Chapter 43 Elementary Particles. High-Energy Particles and Accelerators Beginnings of Elementary...

Chapter 43Elementary Particles

• High-Energy Particles and Accelerators

• Beginnings of Elementary Particle Physics – Particle Exchange

• Particles and Antiparticles

• Particle Interactions and Conservation Laws

• Neutrinos – Recent Results

• Particle Classification

Units of Chapter 43

• Particle Stability and Resonances

• Strange Particles? Charm? Toward a New Model

• Quarks

• The “Standard Model”: Quantum Chromodynamics (QCD) and the Electroweak Theory

• Grand Unified Theories

• Strings and Supersymmetry

Units of Chapter 43

If an incoming particle in a nuclear reaction has enough energy, new particles can be produced.

This effect was first observed in cosmic rays; later particle accelerators were built to provide the necessary energy.

43.1 High-Energy Particles and Accelerators

As the momentum of a particle increases, its wavelength decreases, providing details of smaller and smaller structures:

In addition, with additional kinetic energy more massive particles can be produced.

43.1 High Energy Particles and Accelerators

One early particle accelerator was the cyclotron. Charged particles are maintained in near-circular paths by magnets, while an electric field accelerates them repeatedly. The voltage is alternated so that the particles are accelerated each time they traverse the gap.


Larger accelerators are a type called synchrotrons. Here, the magnetic field is increased as the particles accelerate, so that the radius of the path stays constant. This allows the construction of a narrow circular tunnel to house a ring of magnets.


Synchrotrons can be very large, up to several miles in diameter. These pictures are of Fermilab, a synchrotron outside Chicago, Illinois.


Accelerating particles radiate; this causes them to lose energy. This is called synchrotron radiation for particles in a circular path. For protons this is usually not a problem, but the much lighter electrons can lose substantial amounts. One solution is to construct a linear accelerator for electrons; the largest is about 3 km long.



The maximum possible energy is obtained from an accelerator when two counter-rotating beams of particles collide head-on. Fermilab is able to obtain 1.8 TeV in proton–antiproton collisions; a new accelerator called the Large Hadron Collider (LHC) will reach energies of 14 TeV.

The electromagnetic force acts over a distance – direct contact is not necessary. How does that work?

Because of wave–particle duality, we can regard the electromagnetic force between charged particles as due to:

1. an electromagnetic field, or

2. an exchange of photons.

43.2 Beginnings of Elementary Particle Physics – Particle Exchange

This is a crude analogy for how particle exchange would work to transfer energy and momentum. The force can be either attractive or repulsive.


Physicists visualize interactions using Feynman diagrams, which are a kind of x-t graph.

Here is a Feynman diagram for photon exchange by electrons:


The photon is emitted by one electron and absorbed by the other; it is never visible and is called a virtual photon. The photon carries the electromagnetic force.

Originally, the strong force was thought to be carried by mesons. The mesons have nonzero mass, which is what limits the range of the force, as conservation of energy can only be violated for a short time.


The mass of the meson can be calculated, assuming the range, d, is limited by the uncertainty principle:

For d = 1.5 x 10-15 m, this gives 130 MeV.


This meson was soon discovered, and is called the pi meson, or pion, with the symbol π.

Pions are created in interactions in particle accelerators. Here are two examples:


The weak nuclear force is also carried by particles; they are called the W+, W-, and Z0. They have been directly observed in interactions.

A carrier for the gravitational force, called the graviton, has been proposed, but there is as yet no theory that will accommodate it.



This picture shows the reconstruction of the creation of a Z particle, and the detector that discovered it.

This table details the four known forces, their relative strengths for two protons in a nucleus, and their field particles.


The positron is the same as the electron, except for having the opposite charge (and lepton number). We call the positron the antiparticle of the electron.

Every type of particle has its own antiparticle, with the same mass and most with the opposite quantum number.

A few particles, such as the photon and the π0, are their own antiparticles, as all the relevant quantum numbers are zero for them.

