1. Historical Introduction to the Elementary Particles. This chapter is a kind of 'folk history' of elementary particle physics. Its purpose is to provide a sense of how. 1. Historical Introduction to the Elementary Particles The Classical ERA ( ) The Photon () Mesons () Halzen, Martin: Quarks and Leptons; Wiley Griffiths: Introduction to Elementary Particle Physics; Wiley Perkins: Introduction to High.
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1 Historical Introduction to the Elementary Particles 1.l The Classical Era (1 ) 1 1. The Photon () Mesons (1 ) This introduction to the theory of elementary particles is intended primarily for advanced undergraduates who are majoring in physics. Most of my colleagues. This is the first quantitative treatment of elementary particle theory that is accessible to undergraduates. Using a lively, informal writing style, the.
No prior knowledge of elementary particles or of quantum field theories is assumed. A systematic search showed that in materials with low atomic numbers the penetrating particles are not absorbed by nuclei. We shall often use as their unit the electronvolt eV and its multiples. However, if you place it on your hand and move your hand quickly to and fro, the stick will not fall. Hess, flying aerostatic balloons at high altitudes, discovered that charged particle radiation originated outside the atmosphere, in the cosmos Hess The procedure then constrains the measured quantities, imposing energy and momentum conservation at each vertex.
Please check your email for instructions on resetting your password. If you do not receive an email within 10 minutes, your email address may not be registered, and you may need to create a new Wiley Online Library account. If the address matches an existing account you will receive an email with instructions to retrieve your username. Skip to Main Content. Introduction to Elementary Particles Author s: David Griffiths.
First published: Print ISBN: About this book This is the first quantitative treatment of elementary particle theory that is accessible to undergraduates. Using a lively, informal writing style, the author strikes a balance between quantitative rigor and intuitive understanding. The first chapter provides a detailed historical introduction to the subject. Subsequent chapters offer a consistent and modern presentation, covering the quark model, Feynman diagrams, quantum electrodynamics, and gauge theories.
A clear introduction to the Feynman rules, using a simple model, helps readers learn the calculational techniques without the complications of spin. And an accessible treatment of QED shows how to evaluate tree-level diagrams.
If the energies are high enough, quantum processes happen at an appreciable frequency: In these circumstances, we can no longer speak of a potential. In conclusion, the concept of potential is non-relativistic: It is correct for the electrons in the atoms, to first approximation, but not for the quarks in the nucleons.
Otherwise, energy and momentum cannot be conserved simultaneously. Let us now consider the following processes: This reaction cannot occur. This is just the inverse reaction, it cannot occur either. Let the initial electron be at rest, let Ec be the energy of the photon, Ef, pf the energy and the momentum of the final electron. Setting 1. This process happens in the Coulomb field of the nucleus, in which the electron accelerates and radiates a photon.
The process is known by the German word bremsstrahlung. Consider two bodies of the same mass m moving initially one against the other with the same speed t for example two wax spheres. The two collide and remain attached in a single body of mass M.
The total energy does not vary, but the initial kinetic energy has disappeared. Actually, the rest energy has increased by the same amount. Actually, we have already started to do so. We shall also use the electronvolt instead of the joule as the unit of energy.
Mass, energy and momentum have the same dimensions: For unit conversions the following relationships are useful: We simply use the uncertainty principle: It is sufficient to measure one of the two. The width of the p0 particle is too small to be measured, and so we measure its lifetime; vice versa in the case of the g particle.
Depending on what we measure, we can define the final state with more or fewer details: In each case, when computing the cross section of the observed process we must integrate on the non-observed variables.
Given the two initial particles a and b, we can have different particles in the final state. The sum of all the partial cross sections is the total cross section. Decays Consider, for example, the three-body decay a! Here the quantity to compute is the decay rate in the measured final state. Integrating over all the possible kinematic configurations, one obtains the partial decay rate Cbcd, or partial width, of a into the b c d channel.
The sum of all the partial decay rates is the total width of a. The latter, as we have anticipated in Example 1. For both collisions and decays, one calculates the number of interactions per unit time, normalising in the first case to one target particle and one beam particle, in the second case to one decaying particle. There are two elements: The beam, which contains particles of a definite type moving, approximately, in the same direction and with a certain energy spectrum.
The beam intensity Ib is the number of incident particles per unit time, the beam flux Ub is the intensity per unit normal section. The target, which is a piece of matter. It contains the scattering centres of interest to us, which may be the nuclei, the nucleons, the quarks or the electrons, depending on the case. Let nt be the number of scattering centres per unit volume and Nt be their total number if the beam section is smaller than that of the target, Nt is the number of centres in the beam section.
