Chapter 46

Particle Physics and Cosmology

Atoms as Elementary Particles

Atoms

From the Greek for “indivisible”

Were once thought to be the elementary particles

Atom constituents

Proton, neutron, and electron

After 1932 these were viewed as elementary

All matter was made up of these particles

Introduction

Discovery of New Particles

New particles

Beginning in the 1940s, many “new” particles were discovered in experiments involving high-energy collisions.

Characteristically unstable with short lifetimes

Over 300 have been catalogued

A pattern was needed to understand all these new particles.

Introduction

Elementary Particles – Quarks

Physicists recognize that most particles are made up of quarks.

Exceptions include photons, electrons and a few others

The quark model has reduced the array of particles to a manageable few.

The quark model has successfully predicted new quark combinations that were subsequently found in many experiments.

Section 45.7

Fundamental Forces

All particles in nature are subject to four fundamental forces:

Nuclear force

Electromagnetic force

Weak force

Gravitational force This list is in order of decreasing strength.

Section 46.1

Nuclear Force

Attractive force between nucleons

Strongest of all the fundamental forces

Very short-ranged

Less than 10-15 m

Negligible for separations greater than this

Section 46.1

Electromagnetic Force

Is responsible for the binding of atoms and molecules

About 10-2 times the strength of the nuclear force

A long-range force that decreases in strength as the inverse square of the separation between interacting particles.

Section 46.1

Weak Force

Is responsible for instability in certain nuclei

Is responsible for decay processes

Its strength is about 10-5 times that of the strong force.

Section 46.1

Gravitational Force

A familiar force that holds the planets, stars and galaxies together

Its effect on elementary particles is negligible.

A long-range force

It is about 10-39 times the strength of the strong force.

Weakest of the four fundamental forces

Section 46.1

Explanation of Forces

Forces between particles are often described in terms of the actions of field particles or exchange particles.

Field particles are also called gauge bosons.

The interacting particles continually emit and absorb field particles.

The emission of a field particle by one particle and its absorption by another manifests itself as a force between the two interacting particles.

The force is mediated, or carried, by the field particles.

Section 46.1

Forces and Mediating Particles

Section 46.1

Paul Adrien Maurice Dirac

1902 – 1984

British physicist

Understanding of antimatter

Unification of quantum mechanics and relativity

Contributions of quantum physics and cosmology

Nobel Prize in 1933

Section 46.2

Dirac’s Description of the Electron

Dirac developed a relativistic quantum mechanical description of the electron .

It successfully explained the origin of the electron’s spin and its magnetic moment.

The solutions to the wave equation required negative energy states.

Dirac postulated that all negative energy states were filled.

The electrons occupying these states are collectively called the Dirac sea.

Electrons in the Dirac sea are not directly observable because the exclusion principle does not let them react to external forces.

Section 46.2

Dirac’s Explanation

An interaction may cause the electron to be excited to a positive energy.

The minimum energy required is 2 me c2.

This would leave behind a hole in the Dirac sea.

The hole can react to external forces and is observable.

The hole reacts in a way similar to the electron, except that it has a positive charge.

The hole is the antiparticle of the electron.

The electron’s antiparticle is now called a positron.

Section 46.2

Antiparticles

For practically every known particle, there is an antiparticle.

From Dirac’s version of quantum mechanics that incorporated special relativity.

Some particles are their own antiparticles. Photon and o

An antiparticle of a charged particle has the same mass as the particle, but the opposite charge.

The positron (electron’s antiparticle) was discovered by Anderson in 1932.

Since then, it has been observed in numerous experiments.

Antiprotons and antineutrons have also been discovered.

Section 46.2

Pair Production

A common source of positrons is pair production.

A gamma-ray photon with sufficient energy interacts with a nucleus and an electron-positron pair is created from the photon.

The photon must have a minimum energy equal to 2mec2 to create the pair.

Section 46.2

Pair Production, cont.

