Chapter 5
Particles –Energy states
After the discovery of electrons in 1897,
protons, neutrons, pions, kaons, sigmas, rhos,
and other particles have been discovered.
Some of them in cosmic rays and some
generated in particle collision experiments.
"Everything should be made as simple as possible, but not
simpler."
Albert Einstein
Enrico Fermi, the father of nuclear reactors, once said “Young man, if I could remember the names of
all these particles, I would have been a botanist”. Botanists classify and organize plants into families
according to their structures and functions. They also seek relationships among living
organisms. These methods applied to study of particles are led to the Standard Model for the
material worlds.
Studies of radioactivity developed machines to detect particles. These machines also detected
many particles in the cosmic rays during the 1930s. After the World War II, physicists have
created these particles using accelerators. The study of these particles opened a field called
particle physics or high-energy physics. New breed of particle physicists work to gain
simplified understanding of the materials. They are the modern-day philosophers pursuing the
ultimate understanding of the material world.
Ordinary matter consists of molecules and atoms. Radioactivity revealed the components of
atoms and nuclei. These components are electrons, protons, and neutrons. Theoretical and
experimental physicists poke closer to these particles. They saw more some structure features
of protons and neutrons and suggested that nucleons were composed of quarks.
Furthermore, quarks are the components of other particles. A standard model summarizes
the relations of quarks, electrons, particles and their forces of interaction.
Particles cannot be visualized as tiny analogues of ordinary material objects such as billiard
balls or dust particles. Their properties are different from those of ordinary (or classical)
particles. They are better called energy states. Atoms and molecules also have various energy
states, and their transitions lead to atomic phenomena. The change of states in particles is
usually considered a decay process. Some particle states such as the protons are stable for an
indefinite time, but others exist for a short time. We will take a look at these particles in this
Chapter.
149
Particles and Antiparticles
When we discussed the beta decay process, properties of positrons were introduced, but the
concept of antiparticles was left out.
Every particle (state) has a corresponding antiparticle (another
state). Particles and antiparticles have the same mass, but they
have opposite electric charge, and magnetic moment. We
generally believe the theory because of its simplicity and
symmetry.
The Concept and Discovery of
Antiparticles
Antimatter is a common term used by experts, fictionists, and ordinary writers. Antimatter
refers to antiparticles such as positrons, antiprotons, antineutrons etc. Theoretically,
antiparticles can also combine to give antiatoms and antimolecules, forming a world of
antimatter.

How did the concept of antiparticles originate?
When and who initiated this concept?
What is the theory about?
Why do we believe in it?
Do neutral particles have antiparticle partners?

What experimental evidences show the existence of antiparticles?
In 1930, Paul A.M. Dirac studied the electrons. He combined the theory of relativity with
quantum mechanics and derived a wave function for free electrons. His theory predicted four
energy states, two of which due to the spin. His theory suggested the quantum number +1/2
and –1/2 for the spin, which has already been detected. Two other states are for electrons with
positive charges. Some basic considerations are given below concerning the background
leading to his suggestion of antiparticles.
The linear momentum p is the product of the mass m and its velocity v , p = m v. For a
particle with rest mass m0 moving at a speed v close to that of light, c, its mass m increases
according to Einstein theory of relativity,
m0
m=
.
2
v
1  ( c)
This m is the relativistic mass. The total energy E of the particle is

Dirac, Paul Adrien Maurice (1902-1984), shared the Nobel Prize for Physics with the Austrian physicist Erwin Schrödinger in
1933. He is known for his work in quantum mechanics and for his theory of the spinning electron.
150
2
E=mc =
m0 c 2
1  (v c)2
.
Dirac studied these relationships, and from the above two equations he derived the following
equation,
Derivation of Dirac's equation
E2 = p 2 c 2 + (m0 c 2 ) 2.
Square both side of Einstein's
equation
In which, the quantity m0 c 2 is the energy
corresponding to the rest mass. Taking the square
E 2 = (m c2)2 = m02 c 4/(1-(v/c)2)
root from the above equation gives two expressions
for energy:
From this, we have
E+ = + {(p2 c2 + (m0 c2 )2}1/2 > m0 c2
(m c2)2 - m 2 v 2c 2 = m02 c 4
E– = – {(p2 c2 + (m0 c2 )2}1/2 < m0 c2
Thus,
E 2 = p 2 c 2 + (m0 c 2)2
and
The total energy E+ increases as the particle gathers
speed, but the total energy E– decrease as the particle gathers speed. The E– of a moving
particle is less than that of the rest mass. This notion of negative energy is contrary to the case
of ordinary particles, represented by E+.
Dirac further worked out the wave
function for particles fitting the E–
description. Such a particle should have
opposite spin, charge, and magnetic
moment with respect to the normal
particle. Such a particle is called an
antiparticle.
The Concept of Antiparticle
Positive Energy States
Zero Energy States
In the case of electrons, Dirac further
suggested that in a vacuum, all negativeenergy states are occupied, and positive
Negative Energy States
energy states are completely empty.
Uniformly occupied or unoccupied
(a)
(b)
( c)
(d)
energy states are unobservable, see (a).
When an electron occupies a positive energy state, it is observable, see (b), as is when one of
the filled energy states become unoccupied, (c), it’s an antielectron. However, from the
unobservable condition in (a), an electron can be promoted to the positive energy states, and at
the same time create a vacancy in the negative energy states. This electron-antielectron pair (d)
is observable but energy is required for this promotion. However, an electron-antielectron pair
(d) is unstable, and the electron will return to the negative-energy state in a process called
annihilation. The particle and antiparticle vanish, releasing energy in the form of photon.
151
The positron (e+ or +) is the first antiparticle discovered by Carl D. Anderson in 1932,
when he was a graduate student in R. Millikan’s (he determined the charge on an electron)
research group. Anderson made the discovery while studying cosmic and gamma () rays. He
built a cloud chamber to study cosmic ray tracks under the influence of a magnetic field, and
he observed some tracks similar to those of electrons but bent in the opposite direction.
Millikan thought these tracks were due to protons, but Anderson considered them too thin to
be tracks of protons. He first considered them tracks of electrons entering the cloud chamber
from the opposite direction, and he
Illustration of Electron and Positron
inserted a lead plate in the chamber to see
Tracks Observed by C. Anderson
the effect in order to solve the puzzle.
Lead
When the particle passed the lead, its track
plate
bent more, due to loss of energy. Then, he
reviewed Dirac’s proposal of unoccupied
e+
negative energy states and called the
antiparticle positron.
e–
Anderson observed more positrons, and
he often saw equal numbers of positron
and electron tracks in his cloud chamber. At the end of positron tracks, two tracks due to
gamma photons were observed, and they are due to the annihilation of positrons and
electrons. A year later, the creation of an electron-positron pair using high-energy photon was
confirmed, and this process is called pair production. Today, positrons and electrons are
created routinely using high-energy photons. These particles are created for particle
accelerator. Electrons and positrons move in opposite directions in circular accelerators
accelerated using electric and magnetic fields. When high-energy electrons and positrons
collide, particles with rest mass heavier than electrons are produced. For example, the
Brookhaven National Laboratory on Long Island, New York and CERN (Conseil Européen
pour la Recherche Nucleaire or European Organization for Nuclear Research) on the outskirts
of Geneva are some of the laboratories dedicated to this type of research.
The term positron rather than antielectron is
used more often, and its symbol is e+ or +.
However, the symbol for an antimatter
particle is usually a bar over the
corresponding matter particle symbol. For
example, an antiproton is denoted by p ,
pronounced p-bar.
Annihilation and Pair Production
+ + –  2 
e–
  + + –
Skill Building Questions:
1. What are the four states of electron according to
Paul Dirac's results?

