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Lecture PowerPoint

Chapter 32

Physics: Principles with

Applications, 6th edition

Giancoli

Chapter 32

Elementary Particles

Units of Chapter 32

• 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 32

• Particle Stability and Resonances

• Strange Particles? Charm? Maybe a New

Model Is Needed!

• Quarks

• The “Standard Model”: Quantum

Chromodynamics (QCD) and the Electroweak

Theory

• Grand Unified Theories

• Strings and Supersymmetry

32.1 High Energy Particles and

Accelerators

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.


Accelerators

As the momentum of a particle increases, its

wavelength decreases, providing details of

smaller and smaller structures:

(32-1)

In addition, with additional kinetic energy

more massive particles can be produced.


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.


Accelerators

The frequency of the applied voltage must

equal that of the circulating particles, and is

given by:

(32-2)

This is called the cyclotron frequency.


Accelerators

Larger accelerators are of 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.


Accelerators

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.

32.2 Beginnings of Elementary Particle

Physics – Particle Exchange

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



This is a crude analogy

for how particle

exchange would work to

transfer energy and

momentum. The force

can either be 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:

(32-3)

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, symbol π.

Pions are created in interactions in particle

accelerators; here are two examples:

(32-4)



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 table details the four known forces, their

relative strength for two protons in a nucleus,

and their field particle.

32.3 Particles and Antiparticles

The positron is the same as the electron, except

for having 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 but most quantum numbers

being opposite.

A few particles, such as the photon and the π0,

are their own antiparticles, as all the relevant

quantum numbers are zero for them.


This is a drawing of an

interaction between an

incoming antiproton and a

proton (not seen) that

results in the creation of

several different particles

and antiparticles.

32.4 Particle Interactions and

Conservation Laws

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.


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.


Conservation Laws

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.


Conservation Laws

This accounts for the following decays:

Decays that have an unequal mix of e-type

and μ-type leptons are not allowed.

32.5 Neutrinos – Recent Results

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.

32.5 Neutrinos – Recent Results

This suggests that the individual lepton

numbers are sometimes not strictly conserved,

although there is no evidence that the total

lepton number is no.

In addition, these oscillations cannot take place

unless at least one neutrino type has a nonzero

mass.

32.6 Particle Classification

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).

32.7 Particle Stability and Resonances

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.


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.

32.8 Strange Particles? Charm? Maybe a

New Model Is Needed!

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.



Particles such as the K, Λ, and Σ have S = 1

(and their antiparticles 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.

32.9 Quarks

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.

32.9 Quarks

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.

32.9 Quarks

Here are the quark compositions for some

baryons and mesons:

32.9 Quarks

This table gives the properties of the six known

quarks.

32.9 Quarks

This is a list of some of the hadrons that have

been discovered that contain c, t, or b quarks.

32.9 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.

32.10 The “Standard Model”: Quantum

Chromodynamics (QCD) and the

Electroweak Theory

Soon after the quark theory was proposed, it

was suggested that quarks have another

property, called color, or color charge.



Electroweak Theory

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.



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 to separate

them is less than the energy 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 the

quark level by gluons.



Electroweak Theory

Beta decay is the result of a

weak interaction, and is

mediated by a W± particle.

Here is a Feynman diagram

of beta decay:

32.11 Grand Unified Theories

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.”

32.11 Grand Unified Theories

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.

32.12 Strings and Supersymmetry

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.

Summary of Chapter 32

• Particle accelerators accelerate particles to

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


• Fundamental force carriers are called gauge

bosons

• Leptons interact weakly and

electromagnetically

• Hadrons are made of quarks, and interact

strongly

• Most particles decay quickly, either 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

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