The interaction rate Ri is the number of interactions per unit time the quantity that we measure. To be rigorous, one should consider that the incident flux diminishes with increasing penetration depth in the target, due to the interactions of the beam particles. We shall consider this issue soon. We find Nt by recalling that the number of nucleons in a gram of matter is in all cases, with sufficient accuracy, the Avogadro number NA.
In subnuclear physics the cross sections are smaller and submultiples are used: Let z be the distance travelled by the beam in the target, measured from its entrance point.
We want to find the beam intensity I z as a function of this distance. If dRi is the 1. Equation 1. This expression is somewhat misleading because the number of particles in the target seen by the beam depends on its section.
Evaluate its luminosity. There are two possible expressions of phase space: Obviously the rates W must be identical, implying that the matrix element M is different in the two cases. In the non-relativistic formalism neither the phase space nor the matrix element are Lorentz-invariant. Both factors are invariant in the relativistic formalism, a fact that makes things simpler. We recall that in the non-relativistic formalism the probability that a particle i has the position ri is given by the square modulus of its wave function, jw ri j2.
This is normalised by putting its integral over all volume equal to one. The volume element dV is a scalar in three dimensions, but not in space-time. Under a Lorentz transformation r! To have a Lorentz-invariant probability density, we profit from the energy transformation E!
With n particles in the final state, the volume of the phase space is therefore! Now we consider the collision of two particles, say a and b, resulting in a final state with n particles. We shall give the expression for the cross section. The cross section is normalised to one incident particle; therefore, we must divide by the incident flux. In the laboratory frame the target particles b are at rest, the beam particles a move with a speed of, say, ba.
The flux is the number of particles inside a cylinder of unitary base and height ba. The flux of particles b is their number inside a cylinder of unitary base of height bb. The probability of transition per unit time to the final state f of n particles is! The Standard Model gives the rules to evaluate all the matrix elements in terms of a set of constants. Even if we do not have the theoretical instruments for such calculations, we shall be able to understand the physical essence of the principal predictions of the model and to study their experimental verification.
Now let us consider an important case, the two-body phase space. Let c and d be the two final-state particles of a collision or decay. We choose the centre of mass frame, in which calculations are easiest.
Again let Ea and Eb be the initial energies, Ec and Ed the final ones. Let us restrict ourselves to the case in which neither the beam nor the target is polarised and in which the final polarisations are not measured. Therefore, in the evaluation of the cross section we must sum over the final spin states and average over the initial ones.
Using 1. We shall give here the names of these groups and summarise their properties. The particles of a given type, the electrons for example, are indistinguishable. Take for example a fast proton hitting a stationary one. After the collision, that we assume to be elastic, there are two protons moving in general in different directions with different energies.
It is pointless to try to identify one of these as, say, the incident proton. We recall that the wave function of a system of identical bosons is symmetric under the exchange of any pair of them, while the wave function of a system of identical fermions is antisymmetric. Matter is made up of atoms. Atoms are made of electrons and nuclei bound by the electromagnetic force, whose quantum is the photon. The photons from the Greek word phos meaning light are massless. Their charge is zero and therefore they do not interact among themselves.
Their spin is equal to one; they are bosons. As far as we know they do not have any structure, they are elementary. Nuclei contain most of the mass of the atoms, hence of the matter. They are positively charged and made of protons and neutrons.
Protons from proton meaning the first, in Greek and neutrons have similar masses, slightly less than a GeV. The charge of the proton is positive, opposite and exactly equal to the electron charge; neutrons are globally neutral, but contain charges, as shown, for example, by their non-zero magnetic moment. As anticipated, protons and neutrons are collectively called nucleons.
In , Yukawa formulated a theory of the strong interactions between nucleons Yukawa Nucleons are bound in nuclei by the exchange of a zero spin particle, the quantum of the nuclear force.
Given the finite range of this force, its mediator must be massive. Given the value of the range, about 10—15 m, its mass should be intermediate between the electron and the proton masses; therefore it was called the meson that which is in the middle. More specifically, it is the p meson, also called the pion. We shall describe its properties in the next chapter. Pions come in three charge states: They are somewhat more massive than nucleons and are called baryons that which is heavy or massive.
Notice that nucleons are included in this category. Baryons and mesons are not point-like; instead they have structure and are composite objects. The components of both of them are the quarks. In a first approximation, the baryons are made up of three quarks, the mesons of a quark and an antiquark. Quarks interact via one of the fundamental forces, the strong force, that is mediated by the gluons from glue. As we shall see, there are eight different gluons; all are massless and have spin one.
