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Option J: Particle physics
J1 Particles and interactions
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Option D4
Particles and interactions.
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Option J: Particle physics
J1 Particles and interactions
Description and classification of particles
J.1.1 State what is meant by an elementary
particle.
J.1.2 Identify elementary particles.
J.1.3 Describe particles in terms of mass and
various quantum numbers.
J.1.4 Classify particles according to spin.
J.1.5 State what is meant by an antiparticle.
J.1.6 State the Pauli exclusion principle.
Option J: Particle physics
J1 Particles and interactions
Description and classification of particles
State what is meant by an elementary particle.
An elementary particle is one which has no
internal structure.
PRACTICE: At one time it was
thought that atoms were
elementary particles. Explain
why they are not.
SOLUTION: They have an internal
structure: Namely protons,
neutrons and electrons.
EXAMPLE: At one time it was
thought that protons and
neutrons were elementary particles.
Explain why they are not.
SOLUTION: Protons and neutrons are each built
from three elementary particles called quarks.
Option J: Particle physics
J1 Particles and interactions
Description and classification of particles
Identify elementary particles.
There are three major divisions in the
elementary particles that have been
identified, to date.
The force carriers are the particles
that allow compatible particles to
sense and react to each other’s presence
through exchange of these carriers.
The quarks are the heavier, tightly
bound particles that make up particles
like protons and neutrons.
The leptons are the lighter, more
loosely bound particles like electrons.
FYI
For example, quarks interact via the strong
force particles called gluons.
Option J: Particle physics
J1 Particles and interactions
Description and classification of particles
Identify elementary particles.
The force carriers:
There are four force carriers…
INTERACTION 1: STRONG: Strongest of
all the interactions between particles. We can
give it an arbitrary value of 1 for comparison.
1.0
INTERACTION 2: ELECTROMAGNETIC: This is the NEXT
strongest. In comparison to the strong interac0.01
tion, it has a relative strength of 10-2.
INTERACTION 3: WEAK: This interaction has a
relative strength of 10-6.
0.000001
INTERACTION 4: GRAVITATIONAL: This interaction
has a relative strength of 10-39.
0.000000000000000000000000000000000000001
Option J: Particle physics
J1 Particles and interactions
Description and classification of particles
Identify elementary particles.
The force carriers:
In 1933 Hideki Yukawa developed the
theory of exchange forces.
The basic idea is that all forces are
due to the exchange of particles
between like elementary particles.
Consider two protons in space.
Yukawa postulated that the protons
exchange photons and repel each other
because of this exchange.
FYI
This photon exchange is the electromagnetic
force.
Option J: Particle physics
J1 Particles and interactions
Description and classification of particles
Identify elementary particles.
The force carriers:
Yukawa explained that the electromagnetic force was long range (in fact
infinite in range) because photons
"live forever" until they are absorbed.
Yukawa explained that the strong force
was short range (in fact only in the
nuclear range) because the strong force
exchange particle (the gluon) has a
very short life.
LONG RANGE EXCHANGE PARTICLE
SHORT RANGE EXCHANGE (VIRTUAL) PARTICLE
Option J: Particle physics
J1 Particles and interactions
Description and classification of particles
Identify elementary particles.
The force carriers:
The following table compares the
exchange particles (force carriers) by
range and mass.
INTERACTION
RANGE
EXCHANGE PARTICLE
REST MASS
STRONG
10-15 m
GLUON g
120 MeV / c2
Electromagnetic

