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Chapter 31
Particle Physics
Atoms as
Elementary Particles

Atoms

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From the Greek for “indivisible”
Were once thought to be the elementary
particles
Atom constituents
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Proton, neutron, and electron
After 1932 these were viewed as
elementary
All matter was made up of these particles
Discovery of New Particles
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New particles
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Beginning in 1945, many new particles
were discovered in experiments involving
high-energy collisions
Characteristically unstable with short
lifetimes
Over 300 have been cataloged
A pattern was needed to understand all
these new particles
Elementary Particles – Quarks

Physicists recognize that most particles are
made up of quarks
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Exceptions include photons, electrons and a few
others
The quark model has reduced the array of
particles to a manageable few
Protons and neutrons are not truly
elementary, but are systems of tightly bound
quarks
Fundamental Forces

All particles in nature are subject to four
fundamental forces
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Strong force
Electromagnetic force
Weak force
Gravitational force

This list is in order of decreasing strength
Nuclear Force

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Holds nucleons together
Strongest of all the fundamental forces
Very short-ranged

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Less than 10-15 m
Negligible for separations greater than this
Electromagnetic Force

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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
Weak Force

Is responsible for instability in certain nuclei

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Is responsible for decay processes
Its strength is about 10-5 times that of the
strong force
Scientists now believe the weak and
electromagnetic forces are two manifestions
of a single interaction, the electroweak force
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 10-41 times the strength of the
nuclear force

Weakest of the four fundamental forces
Explanation of Forces

Forces between particles are often
described in terms of the actions of field
particles or exchange particles

The force is mediated, or carried, by the
field particles
Forces and
Mediating Particles
Paul Adrian Maurice Dirac
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1902 – 1984
Understanding of
antimatter
Unification of quantum
mechanics and relativity
Contributions of
quantum physics and
cosmology
Nobel Prize in 1933
Antiparticles

Every particle has a corresponding antiparticle

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
An antiparticle has the same mass as the particle, but
the opposite charge
The positron (electron’s antiparticle) was discovered
by Anderson in 1932

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From Dirac’s version of quantum mechanics that
incorporated special relativity
Since then, it has been observed in numerous experiments
Practically every known elementary particle has a
distinct antiparticle

Among the exceptions are the photon and the neutral pi
particles
Dirac’s Explanation

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The solutions to the relativistic quantum
mechanic equations required negative energy
states
Dirac postulated that all negative energy
states were filled

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These electrons 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
Dirac’s Explanation, cont

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An interaction may
cause the electron
to be excited to a
positive energy state
This would leave
behind a hole in the
Dirac sea
The hole can react
to external forces
and is observable
Dirac’s Explanation, final


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
Pair Production
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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
Pair Production, cont
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A photograph of pair production produced by 300
MeV gamma rays striking a lead sheet
The minimum energy to create the pair is 1.022 MeV
The excess energy appears as kinetic energy of the
two particles
Annihilation
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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+ 
Antimatter, final
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In 1955 a team produced antiprotons and
antineutrons
This established the certainty of the existence
of antiparticles
Every particle has a corresponding
antiparticle with
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equal mass and spin
equal magnitude and opposite sign of charge,
magnetic moment and strangeness
The neutral photon, pion and eta are their
own antiparticles
Hideki Yukawa
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1907 – 1981
Nobel Prize in 1949
for predicting the
existence of mesons
Developed the first
theory to explain the
nature of the nuclear
force
Mesons
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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
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It was called a meson
Mesons, cont
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The proposed particle would have a mass
about 200 times that of the electron
Efforts to establish the existence of the
particle were made by studying cosmic rays
in the late 1930’s
Actually discovered multiple particles
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Pi meson (pion)
Muon
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Not a meson
Pion
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There are three varieties of pions
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+ and 
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0
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Mass of 139.6 MeV/c2
Mass of 135.0 MeV/c2
Pions are very unstable
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For example, the - decays into a muon
and an antineutrino with a lifetime of about
2.6 x10-8 s
Muons
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Two muons exist
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µ- and its antiparticle µ+
The muon is unstable
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It has a mean lifetime of 2.2 µs
It decays into an electron, a neutrino, and
an antineutrino
Richard Feynman
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1918 – 1988
Developed quantum
electrodynamics
Shared the Noble Prize
in 1965
Worked on Challenger
investigation and
demonstrated the
effects of cold
temperatures on the
rubber O-rings used
Feynman Diagrams

A graphical representation of the interaction
between two particles
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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