Baryons and mesons have a similar structure and are collectively called hadrons hard, strong in Greek. All hadrons are unstable, with the exception of the lightest one, the proton. Shooting a beam of electrons or photons at an atom we can free the electrons it contains, provided the beam energy is large enough.
Analogously we can break a nucleus into its constituents by bombarding it, for example, with sufficiently energetic protons. The two situations are similar with quantitative, not qualitative, differences: However, nobody has ever succeeded in breaking a hadron and extracting the quarks, whatever the energy and type of the bombarding particles.
We have been forced to conclude that quarks do not exist in a free state; they exist only inside the hadrons. In order of increasing mass the up-type are: Nucleons, hence nuclei, are composed of up and down quarks, uud the proton, udd the neutron. There are three charged leptons, the electron e, the muon l and the tau s, and three neutral leptons, the neutrinos, one for each of the charged leptons.
The electron is stable, the l and the s are unstable, and all the neutrinos are stable. For every particle there is an antiparticle with the same mass and the same lifetime and all charges of opposite values: One last consideration: We do not know what the rest is made of. There is still a lot to understand beyond the Standard Model see Chapter The Standard Model is the theory that describes all the fundamental interactions, except gravitation.
For the latter, we do not yet have a microscopic theory, but only a macroscopic approximation, so-called general relativity. We anticipate here that the intensity of the interactions depends on the energy scale of the phenomena under study. The source and the receptor of the gravitational interaction is the energymomentum tensor; consequently this interaction is felt by all particles.
However, gravity is extremely weak at all the energy scales experimentally accessible and we shall neglect its effects. Let us find the orders of magnitude by the following dimensional argument. It is enormous, not only in comparison to the energy scale of the Nature around us on Earth eV but also of nuclear MeV and subnuclear GeV physics. We shall Preliminary notions 22 never be able to build an accelerator to reach such an energy scale.
We must search for quantum features of gravity in the violent phenomena naturally occurring in the Universe. All the known particles have weak interactions, with the exception of photons and gluons. This interaction is responsible for beta decay and for many other types of decays.
Their existence becomes evident at energies comparable to those masses. All charged particles have electromagnetic interactions. This interaction is transmitted by the photon, which is massless.
Quarks and gluons have strong interactions; the leptons do not. The interaction amongst quarks in a hadron is confined inside the hadron. The phenomenon is analogous to the van der Waals force that is due to the electromagnetic field leaking out from a molecule. Therefore the nuclear Yukawa forces are not fundamental. As we have said, the charged leptons more massive than the electron are unstable; the lifetime of the muon is about 2 ls, that of the s, 0.
These are large values on the scale of elementary particles, characteristic of weak interactions. All mesons are unstable: All baryons, except for the proton, are unstable. The neutron has a beta decay into a proton with a lifetime of s. This is exceptionally long even for the weak interaction standard because of the very small mass difference between neutrons and protons.
Some of the other baryons, the less massive ones, decay weakly with lifetimes of the order of 0. Evaluate the ratio between the electrostatic and the gravitational forces. Does it depend on r? This discussion is not possible without some knowledge of the physics of the passage of radiation through matter, of the main particle detectors and the sources of high-energy particles.
When a high-energy charged particle or a photon passes through matter, it loses energy that excites and ionises the molecules of the material. It is through experimental observation of these alterations of the medium that elementary particles are detected. Experimental physicists have developed a wealth of detectors aimed at measuring different characteristics of the particles energy, charge, speed, position, etc. This wide and very interesting field is treated in specialised courses and books.
Here we shall only summarise the main conclusions relevant for the experiments we shall discuss in the text and not including, in particular, the most recent developments. Ionisation loss The energy loss of a relativistic charged particle more massive than the electron passing through matter is due to its interaction with the atomic electrons. The process results in a trail of ion—electron pairs along the path of the particle. These free charges can be detected.
Electrons also lose energy through bremsstrahlung in the Coulomb fields of the nuclei. The expression of the average energy loss per unit length of charged particles other than electrons is known as the Bethe—Bloch equation Bethe We give here an approximate expression, which is enough for our purposes. Specific average ionisation loss for relativistic particles of unit charge.
Simplified from Yao et al. The energy loss is a universal function of bc in a very rough approximation, but there are important differences in the different media, as shown in Fig. The energy loss of a minimum ionising particle mip is 0. The Bethe—Bloch formula is only valid in the energy interval corresponding to approximately 0.
The latter is a random variable with a frequency function centred on the expectation-value given by the Bethe—Bloch equation. The variance, called the straggling, is quite large. Notice, in particular, the dispersion around the average values. Energy loss of the electrons Figure 1. As anticipated, electrons and positrons, due to their small mass, lose energy not only by ionisation but also by bremsstrahlung in the nuclear Coulomb field.