A photograph of pair production produced by 300 MeV gamma rays striking a lead sheet.

The minimum energy to create the pair is 1.02 MeV.

The excess energy appears as kinetic energy of the two particles.

Section 46.2

Annihilation

The reverse of pair production can also occur.

Under the proper conditions, an electron and a positron can annihilate each other to produce two gamma ray photons.

e- + e+

Section 46.2

Hideki Yukawa

1907 – 1981

Japanese physicist

Nobel Prize in 1949 for predicting the existence of mesons

Developed the first theory to explain the nature of the nuclear force

Section 46.3

Mesons

Developed from a theory to explain the nuclear force

Yukawa used the idea of forces being mediated by particles to explain the nuclear force.

A new particle was introduced whose exchange between nucleons causes the nuclear force.

It was called a meson.

Section 46.3

Mesons, cont.

The proposed particle would have a mass about 200 times that of the electron.

Efforts to establish the existence of the particle were done by studying cosmic rays in the 1930s.

Actually discovered multiple particles

pi meson (pion)

muon Found first, but determined to not be a meson

Section 46.3

Pion

There are three varieties of pions.

Correspond to three charge states + and -

Each has mass of 139.6 MeV/c2

Antiparticles

o

Mass of 135.0 MeV/c2

Very unstable particles For example, the - decays into a muon and an antineutrino with a mean lifetime of

2.6 x 10-8 s

Section 46.3

Muons

Two muons exist.

µ- and its antiparticle µ+

The muon is unstable.

It has a mean lifetime of 2.2 µs.

It decays into an electron, a neutrino, and an antineutrino.

Section 46.3

Richard Feynman

1918 – 1988

American physicist

Developed quantum electrodynamics

The theory of interaction of light and matter on a relativistic and quantum basis.

Shared the Nobel Prize in 1965

Worked on the Manhattan Project

Worked on Challenger investigation and demonstrated the effects of cold temperatures on the rubber O-rings used

Section 46.3

Feynman Diagrams

A graphical representation of the interaction between two particles.

Feynman diagrams are named for Richard Feynman who developed them.

A Feynman diagram is a qualitative graph of time on the vertical axis and space on the horizontal axis.

Actual values of time and space are not important.

The overall appearance of the graph provides a pictorial representation of the process.

Section 46.3

Feynman Diagram – Two Electrons

The photon is the field particle that mediates the electromagnetic force between the electrons.

The photon transfers energy and momentum from one electron to the other.

The photon is called a virtual photon.

It can never be detected directly because it is absorbed by the second electron very shortly after being emitted by the first electron.

Section 46.3

The Virtual Photon

The existence of the virtual photon seems to violate the law of conservation of energy.

But, due to the uncertainty principle and its very short lifetime, the photon’s excess energy is less than the uncertainty in its energy.

The virtual photon can exist for short time intervals, such that ∆E / 2 ∆t.

Within the constraints of the uncertainty principle, the energy of the system is conserved.

Section 46.3

Feynman Diagram – Proton and Neutron (Yukawa’s Model)

The exchange is via the nuclear force.

The existence of the pion is allowed in spite of conservation of energy if this energy is surrendered in a short enough time.

Analysis predicts the rest energy of the pion to be 100 MeV / c2.

This is in close agreement with experimental results.

Section 46.3

Nucleon Interaction – More About Yukawa’s Model

The time interval required for the pion to transfer from one nucleon to the other is

The distance the pion could travel is c∆t.

Using these pieces of information, the rest energy of the pion is about 100 MeV.

Section 46.3

Nucleon Interaction, final

This concept says that a system of two nucleons can change into two nucleons plus a pion as long as it returns to its original state in a very short time interval.

It is often said that the nucleon undergoes fluctuations as it emits and absorbs field particles.

These fluctuations are a consequence of quantum mechanics and special relativity.

Section 46.3

Feynman Diagram – Weak Interaction

An electron and a neutrino are interacting via the weak force.