PHOTON 
0
WEAK
10-18 m
W+, W- and Z
80 GeV / c2
Gravitation

GRAVITON 
0
Option J: Particle physics
J1 Particles and interactions
Description and classification of particles
Identify elementary particles.
The quarks:
Although you have heard of protons and
neutrons, both of which react to the
strong force exchange particle (the
gluon), you have probably not heard of
most of the following particles:
Particle
Symbol
Particle
Symbol
Particle
Symbol
proton
p
delta
0
sigma
+
neutron
n
delta
-
sigma
0
lambda
0
delta
++
sigma
-
omega
-
delta
+
xi
0
FYI
With the advent of particle research the list of
new particles became endless!
Option J: Particle physics
J1 Particles and interactions
Description and classification of particles
Identify elementary particles.
The quarks:
In 1964 the particle model was looking
quite complex and unsatisfying. Murray
Gell-Mann proposed a model where all the
strong-force particles were made up of
three fundamental particles called
quarks.
Quark
u
d
u
proton
Flavor
Symbol
Up
Down
Strange
Charm
Bottom
Top
u
d
s
c
b
t
Charge
+
+
+
2/3
1/3
1/3
2/3
1/3
2/3
FYI
A proton is uud and a neutron is udd.
Option J: Particle physics
J1 Particles and interactions
Description and classification of particles
Identify elementary particles.
The quarks:
Each quark has an antiquark, which has
the opposite charge as the corresponding
quark.
FYI
Baryons are particles made up of 3 quarks or 3
antiquarks.
Mesons are particles made up of a 1 quark and 1
antiquark.
Option J: Particle physics
J1 Particles and interactions
Description and classification of particles
Identify elementary particles.
The leptons:
You are already familiar with two of
the six leptons: the electron and
the electron neutrino.
Leptons, unlike quarks, do NOT
participate in the strong interaction.
THE LEPTONS
Charged Leptons
Uncharged Leptons
electron
e
electron neutrino
e
muon

muon neutrino

tau

tau neutrino

FYI
Of course the leptons also have their
antiparticles.
Option J: Particle physics
J1 Particles and interactions
Description and classification of particles
Identify elementary particles.
The leptons:
The leptons interact only via the
electromagnetic force carrier, the
photon.
Leptons, unlike quarks, do not react
to the gluon.
Quarks react to both the gluon and the photon.
FYI
Leptons and quarks also react to gravitons.
Option J: Particle physics
J1 Particles and interactions
Description and classification of particles
Identify elementary particles.
The Higgs particle is another particle
that physicists think exists and are in
search of.
This particle is the one that gives
quarks and leptons their mass.
To date the Higgs particle has not yet
been found.
FYI
CERN and the Large Hadron Collider were
developed with the Higgs boson in mind.
The Large Hadron Collider at CERN.
Option J: Particle physics
J1 Particles and interactions
Description and classification of particles
Describe particles in terms of mass and various
quantum numbers.
QUARKS
u (up)
c (charm)
t (top)
Charge / e
+2/3
+2/3
+2/3
Mass / mp
1/3
1.7
186
d (down)
s (strange)
b (bottom)
Charge / e
-1/3
-1/3
-1/3
Mass / mp
1/3
0.5
4.9
LEPTONS
e(electron)
(muon)
(tau)
Charge / e
-1
-1
-1
Mass / mp
0.0005
0.1
1.9
e (e-neutrino)
 (-neutrino)
 (-neutrino)
Charge / e
0
0
0
Mass / mp
0
0
0
Option J: Particle physics
J1 Particles and interactions
Description and classification of particles
Describe particles in terms of mass and various
quantum numbers.
Quarks have a baryon number of 1/3 and antiquarks
have a baryon number of -1/3.
Quark:
B = +1/3
Antiquark: B = -1/3
quark (q) or antiquark (q)
baryon number B
PRACTICE: Find the baryon number of a baryon, a
meson, and an electron:
SOLUTION:
A baryon has three quarks (or three antiquarks):
For qqq we have B = +1/3 + +1/3 + +1/3 = +1.
For qqq we have B = -1/3 + -1/3 + -1/3 = -1.
A meson has a quark and an antiquark:
For qq we have B = +1/3 + -1/3 = 0.
An electron has no quarks and thus has B = 0.
Option J: Particle physics
J1 Particles and interactions
Description and classification of particles
Describe particles in terms of mass and various
quantum numbers.
Leptons have a lepton number of 1 and antileptons
have a lepton number of -1.
Lepton:
L = +1
Antilepton: L = -1
lepton or antilepton
lepton number L
PRACTICE: Find the lepton number of an electron,
a positron, an anti electron neutrino, and a
proton:
SOLUTION:
An electron has a lepton number of L = +1.
A positron is an antiparticle and so has L = -1.
An anti electron neutrino has L = -1.
A proton is not a lepton and so has L = 0.
Option J: Particle physics
J1 Particles and interactions
Description and classification of particles
Describe particles in terms of mass and various
quantum numbers.
Conservation of charge.
Conservation of baryon number.
Conservation of lepton number.
Option J: Particle physics
J1 Particles and interactions
Description and classification of particles
Describe particles in terms of mass and various
quantum numbers.
L = 0
L = 0 + 1 = 1.
Conservation lepton number violated.
We need a particle on the right with
L = -1 (an antilepton).
0
L :
1n
0