e+
e–
Carl D. Anderson (1905-1991) with Victor Francis Hess of Austria, won the Nobel Prize for Physics in 1936 for his discovery
of the positron, or positive electron, the first known particle of antimatter.
152
2. Derive the equation E2 = p2 c2 + (m0 c2 )2 using the statements given in this section. (Only for those
interested in derivation of formulas. It is not difficult.)
3. What properties are the same for particle-antiparticle pairs and what properties are different?
Compare the properties of an electron and a positron?
4. Describe the experiment leading to the discovery of positron and explain annihilation and pair
production.
Antiprotons and Antineutrons
Dirac’s proposal regarding particle-antiparticle pairs is valid for any particle or matter.
Existence of antiparticles for protons and neutrons is very important. There was a race to
detect antiprotons and antineutrons.

Do protons and neutrons have antiparticles?
What are the properties (behavior) of antiprotons and antineutrons?
Where and how can they be detected?

Do all particles have antiparticles?
After the discovery of positrons, everyone is convinced that for every particle, there is an
antiparticle. A race was on to be first to find antiprotons and antineutrons. Researchers in
Berkley built an accelerator called Bevatron to produce particles (protons) with a kinetic energy
of 6.2 GeV, and they hope to find antiprotons when the high-energy protons collide with a
target of fixed protons in liquid hydrogen. In the mean time, there is a belief that antiprotons are
present in cosmic rays.
Simultaneously, many groups looked for
antiprotons. One group led by Emilio
Segrè looked for negatively charged
particles with mass similar to that of a
proton among particles generated from the
bombardment of high-energy protons.
They used a variety of methods for the
detection of fast moving particles. They
realized that an antiproton would
annihilate a proton when it stroke one,
converting both masses to pure energy.
When they observed a set of star-like
tracks called starburst, they thought the
energy of annihilation re-materialized
quickly, converting to many charged
particles including positive and negative

Star-like Tracks Produced by an Antiproton
Annihilating a Proton in a Bubble Chamber
antiproton
Segrè, Emilio (Gino) (1905 - 1989) Owen Chamberlain (1920-) received the Nobel Prize for Physics in 1959 for the discovery
of the antiproton, an antiparticle having the same mass as a proton but opposite in electrical charge.
153
pions (+ and –). In a magnetic field, these pions bend in different directions due to their
positive and negative charges. The starburst is a typical annihilation signature of antiprotons. A
typical one produces 8 pions, 4 – and 4 +. Energies of these particles were estimated from
the tracks, and their total energy is equal to the kinetic energy of the antiproton plus the rest
masses of two protons. More than 100 antiprotons have been detected before their
observations were published in 1955. Segrè and Chamberlain group members included Clyde
Wiegand and Tom Ypsilantis. The star-like tracks were captured in a 72-inch liquid hydrogen
bubble chamber, and how such a chamber works will be discussed in a Chapter discussing
interactions of ionizing particles with material.
After the discovery of antiprotons, attention was directed to antineutrons. A year later, Bruce
Cork, also working in Berkley, thought that when an antiproton neutralized its charge with a
proton, instead of annihilating it, the proton and antiproton pair will convert to a neutron and
antineutron pair,
p + p  n + n.
Cork observed the annihilation of an antineutron and a neutron also produces a star-burst of
charged pions and photons. Particles and antiparticles have opposite electrical charge in the
case of electrons and protons, but antineutrons, have opposite magnetic moment of neutrons.
The detection of antiprotons and antineutrons not only further confirms and generalizes the
Dirac's theory of antiparticles.
Skill Building Questions:
1. What are the properties of protons and antiprotons?
2. The production of neutron and antineutron from proton and antiproton is endothermic. What is the
minimum energy input to the system for this reaction?
3. There so much more matter in the universe than antimatter, why?
Why did matter "win" instead of antimatter?
(The answers to these questions are still being sought for.)
Antihydrogen
Antielectron and antiproton are components of an antihydrogen atom, but …

Is a system consisting of an antielectron and an antiproton stable?
Has an antihydrogen ever been created or detected?
Can antiatoms form antimolecules?
A system consisting of an antielectron and an antiproton is an anti-hydrogen atom. As long as
these atoms do not contact normal hydrogen atoms and they are stable theoretically.
154
Predictions of something to be discovered or made are frontiers of science. A search in the
Encyclopædia Britannica Online on June 8, 1999
<http://www.eb.com:180/bol/topic?eu=123833&sctn=1>
resulted in the following description.
In early 1996 a team of physicists reported achieving that goal, although fleetingly, in the
Low Energy Antiproton Ring (LEAR) storage facility at CERN (European Laboratory
for Particle Physics) near Geneva. The team, led by Walter Oelert of the Institute for
Nuclear Physics Research, Jülich, Ger., began with a stored beam of antiprotons circulating
in the ring and squirted a jet of xenon atoms across its path. Interaction between the xenon
and the antiprotons sometimes produced pairs of electrons and positrons, and very occasionally
one of the positrons teamed up with an antiproton, forming an atom of antihydrogen. Once
made, the neutral antiatoms left the magnetic confinement of the storage ring and were
detected. Over the course of three weeks, the experimenters reported the detection of nine such
antiatoms, which existed for an average of 40 billionths of a second before they annihilated
with normal matter.
The antideuterium, a composite antiparticle consisting of an antiproton and an antineutron,
was first produced with a 30-GeV (giga-electron volt) synchrotron at Brookhaven National
Laboratory, Long Island, N.Y., in 1965. Antideluterium is an antiparticle of deuterium nucleus.
Skill Building Questions:
1. What is the difference between an antiparticle and an antiatom?
2. Is the system consisting of an electron and an antiproton stable, why or why not?
3. What is common between an antiatom and an antideuterium? (Both are composite antiparticles.)
155
The Standard Model and Particles
The standard model (SM) describes material structures in terms of fundamental components
(or building blocks). Chapter 3 mentioned the SM. At that time, ordinary material was
described in terms of electrons, neutrinos, down and up quarks.
In the standard model, two types of fundamental particles are leptons and quarks.
Electrons, positrons, antineutrinos, and neutrinos in beta decays are considered first
generation leptons. Their heavier ancestors are muons, – and +, and muon neutrinos,
and v . Their properties are the same as their first generation counterparts, except that the
muon mass is 207 times that of an electron. The still heavier ancestors called taus are 3500
times the rest mass of the electrons. They are even heavier than protons. The neutrinos have
almost zero mass. All leptons have spin ½. Antiparticles have opposite spins, so do their
associated neutrinos. Charges on corresponding leptons for all generations are the same.
Particles of the Standard model
Leptons
Quarks
Charge
Mass
(GeV)
First Generation
Second Generation
Third Generation
–
–
Electron, e
Muon,  ,
Tau, –,
+
Positron, e
Antimuon, +
Antitau, +,
Up, u;
+2/3;
0.3
Muon-neutrino,
Tauneutrino, 
Neutrino, v e,
Antineutrino, e.
Anti-muon-neutrino, v ,
Antitauneutrino, v 
Down, d
Strange s;
Charm, c
Bottom b; Top, t
–1/3
–1/3;
+2/3
–1/3;
+2/3
0.3
0.5
1.5
4.8
176
Charged particles interact with each other via gauge bosons, whereas the quarks interact with
one another via strong-force carriers called gluons.
Quarks as Fundamental Particles
Up, down, strange, charm, bottom, and top are the six fundamental quarks of three
generations in SM. Ordinary matter is made up of first-generation quarks and leptons: up (u)
and down (d) quarks, and electrons (e–). Particles created by high-energy particle collision
contain heavier quarks s, c, b, and t and leptons  and .