The Z0 is the mediating particle.

The weak force can also be mediated by the W.

The W and Z0 were discovered in 1983 at CERN.

Section 46.3

Nuclear Force and Strong Force

Historically, the nuclear force was called the strong force.

Now the strong force is reserved for the force between quarks.

Or between particles made from quarks

The nuclear force is the force between nucleons.

It is a secondary result of the strong force.

Sometimes called residual strong force

Section 46.3

Classification of Particles

Two broad categories for particles other than field particles

Classified by interactions

Hadrons – interact through strong force

Leptons – interact through weak force

Section 46.4

Hadrons

Interact through the strong force

Two subclasses distinguished by masses and spins

Mesons Integer spins (0 or 1)

Decay finally into electrons, positrons, neutrinos and photons

Baryons Masses equal to or greater than a proton

Half integer spin values (1/2 or 3/2)

Decay into end products that include a proton (except for the proton)

Not elementary, but composed of quarks

Section 46.4

Leptons

Do not interact through strong force

All have spin of ½

Leptons appear truly elementary

No substructure

Point-like particles

Scientists currently believe only six leptons exist, along with their antiparticles.

Electron and electron neutrino

Muon and its neutrino

Tau and its neutrino

Section 46.4

Conservation Laws

A number of conservation laws are important in the study of elementary particles.

Already have seen conservation of

Energy

Linear momentum

Angular momentum

Electric charge

Two additional laws are

Conservation of Baryon Number

Conservation of Lepton Number

Section 46.5

Conservation of Baryon Number

Whenever a baryon is created in a reaction or a decay, an antibaryon is also created.

B is the baryon number.

B = +1 for baryons

B = -1 for antibaryons

B = 0 for all other particles

Conservation of Baryon Number states whenever a nuclear reaction or decay occurs, the sum of the baryon numbers before the process must equal the sum of baryon numbers after the process.

Section 46.5

Conservation of Baryon Number and Proton Stability

There is a debate over whether the proton decays or not.

If baryon number is absolutely conserved, the proton cannot decay.

Some recent theories predict the proton is unstable and so baryon number would not be absolutely conserved.

For now, we can say that the proton has a half-life of at least 1033 years.

Section 46.5

Conservation of Baryon Number, Example

Is baryon number conserved in the following reaction?

Baryon numbers: Before: 1 + 1 = 2 After: 1 + 1 + 1 + (-1) = 2

Baryon number is conserved

The reaction can occur as long as energy is conserved.

Section 46.5

Conservation of Lepton Number

There are three conservation laws, one for each variety of lepton.

The law of conservation of electron lepton number states whenever a nuclear reaction or decay occurs, the sum of electron lepton numbers before the process must equal the sum of the electron lepton number after the process.

Assigning electron lepton numbers:

Le = 1 for the electron and the electron neutrino

Le = -1 for the positron and the electron antineutrino

Le = 0 for all other particles

Section 46.5

Conservation of Lepton Number, cont.

When a process involves muons, muon lepton number must be conserved.

When a process involves tau particles, tau lepton numbers must be conserved.

Muon and tau lepton numbers are assigned similarly to electron lepton numbers.

Section 46.5

Conservation of Lepton Number, Example

Is lepton number conserved in the following reaction?

Check electron lepton numbers: Before: Le

= 0 After: Le = 1 + (-1) + 0 = 0 Electron lepton number is conserved

Check muon lepton numbers: Before: Lµ

= 1 After: Lµ = 0 + 0 + 1 = 1 Muon lepton number is conserved

Both lepton numbers are conserved and on this basis the decay is possible.

Section 46.5

Strange Particles

Some particles discovered in the 1950s were found to exhibit unusual properties in their production and decay and were given the name strange particles.

Peculiar features include:

Always produced in pairs

Although produced by the strong interaction, they do not decay into particles that interact via the strong interaction, but instead into particles that interact via weak interactions. They decay much more slowly than particles decaying via strong interactions.