1
1p
0
+
-1
+ e
1
-1
0e
Option J: Particle physics
J1 Particles and interactions
Description and classification of particles
Describe particles in terms of mass and various
quantum numbers.
PRACTICE: Evaluate each reaction as "possible" or
"not possible“ considering B, L and Q.
p  n + e+ + e POSSIBLE
1
B:
1
0
0 
0
0
-1
1 
L:
1
Q:
0
1
0 
n  p + e- + e POSSIBLE
1
1
0
0 
B:
0
0
1
L:
-1 
Q:
0
1
-1
0 
n + p  e+ + e NOT POSSIBLE
1
B:
1
0
0 
L:
0
0
-1
-1 
Q:
0
1
1
0 
Option J: Particle physics
J1 Particles and interactions
Description and classification of particles
Classify particles according to spin.
A quark (or antiquark) may have spin up (+1/2) or
spin down (-1/2).
Spin is +1/2
quark (q) or
Spin down -1/2
antiquark (q) spin
A baryon is a particle made of three quarks (or
three antiquarks) and so it has a spin of
 1/2 or  3/2
baryon spin (qqq) or (qqq)
A meson is a particle made of one quark and one
antiquark and so it has a spin of
 0 or  1
meson spin (qq)
A fermion is a particle having an odd multiple of
1/2 as a spin.
A boson is a particle having an integer spin.
Option J: Particle physics
J1 Particles and interactions
Description and classification of particles
State what is meant by an antiparticle. Angels and
Every particle has an antiparticle
Demons
which has the same mass but all of its
quantum numbers are the opposite.
Thus an antiproton (p) has the same
mass as a proton (p), but the opposite
charge (-1).
Thus an antielectron (e+ or e) has the
same mass as an electron but the
opposite charge (+1).
FYI
When matter meets antimatter both
annihilate each other to become energy!
Paul Dirac
Option J: Particle physics
J1 Particles and interactions
Description and classification of particles
State the Pauli exclusion principle.
PRACTICE: Electrons and antielectrons have a spin
of 1/2. Are they fermions or bosons?
SOLUTION:
A fermion is a particle having an odd multiple of
1/2 as a spin. A boson has an integral spin.
Thus electron and positrons are fermions (as well
as quarks and baryons). Mesons are bosons.
The Pauli exclusion principle states that no two
identical fermions may have exactly the same set
of quantum numbers.
FYI
We first saw Pauli’s exclusion principle when we
looked at the orbital structure of the elements.
Recall the s, p, d and f suborbitals.
Option J: Particle physics
J1 Particles and interactions
Fundamental interactions
J.1.7 List the fundamental interactions. DONE
J.1.8 Describe the fundamental interactions in
terms of exchange particles. DONE
J.1.9 Discuss the uncertainty principle for timeenergy in the context of particle creation.
Option J: Particle physics
J1 Particles and interactions
Fundamental interactions
Discuss the uncertainty principle for time-energy
in the context of particle creation.
Recall the Heisenberg uncertainty principle:
∆x∆p  h/4 (momentum form)
Heisenberg
∆E∆t  h/4 (energy form)
uncertainty principle
Another way of looking at the time-energy
uncertainty principle is this:
“If the time interval is small enough, the
uncertainty in the energy can be very large.”
This is a way of saying that the conservation of
energy can be violated for very short periods of
time!
The consequences are that particles can be
randomly created out of the void as long as they
annihilate each other in a very short time.
Option J: Particle physics
J1 Particles and interactions
Fundamental interactions
Discuss the uncertainty principle for time-energy
in the context of particle creation.
