Introduction

Abstract

Experimental techniques in high-energy particle physics have been developing very rapidly, despite the experimental principle being relatively simple. Here, we explain the principle first, then the development on top, since the experiments are more complex as the energy of collisions increases.

Experimental techniques in high-energy particle physics have been developing very rapidly, despite the experimental principle being relatively simple. Here, we explain the principle first, then the development on top, since the experiments are more complex as the energy of collisions increases.

The purpose of the high-energy experiments can be classified roughly into two categories: to find any new particle by converting the collision energy to particle mass, and to investigate the nature of the interaction in order to find if any new feature exists there. The first category produces a new particle through resonance or radiation in the final state. The second category may be an indirect detection of new particle contribution in the interaction or discovery of sub-structure of the “elementary” particles through precise measurements of, for example, scattering angles.

Figure 1.1 shows two patterns (Feynman diagrams) of $e^+e^-$ collisions corresponding to the two categories of experiments. The most typical interaction of the first category experiments, production of a new particle, is the resonance of state X in $e^+e^-$ annihilation as depicted in Fig. 1.1a. In most or all collisions, the state X corresponds to known particle(s), for example $Z^{(*)}/\gamma$, but may contain a contribution from a new particle. If there is a contribution from such a new particle, the invariant mass of the decay product reconstructed using the energy and momentum of all the decay particles from X may show a peak from the resonance, corresponding to the mass of the unknown. As the simplest example, if we assume that X decays into two particles, we can observe a peak in the invariant mass spectrum of the two particles.

For the second category of the experiments, namely to investigate interactions and sub-structure of particles, we instead like to use processes where an incoming particle scatters off the other via an exchange of a state $X'$ as represented by Fig. 1.1b. Depending on the nature of the exchange $X'$, the scatters will give a certain prediction on the angular and momentum distribution of the final state particles. For example, for the Coulomb scattering, we know that the scattering angle of an electron beam with a heavy point-like target particle, such as nucleus, behaves like $1/\sin ^4(\theta /2)$, where $\theta$ is the scattering angle with respect to the incoming beam direction in target-rest frame (note that the spin effect to the scattering angle is ignored here). The contribution from a new particle exchanged as the state $X'$ would give a small modification to the fundamental Rutherford scattering behaviour of $1/\sin ^4(\theta /2)$. The effect should be enhanced beyond the energy regime where the momentum transfer squared of the exchanged particle is beyond the mass squared of the particle responsible for the new interaction, such as an unknown new heavy gauge boson.

Fig. 1.1

Feynman diagrams of $e^+e^-$ interactions a annihilating each other producing a virtual particle X (decaying a pair of particles) and b exchanging a particle $X'$ between them

We conduct high-energy experiments for research based on these principals and need to consider detector, data-taking, reconstruction, identification, calibration, analysis, etc. The $2 \rightarrow 2$ processes, as illustrated in Fig. 1.1a, b, can be fully reconstructed if the momenta and energies of these two outgoing particles are measured; the experiment for such a case is simple. In reality, the number of particles to be measured may be more than two in many cases—in fact, far more for typical high-energy scatterings. There may be the radiation of particles from the 2-to-2 process as well as decay products of heavy elementary particles, such as W and Z bosons and top quarks, which decay further into many particles.

The situation is particularly difficult if particles from the outgoing particles may contain neutrinos or any other unknown neutral particles which interact only weakly with detector materials. Such neutral particles escape the detector, practically always. The only way to “detect” them is to measure the so-called “missing momentum” using four-momentum conservation, which corresponds to momentum carried by the neutral particles. For that, we need to measure all the other particles in the final state. The detector, therefore, needs to cover the interaction point almost fully, i.e. the solid angle of the coverage should be close to $4\pi$. Such kind of detector is called a hermetic detector. A neutrino becomes a common object once the energy of the collision is high enough that one can easily produce W and Z bosons, since they produce neutrinos through the decay $W \rightarrow \ell \nu$ or $Z \rightarrow \nu \bar{\nu }$ where $\ell$ is either of $e, \mu , \tau$ and $\nu = \nu _e, \nu _\mu$ or $\nu _\tau$. This is the reason why any modern high-energy collider experiments cover almost all the solid angles to have a hermetic system.

The density of particles in the detector is also an issue at high energies. As the energy of the collision becomes higher, the number of particles increases approximately proportional to $\ln \sqrt{s}$, where s is the square of the centre-of-mass energy of the collision. This makes the angular density higher; in particular, many particles are produced in a small angular area when an energetic quark or gluon is produced and fragmented. These collimated bunches of particles are called jet. The presence of jets also requires the detector to have small segmentation—or fine “granularity”, we often call—such that a pair of particles produced close by each other can be distinguished as two particles. In addition, the increase of the collision energy also asks for more material to stop neutral particles (not neutrinos but neutrons) in order to measure them. The detector becomes thicker with energy, again $\propto \ln \sqrt{s}$, and the overall size of the detector becomes larger.