Section 46.6

Strangeness

To explain these unusual properties, a new quantum number S, called strangeness, was introduced.

A new law, the law of conservation of strangeness was also needed.

It states in a nuclear reaction or decay that occurs via the strong force, strangeness is conserved.

That is, the sum of strangeness numbers before a reaction or a decay must equal the sum of the strangeness numbers after the process.

In processes that occur via the weak interactions, strangeness may not be conserved. Strong and electromagnetic interactions obey the law of conservation of

strangeness.

Section 46.6

Bubble Chamber Example of Strange Particles

The dashed lines represent neutral particles

At the bottom,

π - + p K0 + Λ0

Then Λ0 π - + p and o -K +µ + ì∂ í+→

Section 46.6

Murray Gell-Mann

1929 –

American physicist

Studies dealing with subatomic particles

Named quarks

Developed pattern known as eightfold way

Nobel Prize in 1969

Section 46.7

The Eightfold Way

Many classification schemes have been proposed to group particles into families.

These schemes are based on spin, baryon number, strangeness, etc.

The eightfold way is a symmetric pattern proposed by Gell-Mann and Ne’eman.

There are many symmetrical patterns that can be developed.

The patterns of the eightfold way have much in common with the periodic table.

Including predicting missing particles

Section 46.7

An Eightfold Way for Baryons

A hexagonal pattern for the eight spin ½ baryons

Strangeness vs. charge is plotted on a sloping coordinate system

Six of the baryons form a hexagon with the other two particles at its center.

Section 46.7

An Eightfold Way for Mesons

The mesons with spins of 0 can be plotted.

Strangeness vs. charge on a sloping coordinate system is plotted

A hexagonal pattern emerges .

The particles and their antiparticles are on opposite sides on the perimeter of the hexagon.

The remaining three mesons are at the center.

These three particles form their own antiparticles.

Section 46.7

Eightfold Way for Spin 3/2 Baryons

The nine particles known at the time were arranged as shown.

An empty spot occurred.

Gell-Mann predicted the missing particle and its properties.

About three years later, the particle was found and all its predicted properties were confirmed.

Section 46.7

Quarks

Hadrons are complex particles with size and structure.

Hadrons decay into other hadrons.

There are many different hadrons.

Quarks are proposed as the elementary particles that constitute the hadrons.

Originally proposed independently by Gell-Mann and Zweig

Named by Gell-Mann

Section 46.8

Original Quark Model

Three types or flavors

u – up

d – down

s – strange

Quarks have fractional electrical charges

-a e and b e

Quarks have spin ½

All quarks are fermions

Associated with each quark is an antiquark

The antiquark has opposite charge, baryon number and strangeness

Section 46.8

Original Quark Model – Rules

All the hadrons at the time of the original proposal were explained by three rules:

Mesons consist of one quark and one antiquark. This gives them a baryon number of 0.

Baryons consist of three quarks.

Antibaryons consist of three antiquarks.

Section 46.8

Quark Composition of Particles – Examples

Mesons are quark-antiquark pairs.

Baryons are quark triplets.

Section 46.8

Additions to the Original Quark Model – Charm

Another quark was needed to account for some discrepancies between predictions of the model and experimental results.

A new quantum number, C, was assigned to the property of charm.

Charm would be conserved in strong and electromagnetic interactions, but not in weak interactions.

In 1974, a new meson, the J/, was discovered that was shown to be a charm quark and charm antiquark pair.

Section 46.8

More Additions – Top and Bottom

Discovery led to the need for a more elaborate quark model

This need led to the proposal of two new quarks:

t – top (or truth)

b – bottom (or beauty)

Added quantum numbers of topness and bottomness

Verification

b quark was found in a Y meson in 1977.

t quark was found in 1995 at Fermilab.

Section 46.8

Numbers of Particles

At the present, physicists believe the “building blocks” of matter are complete.