∆x∆p  h/4 (momentum form)
Heisenberg
∆E∆t  h/4 (energy form)
uncertainty principle
EXAMPLE: A proton and an antiproton are created
from the void as allowed by the HUP. How much
time do they exist before annihilating each
other?
SOLUTION: A proton has a mass of 1.6710-27 kg.
From E = mc2 we can calculate the energy of a
proton (or an antiproton) to be
∆E = (1.6710-27)(3.00108)2 = 1.5010-10 J.
Since we need both p and p, the energy doubles.
∆t = h/[4∆E] = 6.6310-34 /[4(3.0010-10)]
= 1.7610-25 s.
Option J: Particle physics
J1 Particles and interactions
Fundamental interactions
Discuss the uncertainty principle for time-energy
in the context of particle creation.
EXAMPLE: Stephen Hawking proposed that
black holes can evaporate because of
virtual particle creation. How can this
work?
SOLUTION:
At the black hole’s boundary (the
Schwarzschild radius) virtual particles
are created in matter-antimatter pairs
out of the void.
If one of the pair happens to be
gobbled up by the hole, and the other has
sufficient velocity to escape from the hole, the
particles will not annihilate, and the black hole
will be lighter by the mass of the one particle!
Option J: Particle physics
J1 Particles and interactions
Feynman diagrams
J.1.10 Describe what is meant by a Feynman
diagram.
J.1.11 Discuss how a Feynman diagram may be used
to calculate probabilities for fundamental
processes.
J.1.12 Describe what is meant by a virtual
particle.
J.1.13 Apply the formula for the range R for
interactions involving the exchange of a
particle.
J.1.14 Describe pair annihilation and pair
production through Feynman diagrams.
J.1.15 Predict particle processes using Feynman
diagrams.
Option J: Particle physics
J1 Particles and interactions
SPACE
Feynman diagrams
Describe what is meant by a Feynman diagram.
Richard Feynman developed a graphic
representation of particle interactions that could be used to predict
the probabilities of the outcomes of
particle collisions.
A typical Feynman diagram consists
of two axes: Space and Time:
TIME
FYI
Some books switch the space and time axis. The
IB presentation is as shown above.
Option J: Particle physics
J1 Particles and interactions
e-
SPACE
Feynman diagrams
Describe what is meant by a Feynman diagram.
Consider two electrons approaching one-another
from the top and the bottom of the page…
A purely spatial sketch of
The bubble of
this interaction would look
ignorance
like this:
But if we also apply a time
eeaxis, the sketch would look
like this:
ee
The Time axis allows us to
draw the reaction in a
TIME
spread-out way to make it clearer.
FYI
The “bubble of ignorance” is the actual place in
the plot that exchange particles do their thing.
Ingoing and outgoing particles are labeled.
e-
Option J: Particle physics
J1 Particles and interactions
Feynman diagrams
Describe what is meant by a Feynman diagram.
Particles are represented with straight arrows,
as were the two electrons in the previous
electron-electron interaction.
Exchange particles are
Electromagnetic and
represented with either
weak exchange
wavy lines (photons, W+,
W- and Z0), or curly lines
Strong exchange
(gluons).
FYI
You may have noticed that the electromagnetic
exchange particle and the weak exchange particles
all have the same wavy symbol. Indeed, it has
been found that the two forces are manifestations
of a single ELECTRO-WEAK force.
Option J: Particle physics
J1 Particles and interactions
EXAMPLE:
Here is a diagram for one
electron emitting a photon:
e-
e-
SPACE