43.3 Particles and Antiparticles

This drawing, from a bubble chamber photograph, is of an interaction between an incoming antiproton and a proton (not seen) that results in the creation of several different particles and antiparticles.

43.3 Particles and Antiparticles

In the study of particle interactions, it was found that certain interactions did not occur, even though they conserve energy and charge, such as:

A new conservation law was proposed: the conservation of baryon number. Baryon number is a generalization of nucleon number to include more exotic particles.

43.4 Particle Interactions and Conservation Laws

Particles such as the proton and neutron have baryon number B = +1; antiprotons, antineutrons, and the like have B = -1; all other particles (electrons, photons, etc.) have B = 0.

There are three types of leptons – the electron, the muon (about 200 times more massive), and the tau (about 3000 electron masses). Each type of lepton is conserved separately.


This accounts for the following decays:

Decays that have an unequal mix of e-type and μ-type leptons are not allowed.


Conceptual Example 43-5: Lepton number in muon decay.

Which of the following decay schemes is possible for muon decay?

(a)

(b)

(c)

All of these particles have Lτ = 0.


Example 43-6: Energy and momentum are conserved.

In addition to the “number” conservation laws which help explain the decay schemes of particles, we can also apply the laws of conservation of energy and momentum. The decay of a Σ+ particle at rest with a mass of 1189 MeV/c2 commonly yields a proton (mass = 938 MeV/c2) and a neutral pion, (mass = 135 MeV/c2):

What are the kinetic energies of the decay products, assuming the Σ+ parent particle was at rest?


Neutrinos are currently a subject of active research. Evidence has shown that a neutrino of one type may change into a neutrino of another type; this is called flavor oscillation.

This suggests that the individual lepton numbers are sometimes not strictly conserved, although there is no evidence that the total lepton number is not.

In addition, these oscillations cannot take place unless at least one neutrino type has a nonzero mass.

43.5 Neutrinos – Recent Results

As work continued, more and more particles of all kinds were discovered. They have now been classified into different categories.

• Gauge bosons are the particles that mediate the forces.

• Leptons interact weakly and (if charged) electromagnetically, but not strongly.

• Hadrons interact strongly; there are two types of hadrons, baryons (B = 1) and mesons (B = 0).

The table of particle properties on the next slide gives some indication of the complexity of the known particles.

43.6 Particle Classification

Example 43-7: Baryon decay.

Show that the decay modes of the Σ+ baryon given in Table 43–2 do not violate the conservation laws we have studied up to now: energy, charge, baryon number, lepton numbers.


Almost all of the particles that have been discovered are unstable. If they decay weakly, their lifetimes are around 10-13 s; if electromagnetically, around 10-16 s; and if strongly, around 10-23 s.

Strongly decaying particles do not travel far enough to be observed; their existence is inferred from their decay products.

43.7 Particle Stability and Resonances

The lifetime of strongly decaying particles is calculated from the variation in their effective mass using the uncertainty principle. These particles are often called resonances.

43.7 Particle Stability and Resonances

When the K, Λ, and Σ particles were first discovered in the early 1950s, there were mysteries associated with them:

• They are always produced in pairs.

• They are created in a strong interaction, decay to strongly interacting particles, but have lifetimes characteristic of the weak interaction.

To explain this, a new quantum number, called strangeness, S, was introduced.

43.8 Strange Particles? Charm? Toward a New Model

Particles such as the K, Λ, and Σ have S = 1 (and their antiparticles have S = -1); other particles have S = 0.

The strangeness number is conserved in strong interactions but not in weak ones; therefore, these particles are produced in particle–antiparticle pairs, and decay weakly.

More recently, another new quantum number called charm was discovered to behave in the same way.


Conceptual Example 43-8: Guess the missing particle.

Using the conservation laws for particle interactions, determine the possibilities for the missing particle in the reaction

in addition to K0 + Λ0 mentioned above.


Due to the regularities seen in the particle tables, as well as electron scattering results that showed internal structure in the proton and neutron, a theory of quarks was developed.