How did the concept of quarks come about?

Are the quarks real particles?
What compelling evidences show their existence?
Why are quarks considered elementary?
156
We have mentioned in an earlier Chapter that the concept of quarks came from the study of
relationship among particles such as baryons and mesons. In 1961, Murray Gell-Mann and
Yuval Ne'eman proposed a particle classification scheme called the Eightfold Way, based on
the mathematical symmetry group SU(3). In 1964 Gell-Mann introduced the name quark
from a passage in James Joyce's novel Finnegans Wake. George Zweig developed a similar
theory independently that same year and called his fundamental particles aces.
Mesons (for example pions and kaons) consist of a quark and an antiquark, whereas baryons
(protons and neutrons) consist of three quarks. Gell-Mann and Ne'eman postulated three
quark types: u, d, and s. Each carries a fractional electric charge, has a mass, and a spin 1/2.
They obey the Pauli exclusion principle. No theory or experiment seems to suggest that they
can be resolved into something smaller. Quarks always seem to occur in combination with
other quarks or antiquarks. No single free quark has been detected yet.
Since no free quark has been detected, investigations continue. Quantum chromodynamics
(QCD) of strong interactions, developed in 1977, introduced the concept of colour, which has
nothing to do with the colours of the everyday world, but as a property of quarks, similar to
the charge as a property of electron. The colours red, green, and blue are ascribed to quarks,
and their opposites, minus-red, minus-green, and minus-blue, to antiquarks. According to
QCD, all combinations of quarks must contain equal mixtures of these imaginary colours so
that they will cancel out one another, with the resulting particle having no net colour.
Similar to exchange of photons between charged particles, massless gluons exchange between
particles having color. Just as photons carry electromagnetic force, gluons transmit the strong
forces that bind quarks together. Quarks change their colour as they emit and absorb gluons,
and the exchange of gluons maintains proper quark colour distribution.
Further support for the quark model comes from the study of interaction between pions and
protons. Pions with certain kinetic energies seem to form a temporary resonance particle with
protons. These unstable resonance particles decay within 10–23 seconds. By studying the direction
of the decay products, the proton was considered to have three centers or quarks. Studies of
electron scattering gave the same conclusions.
Quarks charm ( c) and bottom (b) found in the late 1970s as components of excited kaons and
extended the number of quarks to 5. Quarks are believed to occur in pairs, and a top (t) quark
will complete the pairs. A theory suggests it carries a +2/3 electric charge; its partner, the
bottom quark, has a charge of -1/3. In 1995 two independent groups at Fermi National
Accelerator Laboratory reported that they had found the top quark. A weighted average of
their results gives the top quark a mass of 176 +/- 12 GeV (giga electron volts). (The next
heaviest quark, the bottom, has a mass of 4.8 GeV.) Masses of u and d are believed to be equal
(~ 0.3 GeV or 1/3 of the masses of proton or neutron ~310 MeV). No direct measurement is
available.
157
High energy particle-antiparticle collision
Eight JP = ½+ Baryons
experiments produce baryons sigmas (–, 0, &
+, mass ~1.192 GeV) lambda (, mass 1.115
udd
uud
GeV), and cascade (– & 0, mass 1.317 GeV).
n
p
Using the quark model, these baryons are
related to the stable proton p and neutron n.
dds
uds
uus
–
0
Such a relationship in terms of their quark

 
+
0
composition is shown here. Baryons  and 
are composed of the same quarks, uds, but the
quarks in them have different spin
–
0
dss
uss
combinations,  corresponding to uds
0
and  to uds, where the arrows indicate
the spin of the quarks in the composite
particles. Possible spin combinations and energy states in these composite particles are of great
interest in the field of particle physics. Compared to atoms or atomic nuclei, particles are
relatively simple systems.
Well, if you think that combination of u, d,
and s quarks should produce more particles
than 6, you are right. For J P = 3/2+, there are
10 more combinations, and all corresponding
particles have been detected. These particles
have very short half-lives and they are often
called resonances. As such, their masses have
not been measured accurately. Seven of the
ten J P = 3/2+ resonances are excited states of
the J P = ½+ baryons.
Ten J P = 3/2+ Resonances
ddd ddu duu uuu
–
0 + 2+
dds dus uus
–  0 +
dss uss
–  0
sss
–
Three new resonances or baryons containing the same 3 quarks are interesting. From the
charges of these resonances, we get a sense of why quarks are considered to have their
respective fractional charges, -1/3 for d and s, +2/3 for u.
By combining the u, d, and s quarks, we have shown some interesting relationships for
mesons and baryons. When these are combined with the charm quark c, the bottom b and top
t quarks, many more particles are possible. In fact, discoveries of particles containing c, b, and
t quarks confirm the existence of c, b, and t quarks. A free quark has not been detected,
despite great effort for their search.
Review Questions:
1. What are the quark compositions for mesons?
What forces hold the quarks together in mesons?
2. What are the quark compositions for neutron and protons?
Sigma zero and lambda have the same quark compositions, but the two particles are different, why?
158
Hadrons
Mesons and baryons are collectively called hadrons. They are composed of quarks. Since
there are six quarks, their combinations and permutations give rise to a large number of
hadrons.

