it is very rare to have zero interactions for a bunch crossing. Therefore, we will use the words “bunch crossing” and “particle collision” or “particle interaction” with the same meaning later on if there are no confusions.

So far, we have just discussed the colliders. In addition, there are other types of accelerator experiments, the fixed target experiments. As shown in Fig. 3.1, for example, the Booster, PS, and SPS are used for various fixed target experiments. Particles accelerated by the accelerators are extracted and injected to a fixed target, instead of being collided with each other. With these types of experiments, it is much more difficult to increase the centre-of-mass energy than the colliders, but it is much easier to have high rate interactions at the target due to the large size of the target. For this reason, the fixed target experiments are suitable for getting high statistics, and widely used for rare decay searches.

There is a concept of “spill” at the fixed target experiment, which doesn’t exist in the collider. In the case of the collider experiments, the particle-particle collisions last until the luminosity becomes low because of the beam lifetime. On the other hand, all the particles inside the accelerator are extracted in a certain amount of time, the order of seconds or minutes, at the fixed target experiments. Once all the particles are extracted, new particles are injected through the injector chain to the main accelerator. This cycle is repeated in the fixed target experiments. Therefore, the beam is only available for an experiment when the particles are extracted and hit the target. This period is called “spill”.

3.3 Detector

The particle collisions induced by the collider, fixed target, or cosmic-ray experiments need to be captured by some means. Many particles are produced in these collisions. Some people look for new particles, new decay chains, new patterns in the event kinematics, and so on, which are not discovered yet. Others try to measure the rates of specific reactions such as cross sections or branching ratios of particles. In any case, we want to detect all particles produced by particle reactions and to measure their trajectories, and energies (and flight times if necessary) as precisely as possible. In this regard, geometrical acceptance, detection efficiency, and resolution on measurements are the important figures of merit in considering detectors.

Below, let’s take a close look at $t\bar{t}$ pair-production events, where a pair of the top and anti-top quark is produced, as an example to see what we have to detect and measure in high energy experiments. As the top quark immediately decays to b-quark and W boson with the probability close to 100%, a $t\bar{t}$ pair becomes two pairs of b and W without leaving any trace of top quarks in detectors. The W boson decays to $e\nu _e$, $\mu \nu _{\mu }$, or $\tau \nu _{\tau }$ with the probability of about 11% each, and a quark-anti-quark pair with the probability of about 66%. The former is called a leptonic decay and the latter a hadronic decay. This results in three types of final states.

• Both W decay leptonically, called a dilepton or two-lepton channel.

• One W decays leptonically, and the other hadronically, called a lepton+jet or one-lepton channel.

• Both W decay hadronically, called an all-hadronic or no (or zero)-lepton channel.

We use the lepton+jet channel as a further example in order to describe the particle detection, because the variety of particles in the lepton+jet channel is more than that in the other two channels.

Here, let’s assume one W decays to $e\nu _e$ or $\mu \nu _{\mu }$, and the other hadronically. Then the $t\bar{t}$ final state consists of two b-quarks, one electron (muon), one $\nu _e$ ($\nu _\mu$), and two more light (u, d, c, or s) quarks. The experimentalists want to detect all these particles, and hence try to make the detector more hermetic, i.e. the larger solid angle coverage with respect to the particle interaction point is more preferable. The next question is how to detect and identify all these particles. In the following, we provide an overview of the basics of how each type of particle interacts with materials or detectors, and how they are captured. The detail of the particle identification will be discussed in Chap. 6.

3.3.1 Particle Interaction with Material

3.3.1.1 Electron and Photon

Electrons with the energy of our interest create electromagnetic showers immediately after hitting dense materials such as calorimeters. Hence, the energy and the position can be measured at calorimeters by sensing the energy deposit of electromagnetic showers. At the same time, most of the detectors used in high energy physics have a device to measure trajectories of charged particles, which allows us to measure the momentum in conjunction with the magnetic field provided by a magnet. This is called a magnetic spectrometer. In addition, the precise tracking of charged particles provides the information to find a particle collision point in the collider experiments, and helps particle identification which will be described later in detail.

In addition, photon is a very similar object to electron in terms of detection in high energy regime because photon hitting a material also creates electromagnetic shower. So electromagnetic calorimeter usually measures the energy of both electrons and photons. But there is an important difference, i.e. photon is a neutral particle and hence no track is detected with the charged particle tracking system. This difference is actually used to distinguish photon from electron.

