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Chapter Four Introduction to Particle Physics
4.1. Four basic questions
The development of particle physics is mainly dedicated to find the answers to
the following 4 basic questions:
Q1. What holds matter together?
Four forces responsible for all phenomena and they have different strength.
a) Strong force: inside a nucleus, exists between nucleons, or between quarks.
If we set the strong force between two particles is 1, then:
b) Electromagnetic force is 10-2, and restricted to electrically charged particles
and holds atoms/molecules together.
c) Weak force is 10-8 , exists in radioactive decay and nuclear fusion of subatomic
particles.
d) Gravitational force is 10-45 , exists between particles of mass (all particles).
Q2. How is a force transmitted between particles without direct physical
contact with each other?
In classical physics, the concept of ‘field’ is used, resulting in action at distance.
A particle, by virtue of its presence somewhere, modifies the physical properties
of the space around it, i.e. it ‘creates a field, a second particle, at distance r away,
is embedded in this field. The field ‘acts’ on this second particle. The second
particle experiences the force acted on it by the first particle.
However, when investigating the interaction between particles inside a nucleus,
for example, continuous field theory doesn’t work, because the elementary
particle world is governed by Quantum Mechanics.
In 20th century, particle physicists (quantum mechanics) use the concept of
‘exchange force’: two particles interact with each other by exchanging a (virtual)
particle between them. An exchange particle (‘field quantum’) is created (and
emitted) by one of the interacting particles, is absorbed by the other. This
process produces the interaction specific to an interaction (different exchange
particle is for different interaction).
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As shown in the following figure:
Two ice skaters can push each other apart by
throwing a ball between them. The person on
the left is pushed back when he throws it. The
other on the right is pushed back when he
catches it.
This exchange particle is called a “ virtual “ particle (we may not see it)!
How can energy be conserved during this creation? In Quantum theory: The
uncertainty in energy measurement E is related to the uncertainty in time
measurement t is by Heisenberg uncertainty Principle (HUP):
h
 
2
No extra energy is needed to create it! It is from one particle to another particle
and may exist for short enough t between creation and absorption, for its
energy E to obey HUP and thus not violate energy conservation.
Et 
Q3. How do we describe the physical properties of a particle?
The world of elementary particles is governed by quantum mechanics in which
the physical state of a particle is specified by Quantum numbers.
They are quantised properties of particles that are subject to constraints:
--electric charge: in unit of e;
--energy: quantised by an integer n, E(n);
--angular momentum: in unit of
=1.05457172 × 10