This happens at several MeV. As we have seen in Example 1. In quantum mechanics, the situation is similar: Preliminary notions 26 Therefore, this phenomenon is much more important close to a nucleus than to an atomic electron. Furthermore, for a given external field, the probability is inversely proportional to the mass squared. We understand that for the particle immediately more massive than the electron, the muon that is times heavier, the bremsstrahlung loss becomes important at energies larger by four orders of magnitude.
Comparing different materials, the radiation loss is more important if Z is larger. More specifically, the materials are characterised by their radiation length X0.
A few typical values are: We show in Fig. At low energies the ionisation loss dominates, at high energies the radiation loss becomes more important. The crossover, when the two losses are equal, is called the critical energy. Energy loss of the photons At energies of the order of dozens of electronvolts, the photons lose energy mainly by the photoelectric effect on atomic electrons. Above a few keV, the Compton effect becomes important. Relative energy loss of electrons in lead.
Adapted from Yao et al. Photon cross sections in Pb versus energy; total and calculated contributions of the three principal processes. The situation is shown in Fig. Therefore, X0 determines the general characteristics of the propagation of electrons, positrons and photons. Energy loss of the hadrons High-energy hadrons passing through matter do not lose energy by ionisation only.
Eventually they interact with a nucleus by the strong interaction. This leads to the disappearance of the incoming particle, the production of secondary hadrons and the destruction of the nucleus. At energies larger than several GeV, the total cross sections of different hadrons become equal within a factor of 2 or 3. Comparing with the radiation length we see that collision lengths are larger and do not depend heavily on the material, provided this is solid or liquid.
These observations are important in the construction of calorimeters see Section 1. We shall give, in both cases, only the pieces of information that are necessary for the following discussions. In this section, we discuss the sources, in the next the detectors.
There is a natural source of high-energy particles, the cosmic rays; the artificial sources are the accelerators and the colliders. Cosmic rays In , V. Hess, flying aerostatic balloons at high altitudes, discovered that charged particle radiation originated outside the atmosphere, in the cosmos Hess Fermi formulated a theory of the acceleration mechanism in Fermi Until the early s, when the first high-energy accelerators were built, cosmic rays were the only source of particles with energy larger than a GeV.
The study of cosmic radiation remains, even today, fundamental for both subnuclear physics and astrophysics. We know rather well the energy spectrum of cosmic rays, which is shown in Fig. It extends up to EeV eV , 12 orders of magnitude on the energy scale and 32 orders of magnitude on the flux scale.
At these extreme energies the flux is very low, typically one particle per square kilometre per century. The Pierre Auger observatory in Argentina has an active surface area of km2 and is starting to explore the energy range above EeV. In this region, one may well discover phenomena beyond the Standard Model. The initial discoveries in particle physics, which we shall discuss in the next chapter, used the spectrum around a few GeV, where the flux is largest, tens of particles per square metre per second.
A proton or a nucleus penetrating the atmosphere eventually collides with a nucleus of the air. This strong interaction produces pions, less frequently K mesons and, even 1. The cosmic ray flux. The hadrons produced in the first collision generally have enough energy to produce other hadrons in a further collision, and so on.
This is because the particles of the shower are unstable. Therefore, the composition of the shower becomes richer and richer in muons while travelling through the atmosphere. The hadronic collisions produce not only charged pions but also p0. These latter decay quickly with the electromagnetic reaction p0!
The average distance between such events is the radiation length, which for air at n. In the first part of the shower, the number of electrons, positrons and photons increases, while their average energy diminishes.
When the average energy of the electrons decreases below the critical energy, the number of particles in the shower has reached its maximum and gradually decreases. In B. Rossi discovered that cosmic radiation has two components: From the above discussion we understand that the soft component is the electromagnetic one, the hard component is made up mostly of muons. There is actually a third component, which is extremely difficult to detect: Neutrinos have only weak interactions and can cross the whole Earth without being absorbed.
Sketch of an electromagnetic shower. These observations have led, in the past few years, to the discovery that neutrinos have non-zero masses. Accelerators Several types of accelerators have been developed. We shall discuss here only the synchrotron, the acceleration scheme that has made the most important contributions to subnuclear physics. Synchrotrons can be built to accelerate protons or electrons. Schematically, in a synchrotron, the particles travel in a pipe, in which high vacuum is established.
The orbit of a particle of momentum p in a uniform magnetic field B is a circumference of radius R. These three quantities are related by an equation that we shall often use see Problem 1. In them a radiofrequency electromagnetic field RF is tuned to give a push to the bunches of particles every time they go through. Actually, the beam does not continuously fill the circumference of the pipe, but is divided in bunches, in order to allow the synchronisation of their arrival with the phase of the RF.