3.3.1.2 Muon

Because muons with their momenta under our interests do not make electromagnetic showers in materials, their energy deposits are almost only by the ionisation of detector materials. This feature allows us to discriminate muons from other charged particles by placing enough materials, which are usually a part of the detectors such as calorimeters and/or solenoid magnets. In most collider experiments, there are two charged particle trackers, one located near the particle collision point, and the other after dense materials such as calorimeters. Particles detected after the dense materials can be identified as muons with a high probability. By connecting trajectories measured by the two trackers, one can assure the muon really comes from the particle collision point.

3.3.1.3 Quark (or Gluon)

Any quarks produced by particle collisions or decays from the other particles are immediately hadronised, except for top quarks, because of the feature of QCD (see Sects. 2.5 and 6.4.1). In the $t\bar{t}$ events, there are two b-quarks produced by the decay of top quarks, and two light quarks decayed from W. All four quarks are metamorphosed to hadrons. The number of hadrons that emerged from a single quark mostly depends on the energy of the original quark. As higher the energy, more hadrons are emerged. Because the top quarks or W bosons are much heavier than light quarks, many (O(10)) hadrons are formed for each of the four quarks, which are aligned to the direction of the momentum vector of the original quarks. This cluster of such particles is called a jet, which will be explained in Sect. 6.4.

It would be ideal to measure the momenta of all the particles inside a jet. However, the magnetic spectrometers cannot detect neutral particles such as photons and neutrons. Because a $\pi ^0$ meson immediately decays to two photons with a branching ratio close to 100%, two photons need to be detected. This fact leads us to a tradition that the energy and direction of jets are measured by calorimeters. More specifically, hadrons are measured by a combination of electromagnetic and hadronic calorimeters behind, in contrast to electromagnetic showers such from electrons and photons that are detected by electromagnetic calorimeters.

3.3.1.4 Neutrino

The cross section of neutrinos to interact with materials is too low to detect. Except for dedicated facilities for neutrino experiments, the nominal collision experiments cannot detect neutrinos, causing “missing energy”. In the electron-positron symmetric-energy colliders, for example, the momentum and energy of the initial states is well defined, i.e. the sum of momenta is zero. The momentum conservation allows us to deduce the momentum vector of neutrinos from the missing momentum, assuming the detector is hermetic enough.

One needs to modify the above idea slightly for hadron colliders. A proton consists of many quarks and gluons, i.e. partons, in the picture of the high energy physics. What actually collide with each other in proton-proton colliders, for example, are partons in protons, not protons themselves. This means that even at symmetric-energy hadron colliders, the actual energy used for a collision is asymmetric, because the net energy of colliding partons varies event-by-event, and there is no principle or law that forces two colliding partons to have the same energy. Humankind does not predict which partons actually collide with each other and how large energy they have event-by-event basis, even though we can know the momentum of the protons. Therefore, the momentum of the beam direction cannot be used at the hadron colliders. The momentum conservation law can be used only for the plane perpendicular to the colliding beams. Here, we ignore the Fermi motion of the partons inside protons because its energy is negligibly small compared to the colliding beam energy. Thus at hadron colliders, neutrino momenta can be measured only on the plane perpendicular to the beam, called “missing $p_{\textrm{T}}$” or “missing $E_{\textrm{T}}$”, which could be a vector (x, y components) or a scalar (the magnitude of a vector) depending on the context.

3.3.2 ATLAS Detector

As we have just seen what kinds of particles and what properties need to be detected, we next discuss how they are detected. The layout or configuration of a multi-purpose detector for high energy physics is common for many experiments, because if you want to detect all kinds of particles, the layout would become unique based on the nature of the interaction of each particle. The most inner part is covered by a charged particle tracker with the material as low as possible so that all particles can penetrate the tracker and reach calorimeters for energy measurements. Because radiation length is much shorter than interaction length, i.e. an electromagnetic shower evolves much faster than a hadronic shower, an electromagnetic calorimeter is placed in front of a hadronic calorimeter. A muon is identified by the fact that it is rare to make either electromagnetic or hadronic shower in our energy region, and hence it penetrates through massive materials such as the calorimeters. Therefore, a muon detector is located on the outermost part of a whole detector system. To summarise, the order of detector elements tends to be a charged particle tracker, an electromagnetic calorimeter, a hadron calorimeter for energy frontier experiment, and a muon detector from inside to outside.