What particles have been detected?
How are they related to each other?
How are they related to the material world?

In these relationships, what particles are fundamental or basic?
How are materials related to these fundamental particles?

Via what forces do particles interact with one another?
What forces hold particles together in composite particles?
What are responsible for the exerting the forces between particles?
We have mentioned leptons as fundamental particles. They combine with baryons to form
atom-like systems.
Hadrons (mesons and baryons) are composed of fundamental particles called quarks.
Ordinary materials are composed of 1st generation particles. Particles containing quarks of 2nd
and 3rd generations are formed when large quantities of energy materialize (forming a bound
state). Their lifetimes are short, decaying into particles (states) made up of first generation
leptons and quarks.
Mesons were originally defined as particles with masses heavier than electrons, but lighter
than protons. For example, pions (pi-plus +, pi-minus –, and pi-zero 0) and kaons (K+, K–,
and K0) are well known. However, the J/psi (J/), D, and Upsilon (Y) discovered in the 1970s
with properties similar to those of pions and kaons are much heavier, 3.1 GeV for J/ and 9.5
Gev for Y. Their existence called for a review of the fundamental particle theory. We now
consider particles consisting of a quark and an antiquark mesons. Since quarks have half spin,
mesons have integral spin, 0 or 1. Quark contents and properties of some mesons are listed
below:
159
== Properties of Some Mesons ==
Name Symbol
Mass
Lifetime Charge
Spin
Quarks
Pi-zero
0
Pi-plus
+
Pi-minus –
135 MeV
140 MeV
“
0.8x10–16 s
2.6x10–8 s
“
0
+1
–1
0
0
0
u u or d d
ud
du
K-zero
K0
K-plus
K+
K-minus K–
498 MeV
494 MeV
“
10–8 to 10–10 s 0
1.2x10–8 s
+1
“
–1
0
0
0
ds
us
su
J/psi
D-zero
D-plus
Upsilon
3.1 GeV
1.87 GeV
“
9.46 GeV
10–20 s
10–12 s
4x10–13 s
10–20 s
1
0
0
1
cc
cu
cd
bb
J/
D0
D+
Y
0
0
+1
0
Pi-plus and pi-minus form a particle-antiparticle pair, so do K-plus and K-minus. Pi-zero and
its antiparticle are the same, but K-zero has an antiparticle. These are inferred from their quark
compositions. Some mesons contain quarks from different generations.
The meson J/psi (J/) was independently discovered in 1974 by two teams working at two
facilities: B. Richter at SLAC and S. Ting at BNL. This discovery called for and confirmed the
existence of a charm quark (c ) for the first time. The discovery of D was made in 1976 by a
team led by Goldhaber at SLAC and BNL. A year later, the Upsilon was discovered by
Lederman’s team at Fermilab.
Baryons consist of three quarks and they have some common properties. For example, they
have half-integral spins of ½, 3/2, 5/2 .... The most familiar baryons are the proton and the
neutron. All but protons are short-lived. Some baryons consist of quarks from different
generations, similar to some mesons. Properties of some, but not all, baryons are listed below:

The discovery of this particle, thought to be composed of a charmed quark and its antiquark, led to a significant expansion
and refinement of the quark model. For this discovery Samuel Ting and Burton Richter were awarded the 1976 Nobel Prize
for Physics. Leon Max Lederman, Melvin Schwartz and Jack Steinberger, received the Nobel Prize in 1988 for physics for
having established the identity of muon neutrinos.
160
== Properties of Some Baryons ==
Name
Symbol Mass
Lifetime Charge
Spin Quarks
Proton
Antiproton
p 938.3 MeV
p
“
stable
+1
-1
½
-½
uud
uud
Neutron
Antineutron
n 939.6 MeV
n
“
600 s
0
0
½
-½
udd
udd
Lambda
Antilambda
 1.115 GeV

“
2.6x10–10 s
“
0
0
½
-½
uds
uds
Sigma
0 1.192 GeV 6x10–20 s
Sigma-plus
+ 1.189 GeV 0.8x10–10 s
Sigma-minus – (anti particle of +)
0
+1
-1
½
½
-½
uds
uus
uus
Charmed
lambda
+1
½
udc
c 2.28 GeV
2x10–13 s
Note that the lambda consists of a strange quark. This neutral particle is similar to a neutron,
and a nucleus containing this particle is a hypernucleus. The charmed lambda c contains a
charm quark, it’s charge same as a proton. This table lists some baryons involving only four
quarks. Some baryons contain b and t quarks are not listed here.
The baryons containing the b and t quarks are not listed here yet, due to a lack of definitive
information about them, leaving an opportunity for you to carry out some self-study.
Review Questions:
1. What are the first generation leptons and quarks?
What are second generation leptons and quarks?
2. What are mesons? According to the definition you have given, how many mesons can be derived from six
quarks?
3. What are baryons?
Illustrate with some examples.
Force Carriers
Particles interact with one another. Attraction, repulsion, or the recognition of each other's
existence is an interaction, and such a phenomenon is due to a force between the particles
involved. Without such a force, particles will be indifferent of each other.
161

Is it possible to have an interaction without an exchange of something?
How many kinds of interactions or forces are there among various particles?
What are exchanged for these forces and how do we recognize them?
An interaction is an exchange of something. An exchange usually results in an attraction or
repulsion, which we call a force. Without an exchange, particles will ignore each other, and
they do not experience the existence of each other.
The Newton's law of gravity and Coulomb's law of electromagnetic attraction represent two
types of commonly known forces. As long as particles or objects have masses, they experience
gravitation attraction of each other. As long as the objects or particles are electrically charged,
they experience Coulomb forces or electromagnetic forces. Generally, we assume that
gravitons and photons exchange to give rise to these forces.
Many properties for photons have been
introduced. They interact with charged
particles. Thus, you may find the Feynman
diagram (to be discussed later) a fine
presentation of the electromagnetic force.
Exchange of photon, zigzag line, makes
electrons repulse each other, and photons are
called force carriers.
Feynman Diagram for Electron Scattering
space
e