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Actual values of time and space are not important
The actual paths of the particles are not shown
Feynman Diagram –
Two Electrons
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The photon is the field
particle that mediates the
interaction
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
The Virtual Photon

The existence of the virtual photon
seems to violate the law of conservation
of energy

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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 ΔE   / 2Δt
Feynman Diagram – Proton
and Neutron (Yukawa’s Model)
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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
Nucleon Interaction –
More About Yukawa’s Model

The time interval required for the pion to
transfer from one nucleon to the other is
Dt 
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
2DER 2m c
The distance the pion could travel is cDt
Using these pieces of information, the
rest energy of the pion is about 100
MeV
2
Nucleon Interaction, final

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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
Nuclear Force


The interactions previously described
used the pion as the particles that
mediate the nuclear force
Current understanding indicate that the
nuclear force is more fundamentally
described as an average or residual
effect of the force between quarks
Feynman Diagram –
Weak Interaction

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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
Classification of Particles
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Two broad categories
Classified by interactions
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Hadrons – interact through strong force
Leptons – interact through weak force
Note on terminology

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The strong force is reserved for the force
between quarks
The nuclear force is reserved for the force
between nucleons

The nuclear force is a secondary result of the strong
force
Hadrons
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Interact through the strong force
Two subclasses distinguished by masses and
spins

Mesons
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Baryons
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Decay finally into electrons, positrons, neutrinos and photons
Integer spins (0 or 1)
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
Leptons

Do not interact through strong force
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Do participate in electromagnetic (if
charged) and weak interactions
All have spin of ½
Leptons appear truly elementary

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No substructure
Point-like particles
Leptons, cont

Scientists currently believe only six
leptons exist, along with their
antiparticles
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Electron and electron neutrino
Muon and its neutrino
Tau and its neutrino
Neutrinos may have a small, but
nonzero, mass
Conservation Laws
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A number of conservation laws are important
in the study of elementary particles
Already have seen conservation of
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Energy
Linear momentum
Angular momentum
Electric charge
Two additional laws are
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Conservation of Baryon Number
Conservation of Lepton Number
Conservation of
Baryon Number
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Whenever a baryon is created in a reaction or
a decay, an antibaryon is also created
B is the Baryon Number
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B = +1 for baryons
B = -1 for antibaryons
B = 0 for all other particles
Conservation of Baryon Number states:
the sum of the baryon numbers before a
reaction or a decay must equal the sum of
baryon numbers after the process
Conservation of Baryon
Number and Proton Stability
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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
Conservation of Baryon
Number, Example

Is baryon number conserved in the
following reaction?
 p n  p p n p
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Baryon numbers:
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Before: 1 + 1 = 2
After: 1 + 1 + 1 + (-1) = 2
Baryon number is conserved
The reaction can occur as long as energy
is conserved
Conservation of
Lepton Number
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There are three conservation laws, one
for each variety of lepton
Law of Conservation of Electron-Lepton
Number states that the sum of electronlepton numbers before the process
must equal the sum of the electronlepton number after the process

The process can be a reaction or a decay
Conservation of
Lepton Number, cont

Assigning electron-lepton numbers
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Le = 1 for the electron and the electron neutrino
Le = -1 for the positron and the electron
antineutrino
Le = 0 for all other particles
Similarly, when a process involves muons,
muon-lepton number must be conserved and
when a process involves tau particles, taulepton numbers must be conserved

Muon- and tau-lepton numbers are assigned
similarly to electron-lepton numbers
Conservation of
Lepton Number, Example

Is lepton number conserved in the
following reaction?
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   e   e   
Check electron lepton numbers:
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Before: Le = 0
After: Le = 1 + (-1) + 0 = 0
Electron lepton number is conserved
Check muon lepton numbers:
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Before: Lµ = 1
After: Lµ = 0 + 0 + 1 = 1
Muon lepton number is conserved
Strange Particles
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Some particles discovered in the 1950’s were
found to exhibit unusual properties in their
production and decay and were given the
name strange particles
Peculiar features include
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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
Strangeness
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To explain these unusual properties, a new
quantum number, S, called strangeness, was
introduced
A new law, the conservation of strangeness, was
also needed
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It states that whenever a reaction or decay occurs
via the strong force, the sum of strangeness
numbers before the process must equal the sum of
the strangeness numbers after the process
Strong and electromagnetic interactions obey the
law of conservation of strangeness, but the weak
interaction does not
Bubble Chamber
Example of Strange Particles
The dashed lines
represent neutral
particles
 At the bottom,
- + p  Λ0 + K0
Then Λ0  - + p
and
K 0   0 + µ- +   