In the structure we have briefly described, the particle orbit is unstable; such an accelerator cannot work. The following analogy can help. If you place a rigid stick vertically upwards on a horizontal support, it will fall; the equilibrium is unstable. However, if you place it on your hand and move your hand quickly to and fro, the stick will not fall. The proton energy was 7 GeV, designed to be enough to produce antiprotons.
The search for new physics has demanded that the energy frontier be moved towards higher and higher values. To build a higher-energy synchrotron one needs to increase the length of the ring or increase the magnetic field, or both. Preliminary notions 32 The next generation of proton synchrotrons was ready at the end of the s: Their radius is about 1 km. The synchrotrons of the next generation reached higher energies using field intensities of several tesla with superconducting magnets.
The high-energy experiments generally use the so-called secondary beams. The primary proton beam, once accelerated at the maximum energy, is extracted from the ring and driven onto a target. The strong interactions of the protons with the nuclei of the target produce all types of hadrons.
Beyond the target, a number of devices are used to select one type of particle, possibly within a certain energy range. In such a way, one can build beams of pions, K mesons, neutrons, antiprotons, muons and neutrinos. A typical experiment steers the secondary beam of interest into a secondary target where the interactions to be studied are produced. The target is followed by a set of detectors to measure the characteristics of these interactions. Storage rings The ultimate technique to reach higher-energy scales is that of storage rings, or colliders as they are also called.
The Tevatron beams. The squares represent the experimental halls. A collider consists of two accelerator structures with vacuum pipes, magnets and RF cavities, in which two beams of particles travel in opposite directions. They may be both protons, or protons and antiprotons, or electrons and positrons, or electrons and protons, or also nuclei and nuclei.
The two rings intercept each other at a few positions along the circumference.
The phases of the bunches circulating in the two rings are adjusted to make them meet at the intersections. Then, if the number of particles in the bunches is sufficient, collisions happen at every crossing. Notice that the same particles cross repeatedly a very large number of times. The first pp storage ring became operational at CERN in The protons are first accelerated up to 3. Finally they are transferred in bunches, alternately in the two storage rings. The filling process continues until the intensities reach the design values.
The machine regime is then stable and the experiments can collect data for several hours. The centre of mass energy is very important but it is useless if the interaction rate is too small.
The important parameter is the luminosity of the collider. We can think of the collision as taking place between two gas clouds, the bunches, that have densities much lower than that of condensed matter.
To overcome this problem it is necessary: The CERN machines in the s. The luminosity is proportional to the product of the numbers of particles, n1 and n2, in the two beams. Notice that in a proton—antiproton collider the number of antiprotons is smaller than that of protons, due to the energetic cost of the antiprotons. As particles and antiparticles have opposite charges and exactly the same mass, a single magnetic structure is sufficient to keep the two beams circulating in opposite directions.
The first example of such a structure ADA was conceived and built by B. Touschek at Frascati in Italy as an electron—positron accumulator. Before discussing ADA, we shall complete our review of the hadronic machines. In , C. Rubbia, C. McIntire and D. Cline Rubbia et al. The enterprise had limited costs, because the magnetic structure was left substantially as it was, while it was necessary to improve the vacuum substantially. It was also necessary to develop further the stochastic cooling techniques, already known from the ISR.
In at Fermilab, a proton—antiproton ring based on the same principles became operational. It has been built in the 27 km long tunnel that previously hosted LEP. The magnetic ring is made of superconducting magnets built with the most advanced technology to obtain the maximum possible magnetic field, 8 T.
We now see that this is much higher than that of the highest luminosity colliders. Calculate the 1. This is similar to the LHC luminosity. The proton—antiproton collisions are not simple processes because the two colliding particles are composite, not elementary, objects. Furthermore, these processes happen only in a very small fraction of the collisions. Electrons and positrons are, in contrast, elementary non-composite particles. When they collide they often annihilate; matter disappears in a state of pure energy.
Moreover, this state has well-defined quantum numbers, those of the photon. Touschek, fascinated by these characteristics, was able to put into practice the dream of generating collisions between matter and antimatter beams.
The next year ADA was working Fig. The development of a facility suitable for experimentation was an international effort, mainly by the groups led by F. Amman in Frascati, G. Budker in Novosibirsk and B. Richter in Stanford. Their contribution to particle physics was and still is enormous. Its length was 27 km. With LEP the practical energy limit of circular electron machines was reached.
The issue is the power radiated by the electrons due to the centripetal acceleration, which grows dramatically with increasing energy. The next generation electron—positron collider will have a linear structure; the necessary novel techniques are currently under development.