e’
time
The existence of the gravitons as force
carriers is very reasonable and physicists have
postulated their existence, but their properties are unknown. In fact, we do not know how to
detect them. Their existence is important from theoretical point of view, but their search
progresses slowly.
Gravitational and electromagnetic forces cannot confine nucleons in a nucleus due to
electromagnetic repulsion of the protons. Thus, there must be other types of force acting
between nucleons. For this type of interactions, the quantum field theory suggests strong
force and weak force being responsible. Exchange of the force carrier gluons, equivalent to
photons of the electromagnetic force, gives rise to the strong force. These carriers exchange
between particles such as quarks that have a property called color. This term is absolutely
unrelated to the color we see, but a name for properties similar to the electric charge for the
electron. Only particles with color experience strong force by exchanging gluons.
Radioactive beta decay inter-converts neutrons and protons. The half-lives of beta decays are
long. Interactions leading to these conversions have been called weak interactions, because
they are weak compared to the force binding quarks together. Furthermore, the force carriers
of weak interactions, W and Z have been detected. Although their lifetime are very short.
These bosons are heavy, with masses about 100 times the mass of a proton, and their heavy
masses cause the force appear weak. In radioactive decays, the strength of the weak force is
about 100,000 times less than the strength of the electromagnetic force. However, it is now
known that the weak force has intrinsically the same strength as the electromagnetic force, and
these two apparently distinct forces are believed to be different manifestations of a single
162
"electroweak" force ("weak nuclear force" Encyclopædia Britannica Online
<http://www.eb.com:180/bol/topic?eu=78363&sctn=1> [Accessed June 9, 1999]).
The discussion above introduced four types of forces: gravitational, electromagnetic,
strong, and weak. Force carriers are called gauge bosons. As a summary, the four forces
and their carriers are tabulated below:
Forces and Force Carriers (Gauge Bosons)
Gravitational Electromagnetic
Carrier
Mass
(GeV)
Decay
mode
Lifetime
Charge
Spin
graviton
0
photon (hv)
0
-
-
stable
0
unkown
stable
0
1
Weak
Strong
W+, W–, Z0
8 gluons (g)

W : 83.3
~0
Z: 91.2
W  e,

+ 


Z  e ,e ; 
10–25 s
stable
+1, -1, 0
0
1
1
Some theories predict the existence of one or more Higgs particles, which are massive force
carriers of other fields not familiar to us. Higgs particles are responsible for the masses of all
the other particles. Higgs particle or particles have yet to be found, yet more complicated
theories predict additional particles. For example, supersymmetry predicts existence of
gauginos, sleptons and squarks; additional weak bosons W' and Z' has been predicted; GUT
theories suggest X and Y bosons; the technicolor models require Majorons, familons, axions,
paraleptons, ortholeptons, technipions; Some theories suggests existence of B', a hadron with
4th generation quarks, magnetic monopoles, excited leptons e*, etc. These "exotica" have yet to
be confirmed. The search is on!
Review Questions:
1. How many kinds of force exist in nature?
2. What are the Coulomb's law and the law of gravity?
What are the similarities and differences?
What are the gauge bosons for the gravitational and the electromagnetic forces?
3. What are strong and weak interactions?
What are the force carriers?
163
High-Energy Particles
The previous section summarized the standard model that has given a fundamental description
regarding the structure and interactions (forces) of the material world, from atoms to rare
encountered high-energy particles. A lot of theoretical and experimental work has gone into
the study to give such a summary, and the development from an experimental point of view is
also very interesting. In fact, radioactivity and high energy particles are not printed symbols in
publications or created in sophisticated laboratories, many of them are around us.
Cosmic Rays
After its discovery, radioactivity was detected in all kinds of places: under water, under ground
tunnels, caves, sea level, mountain tops, and high above in the atmosphere. For example, Wulf
observed high radioactivity at the top of Eiffel Tower. Soon after, Victor Hess went high up
with balloons and detected very high radioactivity in the atmosphere. So did Millikan’s and
Rutherford’s groups. These discoveries astonished them.

What particles are actually responsible for this apparent high radioactivity?
What is the source of the high radioactivity high up in the atmosphere?
Is the origin of high radioactivity terrestrial or extraterrestrial?
Millikan thought high-altitude radioactivity was gamma rays from outer space and coined the
phrase cosmic rays for them, and others found penetrating positively charge particles, at sea
level and below. Cosmic rays are also present underground. The planet Earth is constantly
bombarded by cosmic rays.
Measurements by space ship indicate that primary galactic cosmic rays are high-energy
protons (83%), helium nuclei (16%) and other nuclei. Protons with energy 2 GeV are the most
abundant, but some have energy as high as 20 TeV (1012 eV). High-energy particles penetrate
deep into the ocean and solid Earth. They interact with terrestrial atoms producing secondary
cosmic rays of subatomic or high-energy particles.
Intensities of cosmic rays vary with altitude, geological locations, and year. Generally speaking,
intensity at the equator is lower than that at a polar region. Cosmic rays cause interesting
phenomena such as aurora.
Skill Building Questions:
1. What are the components of primary galactic cosmic rays?
What are secondary cosmic rays?
2. What is the energy distribution among particles in the primary cosmic rays?
(Further reading and research required)
164
Leptons
First generation leptons are electrons, neutrinos and their antiparticles. All these are particles
emitted in the beta decay process.

What are higher generation leptons?
What are their masses and spins?
How were they discovered?

How do these particles relate to the fundamental particles of the material world?
In 1936, Anderson and his colleagues observed some denser tracks of positively and negatively
charged particles in the cloud chamber than those made by electrons and positrons. They
thought there were two types of electrons, and they calculated their masses to be 1/9th of that
of protons, or almost 207 times heavier than that of electron. In additional to antielectrons,
they have discovered the electron-like muons.
Muons are charged, and they lose energy by knocking electrons out of atoms (ionization).
Muons were at first thought to be pions, the particle predicted by Yukawa in 1935 as the
strong force carriers. However, muons never interact with nuclei, but decay by the weak
interaction with a lifetime of 10–6 seconds into electrons, electron neutrinos (1st generation
leptons) and muon neutrinos,
 +  e+ + e + 
 –  e– + v e + v 
These properties made muons the second-generation leptons, not strong force carriers.
The third generation lepton tau was discovered in the
Leptons
collision between high-energy (3.6 GeV) electronGenerations
positron beams. Properties of taus are similar to
1st
2nd
3rd
those of electron-positron, muon antimuon pairs
e–, e+ –, + –, +
except that their masses are 3500 times those of
v e, e  v ,  v  , 
electrons, 20 times those of muons, and 2 times
those of protons. The pair discovered by Martin Perl
and his colleague working at SPEAR are called taus,
s,  being the first letter for the Greek word “third”.
Their existence has been predicted, and we believe that they should have their own
accompanying neutrinos. Their discovery in 1974 expanded the number of leptons to six (12 if
antiparticles are considered separately) in three generations.
The rest mass for tau is 1.784 GeV. Taus have many decay modes, and their decays produce
electrons, muons, or hadrons. The pure following leptonic decays of taus are not very
common, but they have been observed,
165
–  e– + v e + v 
+  e+ + e + 
With the discovery of the taus, three generations of leptons are known. The electron, muon,
and tau masses are 0.511, 107 and 1784 MeV respectively. These compared to a rest mass of
938 MeV for the proton. Unlike the electron, which appears to be stable, the muon decays
after an average lifetime of 2.2 microseconds into an electron, a neutrino, and an antineutrino.
This process, like the beta decay of a neutron into a proton, an electron, and an antineutrino,
occurs via the weak nuclear force. Neutrinos at every generation are produced in the decays,
and whether the neutrinos have a mass is an important question.
Skill Developing Questions
1. What are muons?
What their charges and masses are and how do they decay?
What are the second generation leptons?
2. Why is the third generation electron equivalent called tau?
Is it possible that tau particles are present in the cosmic rays?
Masons
Using photographic emulsions as detectors for the study of cosmic rays was C.F. Powell,
working in the Cavendish Laboratory of C. Wilson, the inventor of the cloud chamber. They
recorded precise tracks of many particles in his photographic emulsions. In some of the plates
they exposed to cosmic rays carried high up by balloons, they observed some tracks similar to
muon but slightly heavier, 1/7th (as opposed to 1/9th) of the proton mass.