Since the concept is common for most of the detectors, we use the ATLAS detector [3] in the following as an example to introduce the actual detector. Figure 3.2 shows the ATLAS detector consisting of a barrel and two endcap parts. Each barrel and endcap is actually a collection of various detector components, which will be described later. There is a beam pipe penetrating the middle of the detector to make the proton beams run through it. In addition, there are Solenoid and Toroid magnets to provide a magnetic field, allowing to measure the momentum of charged particles. The Solenoid locates between the charged particle tracker and the electromagnetic calorimeter, and the Toroids outside the hadron calorimeter, covering high-$|\eta |$ regions. The field strength by the Solenoid is 2 Tesla. The integrated field strength by the Toroid varies from 2 to 9 T$\cdot$m depending on $| \eta |$ and $\phi$.

Fig. 3.2

Reprinted under the Terms of Use from [4] ATLAS Experiment © 2008 CERN. All rights reserved

Overview of the ATLAS detector [3].

Surrounding the proton-proton interaction point is the charged particle tracker consisting of the pixel and strip-type silicon detectors; each is referred to as pixel and semiconductor tracker (SCT), respectively. All the charged particles such as electrons, charged pions, muons, and so on interact with the tracker materials, and lose their energy, resulting in the creation of electron and hole pair inside the silicon sensor. These holes and/or electrons are collected by the electric field inside the sensor to the electrode, amplified, and recorded as the signal of the particle hit. The pixel and strip detectors have many layers of sensors, enabling us to “reconstruct” the particle trajectory by connecting the space hit points in many layers.

Outside the silicon detector is another tracking device of charged particles, consisting of many transition radiation tubes, referred to as transition radiation tracker (TRT). The mechanism to detect charged particles is similar to the silicon detectors. Each tube of TRT is filled with gas which acts as the sensor instead of silicon. The charged particles passing through the gas create ion and electron pairs that are read out as a signal through the electrode, either cathode or anode wires. In the case of the silicon detectors, usually they have fine pixel or fine pitch of the strips to achieve good space resolution, typically the order of 10 or 100 $\upmu$m. On the other hand, the gas-based tracking device such as TRT uses time information on top of the discrete hit information collected by wires. By knowing the drift time of the ions and/or electrons in the gas, one can deduce more precisely the location of the particles interacting with gas by recording the time of signal arrival. Although the typical size of the tube is the order of mm, $O(100~\upmu$m) position resolution can be achieved.

Most of the charged and neutral particles penetrate the tracking detectors, and hit into the electromagnetic calorimeter composed of the sandwich structure with lead and liquid argon (LAr). Electrons and photons develop the electromagnetic showers mainly at the lead, which is called “absorber”. The electrons created by the shower deposit their energy in the LAr, inducing the electric signals that are recorded, which is called “detector”. The total radiation length (see Sect. 6.2.1) is more than 24$X_0$ (depending on $| \eta |$), which is large enough to terminate the electromagnetic showers, leading to precise measurements of the energy. In addition to the energy measurement, the segment of the calorimeter allows us to identify the location of the electrons or photons hitting into the calorimeter.

The hadron calorimeter is located outside the electromagnetic calorimeter. There are some varieties in the detector types depending on their locations, but the common concept, also used for the ATLAS hadron calorimeter, is to use a sandwich structure made from the absorber and the active region (detector). The barrel region uses iron as the absorber, and plastic scintillators as the sensor to detect the energy deposit of particles created by the hadron showers. A scintillation light is detected by photomultipliers through the wavelength shifting fibres. The total interaction length¹ is roughly 10 $\lambda _0$. Only muons and neutrinos in the SM can penetrate the hadron calorimeters except for punch-through hadrons. In case particles could not be stopped by the calorimeters, that is, their showers are leaked behind, such particles could be detected by other detectors (practically muon detectors). Such particles are called “punch-through” ones (punch-through hadrons).

Following the hadron calorimeter, the outermost layer of the ATLAS detector is the muon spectrometer consisting of monitored drift tube (MDT) and cathode strip chamber (CSC) for precise tracking, and resistive plate chamber (RPC) and thin gap chamber (TGC) for providing fast signal for triggering. These all are the gas detectors like TRT, which allow us to measure the particle passage. The position resolution of MDT and CSC is the order of 100 $\upmu$m. On top of providing fast signals to form a trigger, RPC and TGC determine the event timing, which means that these detectors resolve in which bunch crossing the interaction occurs. Thus, the timing resolution is required to be high for these detectors.