Six quarks with their antiparticles

Six leptons with their antiparticles

Four field particles

Section 46.8

Quark Composition of Some Baryons

The table shows the quark composition of various baryons.

Baryons are made from three quarks.

Only u and d quarks are contained in hadrons encountered in ordinary matter.

Section 46.8

Particle Properties

Section 46.8

More About Quarks

No isolated quark has ever been observed.

It is believed that at ordinary temperatures, quarks are permanently confined inside ordinary particles due to the strong force.

Current efforts are underway to form a quark-gluon plasma where quarks would be freed from neutrons and protons.

Both RHIC and CERN have announced evidence for a quark-gluon plasma, but neither laboratory has provided definitive data to verify the existence of the plasma.

Section 46.8

Color

It was noted that certain particles had quark compositions that violated the exclusion principle.

Quarks are fermions, with half-integer spins and so should obey the exclusion principle.

The explanation is an additional property called color charge.

The color has nothing to do with the visual sensation from light, it is simply a name.

Section 46.9

Colored Quarks

Color charge occurs in red, blue, or green.

Antiquarks have colors of antired, antiblue, or antigreen.

These are the “quantum numbers” of color charge.

Color obeys the exclusion principle.

A combination of quarks of each color produces white (or colorless).

Baryons and mesons are always colorless.

Section 46.9

Quantum Chromodynamics (QCD)

QCD gave a new theory of how quarks interact with each other by means of color charge.

The strong force between quarks is often called the color force.

The strong force between quarks is mediated by gluons.

Gluons are massless particles.

When a quark emits or absorbs a gluon, its color may change.

Section 46.9

More About Color Charge

Particles with like colors repel and those with opposite colors attract.

Different colors attract, but not as strongly as a color and its anticolor.

The color force between color-neutral hadrons is negligible at large separations.

The strong color force between the constituent quarks does not exactly cancel at small separations.

This residual strong force is the nuclear force that binds the protons and neutrons to form nuclei.

Section 46.9

Quark Structure of a Meson

A green quark is attracted to an antigreen quark.

The quark – antiquark pair forms a meson.

The resulting meson is colorless.

Section 46.9

Quark Structure of a Baryon

Quarks of different colors attract each other.

The quark triplet forms a baryon.

Each baryon contains three quarks with three different colors.

The baryon is colorless.

Section 46.9

QCD Explanation of a Neutron-Proton Interaction

Each quark within the proton and neutron is continually emitting and absorbing gluons.

The energy of the gluon can result in the creation of quark-antiquark pairs.

When close enough, these gluons and quarks can be exchanged, producing the strong force.

This quark model of interactions between nucleons is consistent with the pion-exchange model.

Section 46.9

Elementary Particles – A Current View

Scientists now believe there are three classifications of truly elementary particles:

Leptons

Quarks

Field particles

These three particles are further classified as fermions or bosons.

Quarks and leptons are fermions (spin ½).

Field particles are bosons (integral spin 1 and up).

Section 46.10

Weak Force

The weak force is believed to be mediated by the W+, W-, and Z0 bosons.

These particles are said to have weak charge.

Therefore, each elementary particle can have

Mass

Electric charge

Color charge

Weak charge One or more of these could be zero.

Section 46.10

Electroweak Theory

The electroweak theory unifies electromagnetic and weak interactions.

The theory postulates that the weak and electromagnetic interactions have the same strength when the particles involved have very high energies.

Viewed as two different manifestations of a single unifying electroweak interaction

Section 46.10

The Standard Model

A combination of the electroweak theory and QCD for the strong interaction form the Standard Model.

Essential ingredients of the Standard Model

The strong force, mediated by gluons, holds the quarks together to form composite particles.

Leptons participate only in electromagnetic and weak interactions. Also in gravitational interactions

The electromagnetic force is mediated by photons.

The weak force is mediated by W and Z bosons.