What did Powell discover?
What are the properties of these particles, and into what do they decay?
These particles are unstable, and after traveling a fraction of a millimeter, decay into muons.
Powell' group thought they discovered the strong force carrier pion that had been previously
predicted by Yukawa as strong force carriers. As we shall see later that pions decay into
leptons, and they are not strong force carriers.
What Powell discovered turned out to be pion plus ( +) and pion minus ( –), which are
unstable with average lifetimes of 10–8 seconds. They travel a very short distance in the
emulsion before decaying into muons, accompanied by muon neutrino or antineutrino,
different from electron neutrinos.:
 +  + + 
 –  – + v  .

Powell, Cecil Frank (1903-1969) winner of the Nobel Prize for Physics in 1950 for his development of the photographic
method of studying nuclear processes and for the discovery of the pion (pi-meson).
166
These are most common modes of decay. Pions + – and muons + – are particleantiparticle pairs.
Muons are often referred to as heavy electrons and heavy positrons, 207 times heavier. Muons
and muon neutrinos (4 particles) are the 2nd generation leptons, similar to electrons and
electron neutrinos.
Pions decay by another mode,
converting to electrons and
positrons accompanied by the
emission of electron neutrinos and
antineutrinos
 +  e+ + e
Bubble Tracks from Decay of K–
Interpreted for the Presence of 0
e+
e–
 –  e– + v
Lead plate
A neutral pion (pi-zero),  0, has a


short lifetime of 10–-16 seconds
–
(compared to of 10–8 seconds for
0
the charge pions). Thus, its
detection was much more difficult
K–
than the charged pions. Two years
later R. Bjorkland and colleagues of
  e+ + e –
the Lawrence Berkeley Laboratory
0  
(LBL) discovered 0. They
bombarded metal targets by
K–  0 + –
accelerated protons, and the
experiments produced many pions
with their tracts recorded by a hydrogen bubble chamber. They observed tracks corresponding
to the diagram shown here together with many other (not shown) tracks on the same
photograph. The 0 left no tracks, neither did its decay products, two  photons. The two pairs
of positrons and electrons produced by the  rays when they struck the lead plate implied the
existence of the  photons from 0 decay as predicted. They further calculated all the energy of
the decay products, and the results matched the decay scheme as shown. The diagram on the
left shows only the tracks, but particles of the tracks are indicated on the diagram on the right.
The rest masses of the three pions 0, +, and – are 134.97, 139.57, and 139.95 MeV
respectively. The similarity of their rest masses suggests that they contain similar quarks: (0:
u u or d d , often represented as (u u - d d )/2; –: d u ; +: u d ). As a summary, their decay
modes are given below:
o   + 
 +  e+ + e
 –  e– + v e
167
G. Rochester and C. Butler discovered
Dark Lines Imitating Kaon Tracks
Kaons in 1947, from tracks recorded in
Observed in 1947
their cloud chamber at Manchester
K+
University. Gamma rays leave tracks in
cloud chambers, but not in bubble
K0
chambers. They saw two -ray tracks
Lead Plate
Lead Plate
originating from the same point forming a
V, and they thought a particle of zero
charge named kaon, K0 was responsible for

+
the gamma rays. A track with a sharp kink

appeared on another photograph. After
their analysis of these tracks, they
concluded that a kaon-plus has decayed
into a muon and a muon-neutrino. The latter leaves no tracks in the cloud chamber. Diagrams
are sketched to convey images of their observed tracks, but photographs are much more
complicated.
Kaons, like pions, are mesons. Their masses are intermediate between those of electron and
that of nucleon. Kaons are heavier than pions. Their masses are: K0 498 MeV, K, 494 MeV.
The discovery of kaon confirms the presence of a heavier quark strang. Kaons have many
decay modes
K0  2 
or  + + –
K+ + + v
K– – + v 
or  + + 0 or  + + ++ – or  0 + e+ + ve
or  – +0 or  – + ++ – or  0 + e– + v e
The transition, K0 + + – is forbidden, because the strangeness S is 1 before the decay, but
S is 0 after the transition. The strangeness is attributed to the strange quark (s) for kaons. The
process can only decay by weak interaction. Thus, the lifetimes for kaons are in the order of
10–10 seconds, long compared to the lifetime (10–16 seconds) of 0. This behavior is due to the
strange quark and anti quark in the kaons.
Note that K+ and K– form a particle-antiparticle
pair, whereas the antiparticle of K0 is K 0.
Light Mesons with JP = 0–
S
ds
us
Binding by gluons, a quark and an antiquark forms
K0
K+
a meson. Ideally, three quarks (d, u, and s)
uu or dd
combine to give a total of 8 (23) mesons, but two
du –
0
+ ud
I3
of the combination give rise to the same meson 0.
–
0
K
K
Their relationship led to the Eightfold Way,
su
sd
proposed by Gell-Mann and Ne'eman in 1961,
given in the diagram here. Quark-compositions of
mesons have been given in the summary earlier and the diagram. The diagram is more
interesting if you notice the directions in which the quantum numbers change. The strange
quantum number S (1 for K0 and K+, 0 for ’s and -1 for K–, and K 0) and spin quantum
168
number I3 (-1 for –, - ½ for K0 and K–, 0 for p0, ½ for K+ and K 0, and 1 for p+) change
systematically. Since the angular momentum quantum numbers J for these particles are 0, and
parity P = -1, the state JP is represented by 0–.
Furthermore, high-energy collision experiments between particles and antiparticles have
produced excited states of kaons: *K–, *K0, *K+ with mass ~890 MeV, and excited states of
pions called rho (–, 0, & +, mass ~ 765 MeV). These excited states correspond to the same
set of 8 mesons described earlier, but their angular momentum quantum numbers J = 1 with
parity P = -1, thus, J P = 1– compared to J P = 0– for ground-state pions and kaons.
Formations of groups of mesons and excited mesons suggest the existence of a quark charm.
Other mesons J/psi (J/), D0, D+, and Upsilon (Y) were discovered in 1974, 1976, and 1977
respectively. The existence of J/ signifies the existence of the charm quark.
Review Questions:
1. Make a table listing all properties of pions and kaons?
2. What are the quark compositions (qq), charges (Q), and spins (I) of mesons? Make a table for them.
3. How can the masses of pions and kaons be explained in terms of quarks?
Gauge Bosons as Force Carriers
Photons have been known as electromagnetic force carriers since the 1920s. While mediating
electromagnetic interactions, they manifest themselves as radio, IR, visible, X- and  rays.

