Exam Announcements
2 is on Tuesday 3/30
Review session on Thursday 3/25
You are allowed to bring 5 pages of notes (front
and back) to the exam
Today: The Standard Model
4 forces of Nature
Fundamental particles of Nature
Feynman diagrams
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From large to small
Atoms
Made of nuclei and
electrons. Size: 10-9m
Atomic
Nucleus
Made of neutrons and
proton. Size 10-14 m
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A proton (uud)
Made of quarks:
Size 10-15 m
A neutron has
ddu
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The big picture
Forces come about because of some properties of
particles (charge, mass, weak charge, color
charge). Recall, particles <=> quanta of matter
fields.
The force is transmitted by the exchange of force
carrier particles (photon, graviton, vector boson,
gluon) that are the quanta of some force field
(Electromagnetic, gravitational, Weak, Strong)
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There are two more forces in nature Strong Force
The Strong force
A force that exists between quarks, which have a property
called color charge.
The carrier of the force is the gluon (the gluon also has color
charge)
No isolated quarks are found in nature
The force between protons-proton, protons-neutrons, and
neutrons-neutrons is the result of the exchange of pairs of
quarks called mesons.
The Strong force is responsible for binding atomic nuclei.
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The Weak Force
Weak force
A force between electrons, neutrinos and
protons (or neutrons), due to a property of
matter called weak charge.
The carrier of the force are called weak vector
bosons W+ or W-, Z. The + or tells us the
electric charge of the boson.
This force allows a neutron to change into a
proton and is responsible for most radioactive
decays.
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Weak Potential
quark
WeakPotential
distance
quark
7
The weak force falls off faster than 1/r2 .
6
5
4
Remember, the slope gives the magnitude of
the field (force).
3
2
Electric potential shape - 1/r
1
2
Weak potential
4
6
8
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Distance [am]
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A summary of the 4 forces of nature
Force
Strength
Carrier
Range (m)
Strong
1
Gluon, g, between quarks
Mesons-protons/neutrons
10-15 size of a
proton
Electromagnetic
1/137
photon
infinite
Weak
10-6
Vector Bosons W+, W-, Z0
10-18
Only 0.001 width
of proton
Gravity
6x10-39
Graviton (?)
infinite
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Bosons and Fermions
Particles come in two types
Bosons have the property that they can
overlap. Examples are photons and certain
atoms (helium). They are social.
Fermions can not exist in the same state. They
are anti-social. Examples electrons, protons.
The fermion nature of electrons explains
atomic structure (periodic table and all that)
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The building blocks of nature
Quantum Numbers
Type Charge Lepton Baryon
number number
(e)
e
-1
1
0
0
1
0
u
+2/3 0
1/3
d
-1/3
0
1/3
0
0
W- -1
T. Kondo
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Neutrinos
Subatomic particles that do not have charge, but interact
via the weak force.
These are very unusual particles and we still dont know
much about their properties. They have a mass, but it is so
small we have not been able to measure it.
They come in three types, but the types mix. (Think QM
superpositions)
They account for about 2% of the universe but interact
weakly. One light-year of lead would have only a 50%
chance of stopping one.
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Dinosaur Extinction and Neutrinos?
Neutrinos are like ghosts since they interact with matter so weakly.
However, if you shoot a HUGE # of neutrinos at matter, you could
still do some damage ( I.e., a tiny fraction of a HUGE # is still a
big #!)
HUGE # of
X X Mass extinction
by cancer?
neutrinos
Supernova explosion
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Antiparticles
Every particle has a corresponding antiparticle. When a particle and an
anti particle meet they annihilate giving off energy. All the mass is
converted to energy.
A particle and its antiparticle have opposite values for all quantum
numbers except for spin and mass.
Example: The antiparticle of an electron is a positron. In all other
cases, the name of the antiparticle is anti- in front of the name of the
particle, such as proton and anti-proton.
Antiparticles are written with a line over the top: p vs p (the
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antiproton)
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Antimatter
Antimatter (matter made of anti-particles) is very difficult to
make. It can artificially be produced only at large particle
accelerators (atom smashers).
Matter and anti-matter are created naturally in pairs
So far the total amount of antimatter ever produced by
humankind is a few grams, and that almost immediately
annihilated with matter.
The total energy in 1 g of anti-matter is:
E=mc2 = 0.001 (3 x 108)2 J = 9 x 1013 J = 9 x 104 GJ
enough to run a normal power plant for 1 day.
Cosmic mystery: much more matter than Lecture anti-matter
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Feynman Diagrams
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The big picture
The 4 fundamental forces transmitted by exchange of
force carrier particles that are quanta of the given
force field
Photon (EM field)
Graviton (Gravitational field)
Vector bosons (Weak field)
Gluon (Color field)
Feynman diagram for electric
Force btw. 2 eISP209s10 Lecture 17
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A way to picture forces Feynman Diagrams
g
quark
quark
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Alternative version of the uncertainty principle
Time and energy also also related.
h
#E#t "
4!
h
#x#p "
4!