It is made up of two rings, one for electrons, or positrons, that are accelerated up to 30 GeV, and one for protons that reach GeV energy GeV in the first years. The scattering of the point-like electrons on the protons informs us about the deep internal structure of the latter. Preliminary notions 36 Fig. ADA at Frascati. We shall give here only a summary of the principal classes of detectors. The quantities that we can measure directly are the electric charge, the magnetic moment that we shall not discuss , the lifetime, the velocity, the momentum and the energy.
Let us review the principal detectors. We shall restrict ourselves to the plastic and organic liquid ones. Scintillation counters are made up with transparent plastic plates with a thickness of a centimetre or so and of the required area up to square metres.
The material is doped with molecules that emit light at the passage of an ionising particle. The light is guided by a light guide glued, on the side of the plate, to the photocathode of a photomultiplier. One typically obtains 10 photons per MeV of energy deposit.
The time resolution is very good and can reach 0. Two counters at a certain distance on the path of a particle are used to measure its time of flight between them and, knowing the distance, its velocity. A drawback of plastic and crystal scintillators is that their light attenuation length is not large.
Consequently, when assembled in large volumes, the light collection efficiency is poor. In the next few years, different groups Reynolds et al. These discoveries opened the possibility of building large scintillation detectors at affordable cost. The liquid scintillator technique has been, and is, of enormous importance, in particular for the study of neutrinos, including their discovery Section 2.
Nuclear emulsions Photographic emulsions are made of an emulsion sheet deposited on a transparent plastic or glass support. The emulsions contain grains of silver halides, the sensitive element.
Once exposed to light the emulsions are developed, with a chemical process that reduces to metallic silver only those grains that have absorbed photons. It became known as early as that ionising radiation produces similar 38 Preliminary notions effects.
Therefore, a photographic plate, once developed, shows as trails of silver grains the tracks of the charged particles that have gone through it. In practice, normal photographic emulsions are not suitable for scientific experiments because of their small thickness and low efficiency.
Powell and G. In Kodak developed the first emulsion sensitive to minimum ionising particles; with these, Lattes, Muirhead, Occhialini and Powell discovered the pion Chapter 2.
This is often a drawback. On the positive side, they have an extremely fine granularity, of the order of several micrometres. The coordinates of points along the track are measured with sub-micrometre precision. On the other hand, the extraction of the information from the emulsion is a slow and time-consuming process. With the advent of accelerators, bubble chambers and, later, time projection chambers replaced the emulsions as visualising devices.
But emulsions remain, even today, unsurpassed in spatial resolution and are still used when this is mandatory. Cherenkov detectors In P.
Cherenkov Cherenkov and S. Vavilov Vavilov discovered that gamma rays from radium induce luminous emission in solutions. The light was due to the Compton electrons produced by the gamma rays, as discovered by Cherenkov who experimentally elucidated all the characteristics of the phenomenon.
Frank and I. Another, visible, analogy is the wave produced by a duck moving on the surface of a pond.
The wave front is a triangle with the vertex at the duck, moving forward rigidly with it. The rays of Cherenkov light are directed normally to the V-shaped wave, as shown in Fig. The wave is the envelope of the elementary spherical waves emitted by the moving source at subsequent moments.
In Fig. The spectrum of the Cherenkov light is continuous with important fractions in the visible and in the ultraviolet. Consider the surface limiting the material in which the particle travels.
We can detect the ring by covering the surface with photomultipliers PMs. If the particle travels, say, towards that surface, the photomultipliers see a ring gradually shrinking in time. From this information, we determine the trajectory of the particle. The space resolution is given by the integration time of the PMs, 30 cm for a typical value of 1 ns.
From the radius of the ring, we measure the angle at the vertex of the cone, hence the particle speed. The thickness of the ring, if greater than the experimental resolution, gives information on the nature of the particle.
For example a muon travels straight, an electron scatters much more, giving a thicker ring. It contains 50 t of pure water. The PMs, being inspected by the people on the boat in the picture, cover the entire surface.
The diameter of each PM is half a metre. The detector, in a laboratory under the Japanese Alps, is dedicated to the search for astrophysical neutrinos and proton decay. Preliminary notions 40 Fig. Inside Super-Kamiokande, being filled with water. People on the boat are checking the photomultipliers. The dots correspond to the PMs that gave a signal; the colour, in the original, codes the arrival time.
The Cherenkov counters are much simpler devices of much smaller dimensions. The light is collected by one PM, or by a few, possibly using mirrors. In more sophisticated versions one measures the angle of the cone, hence the speed.