Creating Particles
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Most elementary particles are unstable
and are created in nature only rarely, in
cosmic ray showers
In the laboratory, great numbers of
particles can be created in controlled
collisions between high-energy particles
and a suitable target
Measuring Properties
of Particles

A magnetic field causes the charged particles
to curve
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This allows measurement of their charge and
linear momentum
If the mass and momentum of the incident
particle are known, the product particles’
mass, kinetic energy, and speed can usually
be calculated
The particle’s lifetime can be calculated from
the length of its track and its speed
Resonance Particles

Short-lived particles are known as
resonance particles

They exist for times around 10-20 s
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In the lab, times for around 10-16 s can be
detected
They cannot be detected directly
Their properties can be inferred from
data on their decay products
Murray Gell-Mann
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1929 –
Studies dealing with
subatomic particles
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Named quarks
Developed pattern
known as eightfold
way
Nobel Prize in 1969
The Eightfold Way
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Many classification schemes have been
proposed to group particles into families
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The eightfold way is a symmetric pattern
proposed by Gell-Mann and Ne’eman
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These schemes are based on spin, baryon
number, strangeness, etc.
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
An Eightfold Way for Baryons
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A hexagonal pattern for
the eight spin ½
baryons
Stangeness vs. charge
is plotted on a sloping
coordinate system
Six of the baryons form
a hexagon with the
other two particles at its
center
An Eightfold Way for Mesons
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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
Eightfold Way for
Spin 3/2 Baryons
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

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
Quarks

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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
Original Quark Model

Three types or flavors

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Associated with each quark is an antiquark

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The antiquark has opposite charge, baryon
number and strangeness
Quarks have fractional electrical charges


u – up
d – down
s – strange
+1/3 e and –2/3 e
Quarks are fermions

Half-integral spins
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
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
This gives them a baryon number of 0
Baryons consist of three quarks
Antibaryons consist of three antiquarks
Quark Composition
of Particles – Examples

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Mesons are
quarkantiquark
pairs
Baryons are
quark triplets
Additions to the Original
Quark Model – Charm

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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/Ψ was
discovered that was shown to be a charm
quark and charm antiquark pair
More Additions –
Top and Bottom
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Discovery led to the need for a more
elaborate quark model
This need led to the proposal of two new
quarks
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t – top (or truth)
b – bottom (or beauty)
Added quantum numbers of topness and
bottomness
Verification

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b quark was found in a Y- meson in 1977
t quark was found in 1995 at Fermilab
Numbers of Particles

At the present, physicists believe the
“building blocks” of matter are complete
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Six quarks with their antiparticles
Six leptons with their antiparticles
Particle Properties
More About Quarks
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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
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 the color charge

The color has nothing to do with the visual
sensation from light, it is simply a name
Colored Quarks

Color “charge” occurs in red, blue, or green

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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
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

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Gluons are massless particles
When a quark emits or absorbs a gluon, its
color may change
More About Color Charge

Particles with like colors repel and those with
opposite colors attract

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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
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
Quark Structure of a Baryon


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
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
QCD Explanation of a
Neutron-Proton Interaction

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
Each quark within the
proton and neutron is
continually emitting and
absorbing gluons
The energy of the gluon
can result in the
creation of quarkantiquark pairs
When close enough,
these gluons and
quarks can be
exchanged, producing
the strong force
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
Field particles are bosons
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 charges may be zero
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
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
The electromagnetic force is mediated by photons
The weak force is mediated by W and Z bosons
The standard model does not yet include the
gravitational force
The Standard Model – Chart
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
Particle Paths After a Collision
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
A Brief History of the Universe
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, cont

Hubble’s Law can be
written as v = H R


H is called Hubble’s
constant
H 17 x 10-3 m / s ly
Remaining Questions
About The Universe

Will the universe expand forever?




Today, astronomers are trying to determine the
rate of expansion
The universe seems to be expanding more slowly
than 1 billion years ago
It depends on the average mass density of the
universe compared to a critical density
The critical density is about 3 atoms / m3


If the actual density is less than the critical density, the
expansion will slow, but still continue
If the actual density is more than the critical density,
expansion will stop and contraction will begin
More Questions

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


Exotic particles such as axions, photinos and superstring
particles have been suggested
Neutrinos have also been suggested

It is important to determine the mass of the neutrino since
it will affect predictions about the future of the universe
Another Question

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


It is energy possessed by the vacuum of space
The dark energy results in an effective repulsive
force that causes the expansion rate to increase