Furthermore, the modern high-energy experiments should deal with many different types of stable particles. The detector has to measure electrons, muons and photons very precisely. Hadrons (pions and kaons, practically) are also copiously produced as explained above. The energy measurement of charged hadrons or baryons at high precision is particularly difficult. The identification of the species of hadrons, such as the pion, the kaon and other particles, may be desirable if one needs to study decay chains of particular mesons.

In addition, the presence of b-quark is a very useful signal for investigating physics involving quark flavour, in particular for top quarks, since a top quark decays to W and a b-quark, whose branching ratio is practically 100%. As for leptons, production of high momentum $\tau$ could be an indication of the presence of new physics of special flavour structure, such as some bosons preferentially couple to third generation fermions. Identification of these particles is based on the fact that they fly short distance before decaying, calling for a very precise tracking device.

Thus, modern high-energy collider detectors should be able to deal with all sorts of stable leptons and hadrons. In general, the design of detectors should be optimised to the target physics. For collider detectors, however, the versatility is more respected since there are many different targets; detectors need to measure known Standard-Model (SM) processes precisely while they also cope with some peculiar signals from new particles. Therefore, “general-purpose” detectors are preferred and measurements on both known and unknown processes are performed with good precision.

Yet another to consider at high energy is that the probability of observing particular processes, i.e. cross sections (see Sect. 2.2) decreases with energy of collisions in general. A simple dimensional analysis tells us that the cross section of point-like particles, such as $e^+e^-$ or parton-parton collisions, decreases like 1/s, or by $1/E^2$ in terms of the incoming particle energy E for symmetric collisions. This means that the probability of interactions you like to find is suppressed by $1/E^2$. This should be compensated by increasing luminosity (see Sect. 2.2), which is proportional to the number of collisions of a given process per unit time. This is realised by a shorter time interval of collisions, higher beam current and better focusing of beams in colliders.

Now the problem is that this increases not only signal but also background rates. In particular, for hadron-hadron collisions, the cross section is dominated by a soft process (see Sect. 2.5), which is approximately constant in collision energy instead of $1/E^2$. The soft process is the background for most physics analyses. The increase in the number of collisions per unit of time also leads to a higher probability of pile-up of multiple collisions. The issue of pile-up should be resolved by a detector system with high resolution, both in space and time. Moreover, higher rates impose an additional challenge for data-taking.

Last but not the least, for precision measurements it is also important that experiments are well modelled by simulation. So-called data-driven methods are adopted to reduce uncertainties of measurements for the estimation of background contributions. However, in most cases, we need help with the simulation, which causes additional uncertainties. In data analysis, the cutting-edge technique utilising the modern statistical technique including machine learning should help in increasing the experimental sensitivities.

In summary, modern high-energy experimental physics, specifically the collider experiments, should pay attention to the following items, even though the basic idea of experiments in terms of physics goal remains similar to that of lower energy experiments. Good reconstruction of all sorts of stable particles including neutrinos should be possible with well-calibrated detectors. The detector should also work under harsh conditions of high-rate collisions. Modern statistical and analysis methods and well-modelled simulation of physical processes and detectors should be pursued with support from the rapid advancement of computing powers. Last but not the least, the sensitivity of the experiments ultimately relies on ideas on data analysis based on the human understanding of the physics processes in concern. We believe it even if smarter artificial intelligence is born.

The following chapters of this book provide comprehensive explanations on each of the key elements in the high-energy experiments and data analysis, aiming for helping to understand on the above-mentioned subjects. Chapter 2 starts with an overview of how a collider detector is designed to measure particles and the data are recorded. Also explained is how we extract the physical quantities of interest out of the data analyses. Chapter 3 covers the collider facility, detector in general and data-taking system. Chapter 4 gives basic overview of statistics used in high-energy physics. Chapter 5 describes detector calibration procedure, followed by particle identification in Chap. 6. Chapter 7 is devoted to the explanation of how the simulation of the physical process of collisions is taken place. All these chapters are followed by “exercise” parts in Chap. 8, where we give an explanation of the physics data analysis and results of journal papers as examples on how the reconstructed events are utilised to extract physical properties. They are measurements of Higgs production cross sections through its decay to two photons, a $b\bar{b}$, or a $W^+W^-$ pair. Searches for new particles are also explained.