What are force carriers?
Does the gravitational force have a force carrier?
Are there equivalent force carriers for the strong and weak interactions?

What will be produced when high-energy particle-antiparticle pairs annihilate?
In 1972-3, high-energy particle experiments indicated that neutrinos interact with nuclei
causing some of them to move slightly. A neutral force is responsible for this interaction. The
weak interaction may be mediated by a neutral particle, and Z0 has been suggested as the weak
force carrier. S. Glashow, A. Salam, and S. Weinberg united electromagnetic force with the
weak force in their electroweak theory. The observation and theory gave the scientific
community the confidence to award them the Nobel prize for physics in 1979, although the
three force carrier particles, W+, W– and Z had not been observed at the time. Their masses,
however, have been estimated to be about 90 GeV (actually 83.3 and 91.1 GeV for W and Z
respectively given earlier in this Chapter). The discovery of positrons, antiprotons, and
antineutrons excited many researchers in the high-energy research community, because they
expected the collision and annihilation to produce new particles.
Charged particles and antiparticles are ideal for particle accelerators and collision experiments.
These particles can be accelerated in opposite directions using the same electric and magnetic
169
fields, stored in ring-shape paths, and focused to collide head-on with each other. Energy from
the annihilation of high-energy particles produces new particles.
Accelerators making use of e– and e+ were
Adding a Ring to a Linear Accelerator
built in many research centers. Attached to the
famous 3-km Stanford Linear Accelerator
SPEAR
Center (SLAC), the Stanford Positron
Electron Asymmetric Rings (SPEAR) was
SLAC
added to store high-energy electrons and
positrons from the SLAC for collision
experiments. This was a joint project between
Princeton and Stanford. In other projects, the
Brookhaven National Laboratories (BNL) on
Long Island, New York, the Deutsches
Elektronen Synchrotron Laboratory (DESY), the European Center for Nuclear Research
(CERN) are some of the many laboratories making use of the electron positron beams. Later,
p and p were accelerated to 30 GeV in Fermilab in Chicago. These experiments led to the
discovery of many particles, including W+, W– and Z, which were observed in 1983 and 1984
by teams working in DESY. The tau boson mentioned earlier is also produced by accelerated
particles.
The formation of W and Z can be written as
p + p  W+ + H–
p + p  W– + H+
p + p  Z0 + H0
where H represents one of the hadrons such as proton, antiproton, or neutron, or others.
Theory indicates that the W and Z particles have very short lifetimes, ~ 10–24 seconds. The W
and Z so produced decay by emitting electrons, positrons and muons, and their corresponding
neutrino and antineutrinos. These heavy bosons have many modes of decay and they also emit
protons and neutrons as accompanying particles. For example,
W+  l+ + l ; ( l = e,  or )
W–  n + – + v e (n = neutron)
or
Z0  + + – + v  + 
Z0  hadrons
Discoveries of W, and Z convince us that there are four types of forces interacting among
various particles:
Gravitational force: the long-range force that stabilizes the solar system and governs the
motion of stars and planets in the universe. This force is acting on all matter including
subatomic particles, but due to their tiny mass, the force is insignificant compared to other
types. Physicists suggest the graviton as the force carrier, but the method for its detection has
not been invented. If gravitons exist, they are everywhere.
170
Electromagnetic force: the long-range force that stabilizes the atomic system of nuclei and
electrons. This is also known as the Coulomb interaction. The strength of the force is
proportional to the charge, not to the mass. Electric charges experience forces exerted by each
other via photon exchanges. Photons can be absorbed, or scattered elastically or inelastically.
Photons are the force carriers of electromagnetic force.
Strong interaction: the force that stabilizes the atomic nuclei and among quark containing
particles. In the 1930s, based on the distance (10–15 m) between nucleons. H. Yukawa
estimated the force carriers of strong interaction to be pions () with a mass of 1/7th of a
proton. Later, 8 gluons not pions were suggested and confirmed to be the strong force
carriers, exchange of which gives rise to the strong force. These carriers exchange between
particles such as quarks that have a property called color. There are 8 colors and 8 types of
gluons*.
Weak interaction: the force creates electron before its emission from a nucleus as a beta
particle. Compared to the strong interaction, the force exerted by weak interaction is only
some percent of strong interaction, and thus so named. The force carriers are W+, W–, Z. A
summary is given in the table below:
Type
Gravity
Electromagnetic
Weak
Strong
particles
Act on
carrier
All particles
Charged
particles
All particles
Colored
The Basic Forces
Force
Range
Strength
System
Graviton, g
Photon, h v
1/r2
1/r2
10-39
1/137
Solar system
Atom
W and Z
Gluon
<10-17 m
<10-15 m
10-5
1
Atomic
nucleus
Skill Building Questions:
1. Which one of the four forces is always present for any particle?
Which one is only acting on nucleons?
2. What is the force carrier of electromagnetic force?
What are force carriers of weak interactions?
3. Why are particle and antiparticle pairs ideal to have for particle accelerators?
4. How are W+, W–, Z particles produced?
*
A news release read: The 1995 EPS High Energy and Particle Physics (HEPP) Prize has been awarded to Paul Söding,
DESY-Institute of High-Energy Physics, Zeuthen, Björn Wiik and Günther Wolf, Deutsches Elektronen-Synchrotron
(DESY), Hamburg, and Sau Lan Wu, University of Wisconsin, Madison, WI, USA, for the first evidence for three-jet events
in e+e- collisions at DESY's PETRA collider while working with the TASSO Collaboration.
171
Feynman Diagrams
Feynman represented transformations and interactions of particles by diagrams based on
mathematical and theoretical considerations. Feynman diagrams are particularly useful to
convey particle physics ideas, because they let us visualize the particle process.