Threshold energy for an electron: Threshold energy for a m: A Cherenkov ring in Super-Kamiokande. Courtesy of Super Kamiokande Collaboration 2. The electron is above threshold. Cloud chambers In C. Wilson, fascinated by atmospheric optical phenomena, such as the glories and the coronae he had admired from the observatory that existed on top of Ben Nevis in Scotland, started laboratory research on cloud formation.
He built a container with a glass window, filled with air and saturated water vapour. The volume could be suddenly expanded, bringing the vapour to a supersaturated state. Very soon, Wilson understood that condensation nuclei other than dust particles were present in the air. Maybe, he thought, they are electrically charged atoms or ions. The hypothesis 42 Preliminary notions was confirmed by irradiating the volume with the X-rays that had recently been discovered.
By the end of , Wilson had developed his device to the point of observing the first tracks of alpha and beta particles Wilson Actually, an ionising particle crossing the chamber leaves a trail of ions, which seeds many droplets when the chamber is expanded. By flashing light and taking a picture one can record the track. By the Wilson chamber had been perfected Wilson If the chamber is immersed in a magnetic field B, the tracks are curved. Measuring the curvature radius R, one determines the momentum p by Eq.
The expansion of the Wilson chamber can be triggered. If we want, for example, to observe charged particles coming from above and crossing the chamber, we put one Geiger counter see later above and another below the chamber. We send the two electronic signals to a coincidence circuit, which commands the expansion.
Blackett and Occhialini discovered the positron— electron pairs in cosmic radiation with this method in The coincidence circuit had been invented by B. Rossi in Rossi Bubble chambers The bubble chamber was invented by D. Glaser in Glaser , but it became a scientific instrument only with L. Alvarez see Nobel lecture Alvarez see Example 1. The working principle is similar to that of the cloud chamber, with the difference that the fluid is a liquid which becomes superheated during expansion.
Along the tracks, a trail of gas bubbles is generated. Differently from the cloud chamber, the bubble chamber must be expanded before the arrival of the particle to be detected. Therefore, the bubble chambers cannot be used to detect random events such as cosmic rays, but are a perfect instrument at an accelerator facility, where the arrival time of the beam is known exactly in advance. The bubble chamber acts at the same time both as target and as detector. From this point of view, the advantage over the cloud chamber is the higher density of liquids compared with gases, which makes the interaction probability larger.
Different liquids can be used, depending on the type of experiment: Historically, bubble chambers have been exposed to all available beams protons, antiprotons, pions, K mesons, muons, photons and neutrinos. In a bubble chamber, all the charged tracks are visible. All bubble chambers are in a magnetic field to provide the measurement of the momenta. Bubble chambers made enormous contributions to particle physics: The development of bubble chamber technology and of the related analysis tools took place at Berkeley in the s in the group led by L.
The principal device was a large hydrogen bubble chamber long, wide and deep 1. The chamber could be filled with liquid hydrogen if the targets of the interaction were to be protons or with deuterium if they were to be neutrons. The uniform magnetic field had the intensity of 1. In the example shown in Fig. A picture of the Berkeley 10 inch bubble chamber. From Alavarez 44 Preliminary notions The small curls one sees coming out of the tracks are due to atomic electrons that during the ionisation process received an energy high enough to produce a visible track.
Moving in the liquid they gradually lose energy and the radius of their orbit decreases accordingly. The second beam track, counting from below, disappears soon after entering. A pion has interacted with a proton with all neutrals in the final state. Both are clearly coming from the primary vertex. For every expansion, three pictures are taken with three cameras in different positions, obtaining a stereoscopic view of the events.
The quantitative analysis implies the following steps: For each track, one calculates the energy, assuming in turn the different possible masses proton or pion for example.
The procedure then constrains the measured quantities, imposing energy and momentum conservation at each vertex. The problem is overdetermined.
In this example, one finds that reactions 1. Notice that the known quantities are sufficient to allow the reconstruction of the event even in the presence of one but not more neutral unseen particles.
The resolution in the measurement of the coordinates is typically one-tenth of the bubble radius. The latter ranges from about one millimetre in the heavy liquid chambers, to a tenth of a millimetre in the hydrogen chambers, to about 10 lm in 1. Geometry of the track of a charged particle in a magnetic field. Knowing the field B, Eq. How can we proceed if we measure only three points, as in Fig. The measurements give directly the sagitta s.
Ionisation detectors An ionisation detector contains two electrodes and a fluid, liquid or gas, in between. The ion pairs produced by the passage of a charged particle drift toward the electrodes in the electric field generated by the voltage applied to the electrodes.
Electrons drift faster than ions and the intensity of their current is consequently larger. For low electric field intensity, the electron current intensity is proportional to the primary ionisation. If we know the mass of the particle, we can calculate its momentum; if we do not, we can measure the momentum independently and determine the mass.
