Neutrino mixing

In this chapter we shall discuss the only phenomena that have been discovered beyond the Standard Model. As anticipated in Sections 3.8 and 4.11, neutrinos produced with a certain flavour, νe, νµ or ντ, may be detected at later times with a different flavour. Consequently νe, νµ and ντ are not stationary states with definite mass, which we shall call, ν1, ν2, ν3, but quantum superpositions of them.

Neutrinos change flavour by two mechanisms:

• Oscillation, similar but not identical to the K0 oscillation. It occurs both in vacuum and in matter. It has been discovered in the νµ indirectly produced by cosmic rays in the atmosphere. The energies of these neutrinos range from below one GeV to several GeV. The distance from the production to the detection point can be as large as several thousand kilometres.

• Transformation in matter, which is a dynamical phenomenon due to the interaction of the νes with the electrons, similar to the refractive index of light. The phenomenon can most easily be observed if the flight length is large and if the density is high, as in a star. It has been discovered in the νes coming from the Sun, which have energies of several MeV.

At the mentioned energy scales both phenomena take place on very long characteristic time scales. The corresponding flight lengths are much larger than those that were available on neutrino beams produced at accelerators.

Resonances

The particles we have discussed up to now are metastable, in other words they decay by weak or electromagnetic interactions. The distances between their production and decay points or between the corresponding times are long enough to be separately observable.

If the mass of a hadron is large enough, final states that can be reached by strong interaction, i.e. without violating any selection rule, become accessible to its decay. Therefore, they have extremely short lifetimes, of the order of 10−24 seconds, and decay, from the point of view of an observer, exactly where they were born. To fix the orders of magnitude, consider such a particle produced in the laboratory reference frame with a Lorentz factor as large as γ = 300. In a lifetime, it will travel one femtometre.

These extremely unstable hadrons can be observed as ‘resonances’ in two basic ways: in the process of ‘formation’ as a local maximum in the energy dependence of a cross section or in the ‘production’ process as a maximum in the (invariant) mass distribution of a few particles in the final states of a reaction.

Resonant phenomena are ubiquitous in physics, both at the macroscopic and microscopic levels. Even in very different physical situations, ranging from mechanics to electrodynamics, from acoustics to optics, from atomic to nuclear physics, etc., the fundamental characteristics of this phenomenon are the same. Actually, the classical and the quantum formalisms are also very similar. Resonances have an extremely important role in hadron spectroscopy.

The electroweak interaction

The development of the theoretical model that led to the electroweak unification started at the end of the 1960s. In this model, a single gauge theory, with the symmetry group SU(2) ⊗ U(1), includes the electromagnetic and weak interactions, both neutral current (NC) and charged current (CC). In particular, the electromagnetic and weak coupling constants are not independent but correlated by the theory. On the other hand, electroweak theory and QCD, both being gauge theories, are unified by the theoretical framework while their coupling constants are independent. Electroweak theory and QCD together form the Standard Model of fundamental interactions.

In the first part of this chapter we shall introduce the electroweak theory, as usual without any theoretical rigour. The unification characteristics appear mainly in the NC processes. The transition probabilities of all these processes are predicted by the theory with a single free parameter, the electroweak mixing angle. We shall discuss an example of its determination.

A crucial prediction of the theory is the existence of three vector bosons, W+, W− and Z0, together with predictions of their masses, widths and branching ratios in all their decay channels. All these predictions have been experimentally verified with high accuracy. We shall finally see the experimental proof of the fact that the vector bosons have weak charges themselves and that consequently they interact directly.

This book is mainly intended to be a presentation of subnuclear physics, at an introductory level, for undergraduate physics students, not necessarily for those specialising in the field. The reader is assumed to have already taken, at an introductory level, nuclear physics, special relativity and quantum mechanics, including the Dirac equation. Knowledge of angular momentum, its composition rules and the underlying group theoretical concepts is also assumed at a working level. No prior knowledge of elementary particles or of quantum field theories is assumed.

The Standard Model is the theory of the fundamental constituents of matter and of the fundamental interactions (excluding gravitation). A deep understanding of the ‘gauge’ quantum field theories that are the theoretical building blocks of this model requires skills that the readers are not assumed to have. However, I believe it to be possible to convey the basic physics elements and their beauty even at an elementary level. ‘Elementary’ means that only knowledge of elementary concepts (in relativistic quantum mechanics) is assumed. However it does not mean a superficial discussion. In particular, I have tried not to cut corners and I have avoided hiding difficulties, whenever was the case. I have included only well-established elements with the exception of the final chapter, in which I survey the main challenges of the present experimental frontier.

The text is designed to contain the material that may be accommodated in a typical undergraduate course. This condition forces the author to hard, and sometimes difficult, choices.