e-
eTIME
e-
e-
SPACE
Feynman diagrams
Predict particle processes using
Feynman diagrams.
EXAMPLE:
The complete Feynman diagram
showing the repulsion of two
electrons looks like this:

TIME
Option J: Particle physics
J1 Particles and interactions
e+

e+
e+
TIME
e+
e+
SPACE
EXAMPLE:
Here is a diagram for one
positron emitting a photon:
e+
SPACE
Feynman diagrams
Predict particle processes using
Feynman diagrams.
EXAMPLE:
In a Feynman diagram,
antimatter points backward
in time. This diagram
represents two positrons
repelling each other:

TIME
Option J: Particle physics
J1 Particles and interactions
EXAMPLE:
Here is an electron-positron
pair annihilating to become
a photon:
SPACE
e-

e+
TIME
SPACE
Feynman diagrams
Describe pair annihilation and
pair production through Feynman
diagrams.
EXAMPLE:
Here is a photon producing
an electron-positron pair.
e+

eTIME
Option J: Particle physics
J1 Particles and interactions
SPACE
Feynman diagrams
Discuss how a Feynman diagram may be used to
calculate probabilities for fundamental
processes.
d
u
EXAMPLE:
e
Here is a diagram of a
Wdown quark emitting a Wparticle that decays into
an electron and an
e
antineutrino:
TIME
FYI
One can use Feynman diagrams to map out complete
processes. Using the conservation rules and the
exchange particles, you can predict what kind of
processes can occur.
Option J: Particle physics
J1 Particles and interactions
SPACE
Feynman diagrams
Discuss how a Feynman diagram may be used to
calculate probabilities for fundamental
processes.
EXAMPLE: Explain what has
d
d
u
u
happened in this Feynman
u
diagram.
u
SOLUTION:
d
g
The up quark of a proton
(uud) emits a gluon.
The gluon decays into a
d
down quark and an anti-down
quark.
TIME
FYI
Quarks cannot exist by themselves. Thus the two
quarks produced above will quickly annihilate.
Option J: Particle physics
J1 Particles and interactions
Feynman diagrams
Describe what is meant by a virtual particle.
Exchange particles whose range of influence is
limited are called virtual particles.
INTERACTION
RANGE
EXCHANGE PARTICLE
REST MASS
STRONG
10-15 m
GLUON g
120 MeV / c2
Electromagnetic

PHOTON 
0
WEAK
10-18 m
W+, W- and Z
80 GeV / c2
Gravitation

GRAVITON 
0
Virtual particles can only exist within
their range of influence.
LONG RANGE EXCHANGE PARTICLE
SHORT RANGE EXCHANGE (VIRTUAL) PARTICLE
Option J: Particle physics
J1 Particles and interactions
Feynman diagrams
Apply the formula for the range R for interactions involving the exchange of a particle.
We can use Heisenberg’s uncertainty principle to
estimate the range R of exchange particles. We
use ∆E = mc2 and the assumption that these virtual
particles travel at the speed of light c…

c = R/∆t
(v = d/t)
∆t = R/c
 ∆E∆t  h/4
(HUP)
 ∆ER/c  h/4
(Substitution of ∆t = R/c)
mc2R/c  h/4
(∆E = mc2)
R  h/[4mc]
particle range
FYI
Be able to do this derivation. IBO requires it.
Option J: Particle physics
J1 Particles and interactions
Feynman diagrams
Apply the formula for the range R for interactions involving the exchange of a particle.
R  h/[4mc]
particle range
EXAMPLE: A weak virtual exchange particle called
the W+ boson has a mass of 89 protons. What is its
approximate range of influence?
SOLUTION:
mp = 1.6710-27 kg so that
R  h/[4mc]
= 6.6310-34/[4(89)(1.6710-27)(3.00108)]
= 1.1810-18 m.
FYI
This is about the size of a quark.
Option J: Particle physics
J1 Particles and interactions
SPACE
Feynman diagrams
Predict particle processes using
pu
un
Feynman diagrams.
d
d
EXAMPLE: Explain what has hapd
u
pened in this Feynman diagram.
e
SOLUTION:
W
It is a diagram of a down
quark emitting a W- particle
that decays into an electron
eand an antineutrino:
TIME
Recall that a neutron consists
n  p + e- + e
of an up-down-down quark combo.
Recall that a proton consists of an up-up-down
quark combo.
This is non other than the beta decay (-)we
talked about a long time ago.
Option J: Particle physics
J1 Particles and interactions
Feynman diagrams
Predict particle processes using
Feynman diagrams.
EXAMPLE: Write the reaction (including the
neutrino) for beta(+) decay.
SOLUTION:
+ +
p

n
+
e
Just know it!
FYI
Why is the neutrino not an
anti-neutrino as in the decay?
up
d
u
SPACE
EXAMPLE: Now draw the
Feynman diagram for the
above + decay:
e
nu
d
d
W+
e
e+
TIME
Option J: Particle physics
J1 Particles and interactions
Feynman diagrams
Predict processes using Feynman diagrams.
-1/3
-1
0
A virtual particle is a particle that
has a very short range of influence.
Look at charge… The particle must be a W-.
Option J: Particle physics
J1 Particles and interactions
Feynman diagrams
Predict processes using Feynman diagrams.
Use R  h/[4mc].
m = (100109 eV c-2)(1.610-19 J/eV)(1c /3.00108)2
m = 1.7810-25 kg.
R  (6.6310-34)/[4(1.7810-25)(3.00108)]
R  9.8810-19 m.