At higher field intensities, the process of secondary ionisation sets in, giving the possibility of amplifying the initial charge.
Preliminary notions 46 The Geiger counter The simplest ionisation counter is shown schematically in Fig. It was invented by H. Geiger in at Manchester and later modified by W. The counter consists of a metal tube, usually earthed, bearing a central, insulated, metallic wire, with a diameter of the order of lm.
A high potential, of the order of V, is applied to the wire. The tube is filled with a gas mixture, typically argon and alcohol to quench the discharge. The electrons produced by the passage of a charged particle drift towards the wire where they enter a very intense field.
They accelerate and produce secondary ionisation. An avalanche process starts that triggers the discharge of the capacitance. The time resolution is limited to about a microsecond by the variation from discharge to discharge of the temporal evolution of the avalanche.
Their scheme is shown in Fig. The Geiger counter. The anode plane is enclosed between two cathode planes, which are parallel and at the same distance of several millimetres, as shown in the figure. The MWPC are employed in experiments on secondary beams at an accelerator, in which the particles to be detected leave the target within a limited solid angle around the forward direction.
The chambers are positioned perpendicularly to the average direction. This technique allows large areas several square metres to be covered with detectors whose data can be transferred directly to a computer, differently from bubble chambers. The figure shows the inclined trajectory of a particle. The electric field shape divides the volume of the chamber into cells, one for each sensitive wire.
The ionisation electrons produced in the track segment belonging to a given cell will drift towards the wire of that cell, following the field lines. In the neighbourhood of the anode wire, the charge is amplified, in the proportional regime. Typical amplification factors are of the order of Every wire is serviced by a charge amplifier for its read-out. Typically, thousands of electronic channels are necessary. The coordinate perpendicular to the wires, x in the figure, is determined by the position of the wire or wires that gives a signal above threshold.
The coordinate z, normal to the plane, is known by construction. To measure the third coordinate y at least a second chamber is needed with wires in the x direction.
The spatial resolution is the variance of a uniform distribution with the width of the spacing. One coordinate, as in the MWPC, is given by the position of the wire giving the signal; the second, perpendicular to the wire in the plane of the chamber, is obtained by measuring the time taken by the electron to reach it drift time. The chambers are positioned perpendicularly to the average direction of the tracks. The distance between one of the cathodes and the anode is typically of several centimetres.
Walenta in Walenta et al. The chamber consists of a number of such cells along the x-axis. In the uniform field, and with a correct choice of the gas mixture, one obtains a constant drift velocity. Preliminary notions 48 x cathode cle drift region cathode r ti pa anodic wire drift region z field wire Fig.
A drift chamber geometry. A dipole magnet deflects each particle, by an angle inversely proportional to its momentum, toward one or the other side depending on the sign of its charge. The poles of the magnet are located above and below the plane of the drawing, at the position of the rectangle. The figure shows two tracks of opposite sign. One measures the track directions before and after the magnet as accurately as possible using multi-wire and drift chambers.
The angle between the directions and the known value of the field gives the momenta. The geometry is shown on the right of the figure. To simplify, we assume B to be uniform in the magnet, of length L, and zero outside it.
We also consider only small deflection angles. Consider for 1. This shift can be measured with good precision with a resolution of lm. The dependence on momentum of the deflection angle makes a dipole magnet a dispersive element similar to a prism in the case of light. Time projection chambers TPC have sensitive volumes of cubic metres and give three-dimensional images of the ionising tracks. Their development was due to D.
Nygren at Berkeley Nygren and independently to W. Allison et al. Two coordinates are measured in the same way as in a drift chamber. The third coordinate, the one along the wire, can be determined by measuring the charge at both ends. Cylindrical TPCs of different design are practically always used in collider experiments, in which the tracks leave the interaction point in all the directions.
Silicon microstrip detectors Microstrip detectors were developed in the s. They are based on a silicon wafer, a hundred micrometres or so thick and with surfaces of several square centimetres. A ladder of many n-p diodes is built on the surface of the wafer in the shape of parallel strips with a pitch of tens of micrometres.
The strips are the equivalent of the anode wires in an MWPC and are read-out by charge amplifiers. The device is reverse biased and is fully depleted.
A charged particle produces electron—hole pairs that drift and are collected at the strips. The spatial resolution is very good, of the order of 10 lm. The silicon detectors played an essential role in the study of charmed and beauty particles.
These have lifetimes of the order of a picosecond and are produced with typical energies of a few GeV and decay within millimetres from the production point. To separate the production and decay vertices, devices are built made up of a number, typically four or five, of microstrip planes.