h
, which
2
is called Plank constant
(Js)
--spin of a particle (angular momentum of self rotation):
Bosons: S =0, 1  , 2  , 3  , ……………………
Fermions:
=
 ,  ,  ,  … … ….
There are many more quantised quantities we will know later to describe
different physical properties of elementary particles.
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Q4. Is matter infinitely dividable?
For over 2000 years, people have thought about the fundamental particles from
which all matter is made, starting with gradual development of atomic theory,
followed by a deeper understanding of the quantized atom, leading to the recent
theory of the standard model.
The answer to this question is limited by our knowledge about elementary
particles at different period of time.
In 1920s, we thought p, n, e- are elementary particles, which are undividable.
We now follow the steps of the historical development of particle physics, to
explore the structure and physical features of the elementary particles.
4.2. Neutron Beta decay discovery of Neutrinos
In 1920s, the reaction was found to occur under a certain
physical condition.
as shown by the vertical line in the figure.
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The energy spectrum of the electrons was expected to be a line spectrum.
However the observed is a continuum spectrum, shown by the black solid curve.
Some amount of the energy got lost!
The observed continuous energy spectrum of the electrons appeared to violate
E&P conservation laws, or which inferred unseen product particle. Then it was
suggested that a particle called electron anti-neutrino must be produced to carry
the lost energy,
Now rewrite the reaction equation:
The kinetic energy of electrons: KEe = m c2 – Ev(neutrino)
Since the anti-neutrinos can carry different amounts of energy (Ev ), the kinetic
energy carried by different electrons is different. Therefore the kinetic energy
KEe of the electrons shows a continuous distribution . Neutrino is a type of
elementary particle much smaller than a neutron, without carrying charges. It is a
fermion particles of spin S number of ½. It was originally thought to be mass less,
but it is now known that it carries a very small amount of mass: ~ 0.1 eV/c2 .
Later on, it is found that there were three different types of neutrinos, i.e.,
e,  and  .
4.3 Atomic stability—> discovery of photons
Why are atoms stable? –
F 
q1 q 2
4  0 r 2
Electrostatic force between a nucleus (+ve) and electrons(- ve). If we further
ask: How is this force transmitted between two charged particles not in direct
physical contact with each other?
For this electromagnetic interaction field, the predicted exchange particle is
called photon – another elementary particle!
In Quantum Electrodynamics, charged particles interact by the exchange of
virtual photons, photons that do not exist outside of the interaction and only
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serve as carriers of momentum/force.
Photon is a boson with spin number |S|= 1, massless and zero charge.
4.4 Nuclear stability discovery of pions
If we consider in a nucleus, there are only positive charges, protons, according
to the EM theory, the field of a positive charge exerts a repulsive force to another
positive charge, but why is the nucleus is stable? Why doesn’t it fly apart?
Yukawa potential ( in 1935) suggested a form of the relevant potential function
r
A
V (r )   e R
R: the range of the
r
same form as coulomb potential.
nuclear force, A: constant, which is of the
The question raised was what is the quantum particle of the nuclear force field?
Prediction of the exchange particle for nuclear strong force starts from work on
what is the quantised energy of the particle for the strong nuclear force?
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Use the range of nuclear force: 1.5fm=1.5*10-15m .
The longest time t a particle could exist, if moving with speed of light c, and a
x 1.5  1015 m
t 

