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Study Guide

Textbook Guide Physics: Galactic Center, Electroweak Interaction, Fermilab

10 pages85 viewsFall 2016

Department
Physics
Course Code
PHY131H1
Professor
all

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Quarks, Leptons, and the Big Bang
In this chapter we introduce two topics that are the
core of modern physics research:
Cosmology: What is the universe made of?
Particle Physics: How did the universe come to
be the way it is?
1 General Properties of Elementary
Particles
1.1 Elementary Particles
Just by the time that quantum physics seemed to ex-
plain most questions about the atomic world, a new
wave of particle discoveries started.
Most of these particles (muon, pion, kaon, sigma) ex-
ist only for a few moments before transforming into
other particles following the same laws that govern
nuclei decay.
Consider that the number of any one type of particle
present in a sample is N0at time t= 0. Then the re-
maining number of particles in the sample Nat time
tis:
N=N0eλt (1)
and the rate of decay Ris
R=R0eλt (2)
for an initial rate of decay R0.
In the same way, the half-life of the particle is
T1/2=ln 2
λ=τln 2.(3)
Some of these particles have life spans so short - in
the 1023 to 106seconds - that is impossible to ob-
serve them directly.
So, how do physicists generate the conditions for
creating these particles? They use particle accelera-
tors, like the Fermilab (in Chicago) or the CERN in
Switzerland.
The number of these type of fundamental particles is
in the hundreds by the time this document was pre-
pared.
Is not our goal to account for all of them, but instead
we are going to use the classification known as Stan-
dard Model to classify different types of fundamen-
tal particles.
1.2 Fermions or Bosons
Remember that all particles have an intrinsic angular
momentum called spin ~
S.
In general, we are interested in its magnitude, and
the projection along the z-axis:
Sz=ms~for ms=s, s 1,...,s, (4)
where
msis the spin magnetic quantum number,
sis the spin quantum number.
The spin quantum number is always of the form
s=n
2,for n= 1,2,3,.... (5)
An electron has s= 1/2, so it is called a spin-1
2parti-
cle.
Afermion -named after Enrico Fermi - is any particle
with an spin quantum number of the form
1
2,3
2,5
2, . . .
i.e., its numerator is always an odd number.
Electrons, protons and neutrons are all fermions.
Aboson - named after Satyendra Nath Bose, is a par-
ticle with an integer spin quantum number.
For example, photons have s= 1 are bosons.
Why is so important to make a distinction between
these two groups of particles? For a simple but good
reason: fermions obey the Pauli exclusion principle,
while bosons are not bound by it.
Therefore, bosons can pile up in the quantum state
with lowest energy.
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1.3 Hadron or Lepton
Another dimension that physicists use to classify
particles is using the fundamental force they are
more susceptible to.
Remember that there are four fundamental forces:
1. Gravitational force
2. Electromagnetic force
3. Strong force
4. Weak force
Ahadron is a particle most susceptible to strong
forces.
Alepton is a particle whose dominant forces are ei-
ther electromagnetic or weak.
Ameson is a particle that is both a lepton and a bo-
son.
Abaryon is a hadron that is also a fermion.
1.4 Particle or Antiparticle
We say that two particles with the same mass and
spin, but opposite electric charge are a particle-
antiparticle pair.
Some pairs have different name such as the electron-
positron pair, but for others we just append the prefix
“anti”: proton-antiproton.
The interaction of a particle-antiparticle pair leads to
their annihilation. The particles cease to exist in con-
tact and they reappear in other form.
For example, the interaction of an electron and a
positron creates two gamma-ray photons:
e+e+γ+γ.
Scientist have been able to produce antihydrongen in
the lab. This is an atom with a positron orbiting an
antiproton and is currently being produced at CERN.
These new atoms receive the name of antimatter.
1.5 Typical Particle Events
When two particles interact in a laboratory, they usu-
ally produce a great variety of particles as a product
of their interaction.
We are going to study the bubble-chamber photo-
graph of a moving antiproton ¯pcolliding with an sta-
tionary proton p.
In this new picture, we have identified all particles
produced during the event.
This is the story:
Subevent 1. Proton-Antiproton Annihilation. The
antiproton ¯pcollides with the stationary
proton p.
Note that in the picture most particles
are ejected in the traveling direction of
¯p.
The energy involved in the interaction is
about 1,900 MeV, which is quite enough
to produce eight particles, and is gov-
erned by strong forces.
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p+ ¯p4π+ 4π.(6)
Subevent 2. Pion Decay. Pions are unstable particles
and decay in the order of 108seconds.
The decay produced an antimuon µ+
and a neutrino ν. Note that νleaves
no track because is a uncharged particle
and it does not interact with the mag-
netic field confining the interaction.
π+µ++ν. (7)
This interaction is governed by weak
forces, and µ+and νmust share about
34 MeV of energy for motion.
Subevent 3. Muon Decay. Muons and antimuons
are unstable particles, and they decay in
a lifetime on the order of 106seconds.
µ+e++ν+ ¯nu. (8)
The charge of the particles depends on the curvature
of their trajectory:
Clockwise curvature means negative charge
(green lines)
Counterclockwise curvature means positive
charge (red lines).
During the different subevents several conservation
laws are in play:
Electric charge conservation.
Spin angular moment conservation.
Energy conservation.
2 Leptons, Hadrons, and Strangeness
2.1 Leptons
A lepton is a particle for whom the strong force is not
dominant.
We have seen a couple of examples where a particle
decay produces a neutrino. But are they all the same?
The answer is no. An electron decay produces a elec-
tron neutrino, a muon decay produces a muon neu-
trino and so on.
Conservation of Lepton Number
We will introduce a new quantum number called the
lepton number denoted by L.
If
L= +1 the lepton is normal particle
L=1the lepton corresponds to an antiparti-
cle.
L= 0 the particle is not a lepton.
Conservation of Lepton Number:
In all particle interactions, the net lepton
number is conserved.
Note that there are three types of lepton numbers:
Le: electron lepton number,
Lµ: muon lepton number,
Lτ: tau lepton number.
and each should be separately conserved.
2.2 Hadrons
A hadron (baryons and mesons) are particles whose
interaction is governed by strong forces.
We will introduce the baryon number Bwith similar
rules to the lepton number:
B= +1 for a baryon.
B=1for an antibaryon.
B= 0 for any particle that is neither.
The baryon number also satisfies a conservation law
A particle process cannot occur if it
changes the net baryon number.
2.3 Strangeness Conservation Law
We define the strangeness as the property that if par-
ticle process produces most of the time a pair or par-
ticles, there is a change that they can be observed in-
dividually.
The strangeness number S(not to be confused with
spin) assigns the following values:
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