The Standard Model does not actually yet include the gravitational force.

Section 46.10

The Standard Model – Chart

Section 46.10

Mediator Masses

Why does the photon have no mass while the W and Z bosons do have mass?

Not answered by the Standard Model

The difference in behavior between low and high energies is called symmetry breaking.

The Higgs boson has been proposed to account for the masses.

Large colliders are necessary to achieve the energy needed to find the Higgs boson.

In a collider, particles with equal masses and equal kinetic energies, traveling in opposite directions, collide head-on to produce the required reaction.

Section 46.10

Particle Paths After a Collision – Fermi Lab Example

Section 46.10

The Big Bang

This theory states that the universe had a beginning, and that it was so cataclysmic that it is impossible to look back beyond it.

Also, during the first few minutes after the creation of the universe, all four interactions were unified.

All matter was contained in a quark-gluon plasma.

As time increased and temperature decreased, the forces broke apart.

Section 46.11

A Brief History of the Universe

Section 46.11

Cosmic Background Radiation (CBR)

CBR represents the cosmic “glow” left over from the Big Bang.

The radiation had equal strengths in all directions.

The curve fits a black body at 2.7K.

There are small irregularities that allowed for the formation of galaxies and other objects.

The COBE satellite found that the background radiation had irregularities that corresponded to temperature variations of 0.000 3 K.

Section 46.11

Hubble’s Law

The Big Bang theory predicts that the universe is expanding.

Hubble claimed the whole universe is expanding.

Furthermore, the speeds at which galaxies are receding from the earth is directly proportional to their distance from us.

This is called Hubble’s law.

Hubble’s law can be written as v = HR.

H is called the Hubble constant.

H 22 x 10-3 m/s•ly

Section 46.11

Remaining Questions About the Universe

Will the universe expand forever?

Today, astronomers and physicists are trying to determine the rate of expansion.

It depends on the average mass density of the universe compared to a critical density.

Missing mass in the universe

The amount of non-luminous (dark) matter seems to be much greater than what we can see.

Various particles have been proposed to make up this dark matter.

Section 46.11

Another Remaining Question About the Universe

Is there mysterious energy in the universe?

Observations have led to the idea that the expansion of the universe is accelerating.

To explain this acceleration, dark energy has been proposed.

The dark energy results in an effective repulsive force that causes the expansion rate to increase.

Section 46.11

Some Questions in Particle Physics

Why so little antimatter in the Universe?

Is it possible to unify electroweak and strong forces?

Why do quarks and leptons form similar but distinct families?

Are muons the same as electrons apart from their difference in mass?

Why are some particles charged and others not?

Why do quarks carry fractional charge?

What determines the masses of fundamental particles?

Can isolated quarks exist?

Do leptons and quarks have an underlying structure?

Section 46.12

A New Perspective – String Theory

String theory is one current effort at answering some of the previous questions.

It is an effort to unify the four fundamental forces by modeling all particles as various vibrational modes of an incredibly small string.

The typical length of a string is 10-35 m

This is called the Planck length.

According to the string theory, each quantized mode of vibration of the string corresponds to a different elementary particle in the Standard Model.

Section 46.12

Complications of the String Theory

It requires space-time to have ten dimensions.

Four of the ten dimensions are visible to us, the other six are compactified (curled).

Another complication is that it is difficult for theorists to guide experimentalists as to what to look for in an experiment.

Direct experimentation on strings is impossible.

Section 46.12

String Theory Prediction – SUSY

One prediction of string theory is supersymmetry (SUSY).

It suggests that every elementary particle has a superpartner that has not yet been observed.

Supersymmetry is a broken symmetry and the masses of the superpartners are above our current capabilities to detect.

Section 46.12

Another Perspective – M-Theory

M-theory is an eleven-dimensional theory based on membranes rather than strings.

M-theory is claimed to reduce to string theory if one compactifies from the eleven dimensions to ten.