 5  10 24 s
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c
3  10 m / s
The corresponding energy E related to t by the HUP, would be:
 1.051034 J .s
1
E  
 131MeV
 24
13
t
5 10 s 1.6 10 J / MeV
This predicted (in 1935, by Hideki Yukawa) a new particle of 131MeV rest
energy. In 1947, a new particle called pion is discovered and the measured rest
energy
Therefore Pion was thought as another type of “elementary particle” !
Later on, it was found that there were three types pions:
m(  )  m(  )  140MeV/ c2 ; m( 0 )  135MeV/ c2
Pions have different charges, e, and 0. ---They are all bosons, have spin
number 0.
4.5 The decaying of pions Muons
The muon is produced in the upper atmosphere by the decay of pions produced
by cosmic rays.
With a lifetime: 2.20x10-6s; m(+)=m( -)=105.7MeV/c2
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They are unstable and decay into electrons and neutrinos:
v and ve are different particles, v are associated with muons and ve are
associated with electrons in reactions.
4.6 Weak Interaction W+, W-, and Z particles
Let’s go back to the beta decay, which led to the discovery of neutrinos.
Question: what interaction causes beta decay?
The decay Involves neutrinos, but neutrinos experience neither strong nor
electromagnetic interactions.
Also more such decays were discovered:
But everything that happens, every reaction and decay, is caused by something
‘interacting’ with something else.
There must be a new type of interaction, the so-called weak interaction, which
exists between muons, electrons and neutrinos, and causes beta decay and some
other types of decay processes.
Later, it was found that the carrier particles of the weak interactions are the
W+, W-, and the Z particles.
--The W's are electrically charged () and the Z is neutral.
-- They are bosons with spin number |S|=1.
-- heavy particles, with masses of m(W+) = m( W-)=80GeV/c2, m(Z)=91GeV/c2.
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After that, a lot of new particles appear in pairs, they are called particles and
antiparticles.
4.7. Particles and Antiparticles
Since the first positive electron (position) discovered by Carl Anderson in 1932,
From observations and lab experiments, it is found that particles come in pairs.
Antiparticle has the same mass and spin number as its opposite particle, but
opposite charge, and other charge-like quantities:
Particles
----------------- Antiparticles
proton p
---------------- antiproton
Neutron n
---------------- antineutron
Electron e-
----------------- positron e+
Electron neutrino e
----------------- electron antineutrino
Muon minus -
------------------ muon plus +
Muon neutrino 
------------------ muon antineutrino
Pi minus -
----------------- pi plus +
Pi zero 0
----------------- pi zero 0
Photon 
----------------- photon 
Parti. + anti.parti. - annihilates  produce other kind of particles.
It is interesting to see that a neutron has an antiparticle too, the difference in
their sub-structure will be known later after standard model of particles physics is
introduced.
4.8. Discovery of Strange Particles
In 1947, Rochester and Butler reported so called V0 events in cloud chamber
experiment with charged cosmic particles hitting a lead target plate, many
different new particles were produced.
 - + p+   + K0
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These produced new particles were called hadrons and were classified as two
groups:
Baryons: particles with half-integer spin number;
Mesons: particles with zero or integer spin number;
Theoretical calculation showed that the neutral particles were produced with
large reaction cross-section area, so this reaction is via strong force
interaction.
 particle has a short half-life time 1/2 = 2.6*10-10s,
 p+ +  -
K0 particle has a shorter half-life time 1/2=0.9*10-10s, K0   + +  Theoretical calculation showed that the cross section area for these decaying
processes was very small, so they were via weak force interaction.
These particles are called strange particle because their formation (, K0 etc) is
via strong interaction but their decaying via weak interaction.
Abraham Pais in 1952 suggested introducing a new quantum number called
Strangeness S for all of these found strange particles, with the following rules:
a) every of strange particle is offered a quantum number called Strangeness
quantum number, e.g.,
+, -, 0,: S = 0
p, n,:
S=0
:
S = -1
K:
S=1
b) In the strong interaction, S is conserved, S = 0.
In weak interaction, S is not conserved, S  0 .
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K and  are not the only strange particles. By 1960s, more strange particles were
discovered as listed in the following:
--8 (at the time) particles with strong interaction and spin (1/2) (baryons); and
--9 strongly interacting particles with spin 0 (mesons) .
In 1960s, more than 200 new particles were discovered. Physicist realized that a
more important issue was actually:
Q: are they ALL elementary ?
A physicist called Murray Gell-Mann (at the
same time also Yuvan Ne’eman) observed
patterns of symmetry in the discovered
mesons and baryons.
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He plotted the spin ½ baryons and spin 0 mesons in so-called octets. There is a
similarity between Mendeleev’s periodic table of elements and the super
multiples of particles of Gell Mann. Both
pointed out a deeper structure of matter.
The strangeness QN is plotted vertically and
decreases from 0 to -2. The red parallel lines
are for charges of baryons.
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4.9 Quark model:
To explain the structures of baryons & mesons: 3 quarks called ‘up’, ‘down’,
‘strange’, and three of their ‘anti-’s were suggested. All of quarks are Fermions
(with spin number: ½)
-- A baryon consists of 3 quarks: (q1q2q3), while a meson consists of (
).
Because 2 quarks cannot make baryon of Q=integer, and S=-2, so a set of three
quarks have to be used.
--Mesons can be their own anti-particle (
) =(
,
), baryon cannot.
Now let’s how these strange particles can be combined:
For a neutron n: strangeness Quantum Number (QN): S = 0 , Q =0,
it is composed of three quarks (udd): S=0+2*0=0, Q=2/3 +(-1/3) +(-1/3)=0.
For a proton: p: strangeness QN: S=0, Q=1,
It is composed of three quarks (uud): S= 0+2*0 =0, Q=2*2/3-1/3 = 1.
Now we can explain the question why a neutron has its anti-particle,
which is different from n.
=( , , ̅ )
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For Mesons: Ko: S=1, Q=0, (d, ̅ )
S=0+1=1, Q=-1/3 +1/3=0.
We now can deduce the total number of mesons and baryons there should be
according to the defaulted quark combinations.
For mesons’ structure is (
) , three different quarks and anti-quarks can be
arranged in two positions, there should be 3*3= 9 different combinations.
Therefore we have found 9 mesons.
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However for baryons, (q1q2q3), there should be 3*3*3 different combinations,
which means there should be 27 baryons, why there were only 8+9=17?
It turned out that the other 10 baryons were found later.
Now we can construct a picture of particle hierarchy.
We are in place to understand the so-called standard model of particles.
4.10. Standard model-- elementary particles
We now know that the structure of newly discovered hadrons are composite
particles by using 3 quarks and their anti-quarks. The investigation of particle
physics revealed that In order to explain all of the structure of known particles,
another 3 quarks and their anti-quarks has to be introduced, together with 6
leptons (means ‘small mass’ in Greek) particles. Everything in the universe is
made from quarks and leptons. The following table shows a summary of the
properties of these quarks and leptons.
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-- All quarks and leptons have antiparticle partners with all of the quantum
numbers reversed, but with the same masses.
Quarks behave differently from leptons. Let’s first discuss the properties of
a) Leptons – small mass particles:
L
Le
L
L
M (MeV/c2)
e-
1
1
0
0
0.5