3.3.3 Trigger

The total inelastic cross section of the proton-proton collisions is about 100 mb at $\sqrt{s}=14$ TeV in the LHC. When the instantaneous luminosity of the LHC accelerator is reached at $2 \times 10^{34}~\textrm{cm}^{-2}\textrm{s}^{-1}$, the rate of the inelastic proton-proton interaction is expected to be about 2 GHz. Since the frequency of the bunch crossing in the LHC is designed as 40 MHz, we expect 50 proton-proton collisions in every bunch crossing as discussed in Sect. 3.2 that is called pile-up events. As the instantaneous luminosity goes up with the fixed rate of the bunch crossing, the number of the pile-up events increases more. On the other hand, the event rates of physics of interest, such as the production of the Higgs boson, are expected to be the order of 1–10 Hz or much less, depending on physics processes, as shown in Table 3.1. Thus, the inelastic cross section is huge so that even if events are produced from interesting physics processes, they are overlapped with lots of pile-up events.

The total number of channels of the ATLAS detector is about 2 $\times$ $10^8$. The detector sends 40 MHz $\times$ 2 $\times$ $10^8 \simeq 10^{16}$ bits $\simeq$ $10^{15}$ bytes (1 Peta bytes) data every second, in case each of the channels sends a binary digit every collision. Although the data size per event can be reduced by a factor of about 100 using the noise-like data suppression and a bunch of zero-data suppression techniques, it is still inefficient to record all data of the proton collisions into the data storage system. Before accumulating data of an event into the data storage, its event is analysed online and a decision is made whether or not to keep the event for later offline study. This process is called “trigger”. The current ATLAS trigger and data acquisition (DAQ) system is based on two levels of online event selection, called level 1 trigger (L1 trigger) and high level trigger (HLT), respectively, as shown in Fig. 3.3 [5].

Table 3.1 The rough cross section and the event rate for typical processes. The centre-of-mass energy and the instantaneous luminosity in the LHC are assumed to be 13 TeV and $2 \times 10^{34}~\textrm{cm}^{-2}\textrm{s}^{-1}$, respectively

Fig. 3.3

Reprinted under the Creative Commons Attribution 4.0 International License from [5] © CERN for the benefit of the ATLAS collaboration 2017

ATLAS trigger and DAQ scheme.

3.3.3.1 Level 1 Trigger

The L1 trigger makes an initial selection based on a huge amount of electronic modules (printed circuit boards equipped with application-specific integrated circuits (ASICs) and field-programmable gate arrays (FPGAs), forming multi-chip modules) and their interconnections using information with reduced granularity as inputs from a subset of detectors. There are two main L1 trigger systems in ATLAS. The L1 calorimeter trigger (Level-1 Calo in Fig. 3.3) is based on reduced-granularity information from electromagnetic and hadronic calorimeters, and searches for the high $p_{\textrm{T}}$ electrons and photons, jets, and taus decaying into hadrons, as well as large missing and total transverse energy. The L1 muon trigger (Level-1 Muon) is based on information from so-called trigger chambers; resistive plate chambers (RPC) in the barrel and thin gap chambers (TGC) in the endcaps, and selects high $p_{\textrm{T}}$ muons.

The number of objects such as muons, electrons and photons, jets, and taus above the set of threshold of $p_{\textrm{T}}$ or $E_{\textrm{T}}$ (for example, the threshold of the muon momentum is set as 6, 10, 15, 20 GeV, and so on) in the fiducial region are counted and sent to the L1 central trigger processor (Central Trigger). The L1 trigger provides “region-of-interest (RoI)” information including position ($\eta$ and $\phi$) and $p_{\textrm{T}}$ range of candidate objects for the input of HLT. In the case of the trigger based on the missing and total transverse energy, the information on whether an event passes through the criterion of the threshold is sent to the L1 central trigger processor. The central trigger processor makes an L1 trigger decision based on the combination of objects required in coincidence or veto and provides the signal of the “L1 accept” (Level-1 Accept). The L1 trigger makes a trigger decision within about 2.5 $\upmu$s and reduces the event rate from 40 MHz to 100 kHz. During the process of the trigger decision, information for all detector channels has to be retained in “pipeline” memories, which are placed on usually front-end electronics systems of the detectors (FE in Fig. 3.3). The depth of the pipeline memories depends on the size of data per event, the frequency of the trigger latency.²