It is possible to violate conservation of energy by an amount E,
but it has to be paid back in a time t.
On the very small scale, empty space is alive with fluctuations.
Particles can pop into and out of existence.
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Quantum Chromo Dynamics - QCD
Strong force between neutrons and protons
Looks
like
At low energies, we can
pretend ns and ps are
fundamental particles
Interacting by exchanging
a pion (quark-anti-quark)
Rule of thumb: The heavier the exchanged force carrier particle,
the shorter the range of the force in space.
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The problem with QCD
Gluons themselves have color charge!
This is also possible.
normal
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Equations sort of
Rules for Feynman Diagrams:
1). The number of leptons and baryons must be conserved.
allowed
2). Charge must be conserved.
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Not
allowed
since lepton
number not
conserved
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Equations sort of
Rules for Feynman Diagrams:
1). The lepton number and baryon number must be conserved.
Total lepton and baryon numbers for the top and bottom
of the diagram should be the same.
2). Charge must be conserved.
Total electric charge for the top and bottom
of the diagram should be the same.
Total energy and momentum are always conserved as well.
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Back to the weak and electromagnetic forces
proton
(udu)
W-
e
electron
e
photon
e
e
e
(udd)
neutron
Repulsive force between two
Transformation of a neutron into a
proton by an interaction with a neutrino electrons.
via the Weak force.
neutrino
In the process: Energy (including mass); momentum,
charge, baryon number, lepton number, are conserved.
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Quantum Electrodynamics - QED
The description of the forces on the previous page is based on a
theory called quantum electrodynamics.
Most successful theory every devised it has at the moment no
known problems and describes all electric, magnetic and weak
interactions.
Strength of the EM force:
1
!=
theory
137.03599941(56)
1
!=
experiment
137.03599979(32)
Unification of EM and Weak Forces is called Electroweak theory
Theory of the strong force is called Quantum Chromodynamics
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Example 1
L#(TOP) = 0 + 0 = 0
B#(TOP) = 1/3 + 1/3 = 2/3
C#(TOP) = 2/3 + 2/3 = 4/3
L#(BOT) = 0 + 0 = 0
B#(BOT) = 1/3+1/3 = 2/3
C#(BOT) = 2/3+2/3 = 4/3
Lepton #, Baryon #, and Charge are all conserved. This represents
an allowable process.
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Example 2
L#(TOP) = 0 + 0 = 0
B#(TOP) = 1/3+1/3 = 2/3
C#(TOP) = 2/3-1/3 = 1/3
L#(BOT) = 1 + 0 = 1
B#(BOT) = 0 + 1/3= 1/3
C#(BOT) = -1 + 2/3 = -1/3
NOT an allowable process since Lepton, Baryon, and Charge #
are not conserved.
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Example 3
L#(TOP) = 1 - 1(*) = 0
B#(TOP) = 0 + 0 =0
C#(TOP) = 0 + 1(*) =1
This is a physically allowable process.
L#(BOT) = 0 + 0 =0
B#(BOT) = -1/3(*) + 1/3 = 0
C#(BOT) = 2/3(*) + 1/3 = 1
(*) anti-particles have opposite sign values of L#, B#, C# than
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Example 4
proton
(udu)
W-
(udd)
neutron
e
electron
neutrino
L#(TOP) = 0+0+0 + 1 = 1
B#(TOP) = 1/3+1/3+1/3 + 0 = 1
C#(TOP) = 2/3 -1/3+2/3 - 1 = 0
L#(BOT) = 0+0+0 + 1 = 1
B#(BOT) = 1/3+1/3+1/3 + 0 = 1
C#(BOT) = 2/3 - 1/3 -1/3 +0 = 0
This is a real physical process since L#, B#, C# are conserved.
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Clicker #1
What is meant by the symbol:
A)
B)
C)
D)
E)
anti-electron with a charge of -1
anti-electron with a charge of +1
average energy of an electron
electron
none of these
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Clicker #2
What process does this Feynman diagram show?
A) Creation of electron and anti-electron
by a photon
B) An electron scattering off a photon
C) 2 electrons experiencing electric
repulsion transmitted by a photon
D) None of these is correct
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Clicker #3
Is the following process possible? (Hint: Check if certain quantities
are conserved or not.)
A) YES
B) NO
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Clicker #4 - What is this process?
A) Electrons interacting by the weak
force
B) Electrons and quarks interacting
by the strong force
C) An electron and anti-electron
annihilating, leading to the creation
of a quark and anti-quark.
D) Electric force between electrons
and quarks
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