There are six different “flavors” of quarks; each has baryon number B = ⅓.

Hadrons are made of three quarks; mesons are a quark–antiquark pair.

43.9 Quarks

Here are the quark compositions for some baryons and mesons:

43.9 Quarks

This table gives the properties of the six known quarks.

43.9 Quarks

This is a list of some of the hadrons that have been discovered that contain c, t, or b quarks.

43.9 Quarks

The particles that we now consider to be truly elementary – having no internal structure – are the quarks, the gauge bosons, and the leptons. The quarks and leptons are arranged in three “generations”; each has the same pattern of electric charge, but the masses increase from generation to generation.

43.9 Quarks

43.9 Quarks

Conceptual Example 43-9: Quark combinations.

Find the baryon number, charge, and strangeness for the following quark combinations, and identify the hadron particle that is made up of these quark combinations: (a) udd, (b) uū, (c) uss, (d) sdd, and (e) bū.

Soon after the quark theory was proposed, it was suggested that quarks have another property, called color, or color charge.

Unlike other quantum numbers, color takes on three values. Real particles must be colorless; this explains why only 3-quark and quark–antiquark configurations are seen. Color also ensures that the exclusion principle is still valid.

43.10 The “Standard Model”: Quantum Chromodynamics (QCD) and the

Electroweak Theory

Each quark carries a color charge, and the force between them is called the color force – hence the name quantum chromodynamics.

The particles that transmit the color force are called gluons; there are eight different ones, with all possible color–anticolor combinations.


Electroweak Theory

The color force becomes much larger as quarks separate; quarks are therefore never seen as individual particles, as the energy needed to separate them is less than the energy needed to create a new quark–antiquark pair.

Conversely, when the quarks are very close together, the force is very small.


Electroweak Theory

These Feynman diagrams show a quark–quark interaction mediated by a gluon; a baryon–baryon interaction mediated by a meson; and the baryon–baryon interaction as mediated on a quark level by gluons.


Electroweak Theory

Figure 43-16 goes here.

A Grand Unified Theory (GUT) would unite the strong, electromagnetic, and weak forces into one. There would be (rare) transitions that would transform quarks into leptons and vice versa.

This unification would occur at extremely high energies; at lower energies the forces would “freeze out” into the ones we are familiar with.

This is called “symmetry breaking.”

43.11 Grand Unified Theories


Conceptual Example 43-12: Symmetry.

The table shown has four identical place settings. Four people sit down to eat. Describe the symmetry of this table and what happens to it when someone starts the meal.

GUTs predict that the proton will eventually decay; in fact, the simplest GUT predicts a lifetime for the proton that is shorter than the measured limit, so a more complex GUT must be the correct theory.


Finally, there are theories that attempt to include the gravitational force as well.

String theory models the fundamental particles as different resonances on tiny loops of “string”.

Supersymmetry postulates a fermion partner for each boson, and vice versa.

Neither of these theories has any experimental evidence either favoring or disfavoring it at the moment.

43.12 Strings and Supersymmetry

• Particle accelerators accelerate particles to a very high energy, to probe the detailed structure of matter and to produce new massive particles.

• Every particle has an antiparticle, with the same mass and opposite charge (and some other quantum numbers).

• Other quantum numbers: baryon number, lepton number, strangeness, charm, topness, bottomness

• Strong force is mediated by gluons.

Summary of Chapter 43

• Fundamental force carriers are called gauge bosons.

• Leptons interact weakly and electromagnetically.

• Hadrons are made of quarks, and interact strongly.

• Most particles decay quickly, weakly, electromagnetically, or strongly.

• There are six quarks and six leptons.


• The quarks also carry color charge.

• Quantum chromodynamics is the theory of the strong interaction.

• Electroweak theory unites the electromagnetic and weak forces.

• Grand unified theories attempt to unite all three forces.


Chapter 43 Elementary Particles. High-Energy Particles and Accelerators Beginnings of Elementary...

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