1
0
1
0
106

1
0
0
1
1784
e
1
1
0
0
0.1-a few 10-6

1
0
1
0
0.1-a few 10-6

1
0
0
1
0.1-a few 10-6
It is worth noting that
decay.
and
are not elementary particles, because they can
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Charge: three of leptons have electrical charge and three of which do not.
Decay: The heavier leptons,  and , are not found in ordinary matter at all, for
when they are produced they very quickly decay, or transform, into lighter
leptons.
All anti-leptons have negative sign for all of the 4 lepton numbers.
When heavy leptons decay into lighter lepton:
--L, Le, Lu, L QNs must be conserved;
--A particle and an antiparticle in the same family "cancel out" to make the
total of them equal to zero.
Which of the following lepton decaying is possible (assuming decaying particle
is initially motionless, v =0) ?
Therefore this decaying is possible.
Because L: 0 1+0; and L : 1 2;
Now try a tricky one:
L, L, Le, momentum are all conserved, Energy: m(e) << m (-1) mic2 << mfc2
 + n e+ + e- + n pair electron production
Le: 0 0  -1 +1 + 0
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+  + + 
pion decay
L: 0  -1
+1
b) Quarks: are sociable and only exist in composite particles with other quarks
Six different Quarks, up, down, charm, strange, top and bottom.
Electric charges: each of them has fractional electric charge.
u,d, and t have 2e/3, d, s and b have -1e/3.
Like social elephants, quarks only exist in groups with other quarks and are never
found alone. Composite particles made of quarks are called Hadrons.
Since quarks cannot exist in isolation, the notion of "mass" is not very well
defined.
Top ~ 175 GeV;
Charm - 1.5 GeV ;
up - 2- 8 MeV;
Bottom: 4.5 GeV
Strange: 100-300 MeV
down: 5 - 15 MeV
Although individual quarks have fractional electrical charges, they combine such
that hadrons have a net integer electric charge.
For example: p has a mass of 0.938 GeV: its quarks’ composite is:
u+u+d = p
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But the sum of the mass of its composite quarks:
0.003 + 0.003 + 0.006 =0.012 GeV << 0.938GeV.
Most of the mass in Hadrons comes from the KE and PE, which converted into
mass according to Einstein’s E-Mass formula.
Only very small part of the mass of a hadron is due to the quarks in it.
In general, Quarks and leptons can be arranged in 3 ‘generations’ according to
their stabilities, from left to right of the table particles. Normal particles are
made of members in G1 and other neutrinos, the 2nd generation particles are
unstable, they decay into G1 particles and neutrions; the third generation are
very unstable, they decay into G2 particles, if physical conditions allow.
Heavier quarks can only be created in high energy condition, such as in cosmic
rays.
Now we discuss the nature of the force exchange particles.
4.11 Standard model—Forces and their carriers
In the QM frame, forces take effect through exchange particles.—force carries.
Mesons are not fundamental particles, they are composites of quarks!
To a fundamental level, the question is: What holds quarks together?
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Quarks have electromagnetic charge, but it should not play a major role. (why??
A proton cannot exist if EM force plays a major role.)
Quarks also have a different kind of charge called colour charge. The force
between color-charged particles is very strong, so this force is "creatively" called
strong, which holds quarks together to form hadrons. The carrier particles for
the strong force are called gluons because they so tightly "glue" quarks
together.
While quarks have colour charge, composite particles made out of quarks have
no net colour charge (they are colour neutral).
Quarks and gluons are colour-charged particles, 
colour-charged particles exchange gluons in strong
interactions create a very strong colour force
field that binds the quarks together
So now we know that the strong force binds
quarks together because quarks have colour charge.
Furthermore we can understand what
holds protons and neutrons in a nucleus
together. Although positive protons repel
each other with electromagnetic force,
and protons and neutrons are colourneutral, the strong force between the
quarks in one proton and the quarks in
another proton is strong enough to
overwhelm the repulsive electromagnetic
force as shown in the picture.
This is called the, and it is what "glues" the nucleus together.
We have known the force carriers (exchange particles) for three types of force.
The only one not yet discussed is the exchange particle for gravity: Graviton
which has not yet found.
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However we still have questions about those force exchange particles, why some
of them are massless, but some of them are very heavy. Particles physicists have
suggested the existence of a kind of elementary particle called the Higgs boson, it
is the smallest possible excitation of the Higgs field – a field that takes a non-zero
constant value almost everywhere. The presence of this field can explain the
above and some other more fundamental questions. The Higgs particle has
recently been detected.
4.12 Quantum Numbers and conservation Laws
Whether a particle can decay into more basic particles or two particles can make
a new particle, depends on if their occurrence will break the conservation Laws.
e.g.,
6. Baryon Number
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Baryon Number B is conserved in Strong, EM and Weak interactions.
Total B No. before and after an interaction (quarks – antiquarks) is a constant.
7 Lepton number
Lepton number L is conserved in Strong EM and Weak interactions
L
Le
L
L
e-
1
1
0
0