What do Feynman diagrams show?
How do particles interact with one another?
Feynman diagrams show the interactions of particles by way of force carriers. Solid lines
represent particles (usually Fermions), and zigzag lines represent force carriers (bosons).
Normal progressing in time goes from the left to right. An arrow pointing to the right
represents location change of a particle as time progresses, and a left-pointing arrow represents
a particle moving in reverse time. When the arrow or line changes direction, the particle
changes state.
For example, the Feynman diagram
Feynman Diagram for Electron Scattering
representing the scattering of two electrons is
space
shown here. The electron e emits a photon,
which is absorbed by e’, because the zigzag
line moves to the right. The two electrons
e
experience the presence of each other by

exchange the photon. This diagram represents
the interaction of any charged particle via a 
e’
photon.
time
For the strong interaction between quarks via
the force carrier gluon, a similar diagram may be used. The solid lines represent quarks, and the
zigzag line represents a gluon. For strong interactions, types of gluons must match the types of
quarks. The types are often labeled by colors: red, green, yellow, etc. reflecting the colour (a
property) of quarks.
Feynman Diagram for the Stable
Hydrogen Atom
electron
proton
The interactions between the proton and the
electron in a hydrogen atom are the constant
exchange of photons between the two particles.
The Feynman diagram is shown here. Since no
photon is absorbed or emitted, this state is stable.
Of course, when a photon is absorbed or emitted,
the process can also be represented by zigzag lines
entering or leaving the stable hydrogen atom.
Feynman diagram let us visualize the mystery of
force, force carriers, and change of state.
172
Feyman diagrams for the decay of kaons into pions
with emission of electrons and positrons,
Feynmam Diagrams for Kaon Decays
K–  0 + e– + 
K+  0 + e+ + ,

e
are given here. The two diagrams are essentially the
same, if the positron is equivalent to an electron
moving backward in time. We simply represent the
neutrino by  in both cases. On the other hand, we
may also reverse the arrow for antineutrino, and make
the diagrams look different. There are many ways to
draw Feynman diagrams. A process may take place in
various time sequences, and each may be represented
by a Feynman diagram. In his book (see Further
reading) QED, Feynman drew the time axis vertically,
and the space axis horizontally. The choice is a
personal preference as long as his guide lines are
followed.
The beta decay is a process involving weak
interactions. In this process, a neutron is
converted into a proton, with the emission of an
electron. If we look at the quark level, a neutron
(udd) and a proton (uud) differ by one quark.
Converting a d quark in neutron into a u quark
changes the neutron into a proton. The force
carrier W– mediates the conversion of a quark d
into u. The charge on a d quark is -1/3, and the
charge on a u quark is 2/3. Thus, the net charge
change is –1, which is emitted as the  particle.
–

K–

e+

K+
Feynman Diagram for Beta Decay
v
e
e–
W–
udd
uud+
Skill Building Questions:
1. Draw a Feynman diagram for the electron-positron annihilation process producing two photons.
2. Draw a Feynman diagram for the pair production process of gamma rays.
3. Draw a Feynman diagram corresponding to the reaction: e– +   e– + .
What is the force carrier in this case? Explain your choice.
Particle Weak Interactions and Decay
Feynman diagrams shows the similarity between strong and weak particle interactions.
However, the two interactions have their unique features.
173

How can the strong and weak interactions between particles be distinguished?
Usually, formations of particles and their decays are represented by a equation. For example,
n + e  p+ + e–
The force of interaction between particles can be a strong or a weak force.
A reaction involving only strong forces rearranges quarks or creates quark-antiquark pairs
from other quark-antiquark pairs. Rearrangement does not change one type of quark into
another type. The following two processes rearrange quarks by strong forces.
0 + n  p+ + –
u u + udd = uud + d u
K– + p+  0 + 0
s u + uud = uds + u u
An example of creating a quark-antiquark pair from other quark-antiquark pair is given below:
– + p+  K0 + 0
d u + uud = d s + uds
In this case, a gluon converts u u in to s s .
In reactions or decays involving weak interactions, a weak force carrier is involved. The force
carrier can convert one type of quark into
The Feynman Diagram of
another type of quark. For example, the decay
a Weak Interaction
of L0 is such a case.
u
L0  – + p+
uds = d u + uud
In this process, s is converted into d mediated
by a weak force carrier W–, which decays into a
u u pair. The five quarks split forming a +, –,
and a proton p+. A Feynman diagram is shown.
s
u
d
Skill Building Questions:
1. What causes particles to decay?
2. Exemplify reactions mediated by a strong force by weak force carriers?
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W–
u
d
u
d
Exercises
1. What is an antiparticle? How did the concept of antiparticle come about? How is a particle
different from its antiparticle?
2. Give the mass, charge, spin, magnetic moment, and parity for electron and a positron:.
3. Make a table listing mass, charge, spin, magnetic moment, and parity of protons,
antiprotons, neutrons, and antineutrons.
4. Is the process of converting a pair of proton and antiproton into neutron and antineutron
exothermic or endothermic? How much energy is required or released in this conversion?
How can the energy be supplied or removed in this process?
5. Give six particles for each of these categories: gauge bosons, leptons, mesons, baryons.
6. What study leads to the requirement quarks? What are quarks?
7. What are leptons, hadrons, mesons, and baryons?
8. How many mesons can be made up using u, d, and s quarks? What are these mesons?
9. How many baryons can be made up using u, d, and s quarks? (Further reading and
research is required.)
10. How many u and d quarks do the nuclei of 2D, 4He, 56Fe, and 235U have?
11. What are the products for the annihilation of a proton and an antiproton? Write an
equation to represent the reaction.
12. What are the forces acting between particles? What are the force carriers in each case?
What force binds the quarks and antiquarks in mesons?
13. What baryon have +1, 0 and -1 charges?
14. What is the most abundant particle in galactic cosmic rays? Protons at what energy are
most common in cosmic rays? What are secondary cosmic rays?
15. Give the decay scheme of pions and kaons.
16. How are an electron and a positron represented in a Feynman diagram.
17. Draw Feynman diagrams for the scattering of an electron by a proton, annihilation of an
electron-positron pair, and beta-decay process.
175
Further Reading and Literature Cited

The Particle Explosion, by F. Close, M. Marten, & C. Sutton, Oxford University Press (1987).
This book has fantastic photographs of particle tracks in cloud chambers, emulsions, and
bubble chambers.

QED, The Strange Theory of Light and Matter, by Richard P. Feynman, Princeton University
Press (1985).

The Particle Data Book, published every two years; the most recent edition is Physical
Review D Vol.54, page 1-720 (1996). Many topics are given in this biannual review, and it
lists details of the properties of particles. Some of the reviews in it are very interesting.
These articles and tables are also available on the inter-net. For example:
Particle Properties Data: http://pdg.lbl.gov/
Particle Physics Booklet: http://pdg.lbl.gov/rpp/booklet/contents.html
Particle Properties: http://durpdg.ac.uk/hepdata/part
Computer Readable Files: http://pdg.lbl.gov/computer_read.html
Standard Model Matter Particles:
http://www.pdg.lbl.gov.80/www/cpep/sm_matter_particles.html

A Tour of the Subatomic Zoo, by C. Schwarz, American Institute of Physics (AIP, 1992). l

Introduction to High Energy Physics, by Perkins .

Experimental Foundations of Particle Physics, by Cahn and Goldhaber.
Internet sites
About hypernucleus.:
http://www.phy.bnl.gov/~bnlhyp/me.html
Nobel prize about quarks:
http://www.nobel.se/laureates/physics-1990-press.html
The particle adventure home page containing animations
http://wwwpdg.cern.ch/pdg/cpep/adventure_home.html
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