3.3.3.2 High Level Trigger

Only events selected by the L1 trigger are read out from the front-end electronics systems to the readout systems (ROS). Further trigger selections are done by the HLT. The HLT makes a more precise selection based on a huge amount of processors. Using the RoI information, the HLT selectively accesses data from readout systems. Typically, only data from a small fraction of the detector, corresponding to RoI information provided by the L1 trigger, are needed by the HLT. Hence, usually only a few per cent of the full event data are required for the event processing. The HLT makes use of information from muons, electrons, photons, jets, taus decaying into hadrons, missing and total transverse energy, and the charged particle tracks provided by the inner tracking system. More specifically, combination of $p_{\textrm{T}}$ or $E_{\textrm{T}}$ of the objects above, and topologies of events such as invariant mass and angles between the objects are used for a decision of the HLT. Only events accepted by the HLT are recorded in the data storage. The HLT reduces the event rate from 100 kHz to a few kHz.

3.3.3.3 Trigger Requirements for Selecting Physics Events

The trigger should reduce the data while keeping candidate events for further physics analyses. The target physics can be the SM process including the production of Higgs, W and Z bosons, and searches for signatures beyond the SM such as supersymmetry or other theoretical models. The trigger needs to cover all signatures for these target physics processes using electrons, photons, muons, jets, taus, b-jets, and missing transverse energy. A few thousands of different trigger conditions are prepared, and the list of these triggers is called a “trigger menu”. The trigger menu is frequently updated depending on the accelerator conditions and physics of interest. Practically, before starting your physics analysis, you need to design the trigger condition to store events of your interest adequately while keeping the trigger rate of background events low enough.

Fig. 3.4

Reprinted under the Creative Commons Attribution 4.0 International License from [5] © CERN for the benefit of the ATLAS collaboration 2017. Top and bottom show the trigger efficiencies for the barrel region and the endcap region, respectively. The efficiency of the barrel region is lower, because in some regions it is hard to place the muon chambers due to the interference of the toroidal magnet

The efficiency of the muon trigger.

Fig. 3.5

Reprinted under the Creative Commons Attribution 4.0 International License from [5] © CERN for the benefit of the ATLAS collaboration 2017

The rate of the muon trigger.

For example, the candidates of Higgs production followed by the decay of $H \rightarrow ZZ^* \rightarrow \mu \mu \mu \mu$ can be collected by a combination of the L1 muon trigger with $p_{\textrm{T}}>15$ GeV threshold and the HLT with $p_{\textrm{T}}>20$ GeV threshold. In this case, the trigger efficiency is high enough for muons reconstructed to be really above the “turn-on curve” i.e. $p_{\textrm{T}}>15$ GeV for L1 and $p_{\textrm{T}}>20$ GeV for HLT, while the efficiency is low if the muons are well below these thresholds (Fig. 3.4). If at least one muon out of four muons from Higgs decay passes through the fiducial detector volume and has $p_{\textrm{T}}>20$ GeV, this kind of event can be kept for later physics analysis. Background events from the inelastic proton-proton interaction with a lot of low $p_{\textrm{T}}$ particles, mostly hadrons, may be effectively rejected by the muon trigger with the high $p_{\textrm{T}}$ threshold. However, there are background events that are not removed by the trigger, where a charged hadron is misidentified as a muon, a low $p_{\textrm{T}}$ muon is mismeasured as a high $p_{\textrm{T}}$ muon, or a few low $p_{\textrm{T}}$ tracks are combinatorially reconstructed as one high $p_{\textrm{T}}$ muon. As discussed at the beginning of this section, since the cross section of the inelastic proton-proton interaction is very high compared to that of the interesting physics processes in most cases, the trigger rate can be dominated by background events even though the misidentification and the mismeasurement of muons are rare. The trigger rate needs to be monitored as a function of the instantaneous luminosity shown in Fig. 3.5 and controlled by optimising, for example, the threshold for $p_{\textrm{T}}$ of the objects in concern.

3.3.4 Optimisation of Detector Performance

If the frequency of the event that needs to be recorded is low, the detector can be optimised for its resolution and/or efficiency. In order to achieve high position resolutions, for example, one might decrease the size of each pixel in the pixel detector for the tracking. However, this increases the number of channels to be read out, and might limit the DAQ speed, which should be improved if necessary. Therefore, the optimisation and compromise are necessary when designing a detector, and their balance depends on many constraints, for example, physics requirements, detector technologies, and some from budgets.

The readers should be aware of the fact that not only detectors but also experiments themselves are strongly constrained by such boundary conditions in reality. It would be instructive to think about or imagine the constraints which are imposed on the detector under study, and why such a particular design was chosen. Such training will help to design and build your own detectors and experiments.