1
0
1
0

1
0
0
1
e
1
1
0
0

1
0
1
0

1
0
0
1
Now let’s have a look at the occurring possibility for following interactions:
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***
1
n  p  ethis
 vdecay
e
L is conserved but neither Le nor Lu separately,
has not be observed.
***
n  p  e 1  ve
Le : 0  0 1 1
Charge, Energy, momentum conservation checking no problem, so it is observed.
***n  p + -1 , Q is ok, no Lepton involved, B is ok, but rest energy is not
conserved
E: 939.6938.3 + 139.6 (MeV/c2), energy is not conserved, except the n is
pumped to a very high energy to contain the requested 139.6 MeV/c 2. This decay
has not been observed.
***0  p - + +
Q: is ok, no lepton involved;
E: 1116 938.3 +139.6=1077.9 (MeV), with some energy lost to the kinetic
energy of the decayed particles.
B: +1  -1, not conserved! This is not possible.
***-1e-1 + 
Lu: 1 0+0; Le: 0 1+0, both not conserved! Decay is not possible.
*** -1e-1 + ve + vu
Lu: 1  0 +0+1; Le: 0 1 -1 + 0 so both conserved. The decay is possible.
4.13. Beyond the Standard model
The Standard Model answers many of the questions about the structure and
stability of matter with its six types of quarks, six types of leptons, and four
forces.
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The stand model is a good theory. Experiments have verified its predictions to
incredible precision, and all the particles predicted by this theory have been
found. But it does not explain everything, i.e., the Standard Model is not
complete, e.g. gravity is not included
There are still many unanswered questions
1. Why do we observe matter and almost no antimatter if we believe there is a
symmetry between the two in the universe?
2. Are quarks and leptons actually fundamental, or made up of even more
fundamental particles?
3. Why are there exactly three generations of quarks and leptons?
4. How does gravity fit into all of this?
What are particle physicists doing now is to try to find the solutions for the above
questions.
4.14. Grand Unified theory
Today, one of the major goals of particle physics is to unify the various
fundamental forces in a Grand Unified Theory which could offer a more elegant
understanding of the organization of the universe. Such a simplification of the
Standard Model might well help to answer our questions and points toward
future areas of study
James Maxwell took a big step toward this goal when he unified electricity and
magnetism, and physicists now understand that at high energies the
electromagnetic and weak forces are aspects of the same force.
In his later years Einstein attempted, but failed, to write a theory which united
gravity and electricity.
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