The basic motive which drives the scientist to new discoveries and understanding of nature is curiosity. Progress is achieved by carefully directed questions to nature, by experiments. To be able to analyse these experiments, results must be recorded. The most simple instruments are the human senses, but for modern questions, these natural detection devices are not sufficiently sensitive or they have a range which is too limited. This becomes obvious if one considers the human eye. To have a visual impression of light, the eye requires approximately 20 photons. A photo-multiplier, however, is able to ‘see’ single photons. The dynamical range of the human eye comprises half a frequency decade (wavelengths from 400 nm to 800 nm), while the spectrum of electromagnetic waves from domestic current over radio waves, microwaves, infrared radiation, visible light, ultraviolet light, X-rays and gamma rays covers 23 frequency decades!

Therefore, for many questions to nature, precise measurement devices or detectors had to be developed to deliver objective results over a large dynamical range. In this way, the human being has sharpened his ‘senses’ and has developed new ones. For many experiments, new and special detectors are required and these involve in most cases not only just one sort of measurement. However, a multifunctional detector which allows one to determine all parameters at the same time does not exist yet.

Particles and radiation can be detected only through their interactions with matter. There are specific interactions for charged particles which are different from those of neutral particles, e.g. of photons. One can say that every interaction process can be used as a basis for a detector concept. The variety of these processes is quite rich and, as a consequence, a large number of detection devices for particles and radiation exist. In addition, for one and the same particle, different interaction processes at different energies may be relevant.

In this chapter, the main interaction mechanisms will be presented in a comprehensive fashion. Special effects will be dealt with when the individual detectors are being presented. The interaction processes and their cross sections will not be derived from basic principles but are presented only in their results, as they are used for particle detectors.

The main interactions of charged particles with matter are ionisation and excitation. For relativistic particles, bremsstrahlung energy losses must also be considered. Neutral particles must produce charged particles in an interaction that are then detected via their characteristic interaction processes.

The scope of detection techniques is very wide and diverse. Depending on the aim of the measurement, different physics effects are used. Basically, each physics phenomenon can be the basis for a particle detector. If complex experimental problems are to be solved, it is desirable to develop a multipurpose detector which allows one to unify a large variety of different measurement techniques. This would include a high (possibly 100%) efficiency, excellent time, spatial and energy resolution with particle identification. For certain energies these requirements can be fulfilled, e.g. with suitably instrumented calorimeters. Calorimetric detectors for the multi-GeV and for the eV range, however, have to be basically different.

The discovery of new physics phenomena allows one to develop new detector concepts and to investigate difficult physics problems. For example, superconductivity provides a means to measure extremely small energy depositions with high resolution. The improvement of such measurement techniques, e.g. for the discovery and detection of Weakly Interacting Massive Particles (WIMPs), predicted by supersymmetry or cosmological neutrinos, would be of large astrophysical and cosmological interest.

In addition to the measurement of low-energy particles, the detection of extremely small changes of length may be of considerable importance.

A present-day experiment in high energy physics usually requires a multipurpose experimental setup consisting of at least several (or many) subsystems. This setup (called commonly ‘detector’) contains a multitude of sensitive channels which are necessary to measure the characteristics of particles produced in collisions or decays of the initial particles. A typical set of detector properties includes abilities of tracking, i.e. measurement of vertex coordinates and charged-particle angles, measurements of charged-particle momenta, particle energy determination and particle identification. A very important system is the trigger which detects the occurrence of an event of interest and produces a signal to start the readout of the information from the relevant channels. Since high energy physics experiments are running for months or years, the important task is to monitor and control the parameters of the detector and to keep them as stable as possible. To fulfil this task the detector is usually equipped with a so-called slow control system, which continuously records hundreds of experimental parameters and warns experimentalists if some of them are beyond certain boundaries.

To control the process of accumulating statistics and calculating the cross sections and decay rates, a luminosity measurement system is mandatory (for the term definition, see Chap. 4).

A particular type of detector does not necessarily make only one sort of measurement. For example, a segmented calorimeter can be used to determine particle tracks; however, the primary aim of such a detector is to measure the energy. The main aim of drift chambers is a measurement of particle trajectories but these devices are often used for particle identification by ionisation measurements. There is a number of such examples.

This chapter considers the main physical principles used for particle detection as well as the main types of counters (detector elements). The detectors intended for the measurement of certain particle characteristics are described in the next chapters. A brief introduction to different types of detectors can be found in [1].

Ionisation counters

Ionisation counters without amplification

An ionisation counter is a gaseous detector which measures the amount of ionisation produced by a charged particle passing through the gas volume. Neutral particles can also be detected by this device via secondary charged particles resulting from the interaction of the primary ones with electrons or nuclei. Charged particles are measured by separating the charge-carrier pairs produced by their ionisation in an electric field and guiding the ionisation products to the anode or cathode, respectively, where corresponding signals can be recorded.