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Textbook Guide Physics: Galactic Center, Electroweak Interaction, Fermilab

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Fall 2016

Department
Physics
Course Code
PHY131H1

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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.
1
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.
2
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:
3

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Description
Quarks, Leptons, and the Big Bang In this chapter we introduce two topics that are the Is not our goal to account for all of them, but instead core of modern physics research: we are going to use the classification known as Stan- dard Model to classify different types of fundamen- ▯ Cosmology: What is the universe made of? tal particles. ▯ Particle Physics: How did the universe come to be the way it is? 1.2 Fermions or Bosons Remember that all particles have an intrinsic angular 1 General Properties of Elementary ~ momentum called spin S. Particles In general, we are interested in its magnitude, and the projection along the z-axis: 1.1 Elementary Particles S z m ~ s for m s s;s ▯ 1;:::;▯s; (4) Just by the time that quantum physics seemed to ex- plain most questions about the atomic world, a new where wave of particle discoveries started. Most of these particles (muon, pion, kaon, sigma) ex- ▯ m is the spin magnetic quantum number, s ist only for a few moments before transforming into other particles following the same laws that govern ▯ s is the spin quantum number. nuclei decay. Consider that the number of any one type of particle The spin quantum number is always of the form present in a sample is N at time t = 0. Then the re- 0 n maining number of particles in the sample N at time s = ; for n = 1;2;3;:::: (5) t is: 2 ▯▯t N = N e0 (1) 1 An electron has s = 1=2, so it is called a spi2- parti- and the rate of decay R is cle. ▯▯t R = R e0 (2) A fermion -named after Enrico Fermi - is any particle with an spin quantum number of the form for an initial rate of decay R . 0 In the same way, the half-life of the particle is 1; ; ;::: 2 2 2 ln2 T 1=2= = ▯ ln2: (3) i.e., its numerator is always an odd number. ▯ Electrons, protons and neutrons are all fermions. Some of these particles have life spans so short - in ▯23 ▯6 A boson - named after Satyendra Nath Bose, is a par- the 10 to 10 seconds - that is impossible to ob- serve them directly. ticle with an integer spin quantum number. For example, photons have s = 1 are bosons. So, how do physicists generate the conditions for creating these particles? They use particle accelera- Why is so important to make a distinction between tors, like the Fermilab (in Chicago) or the CERN in these two groups of particles? For a simple but good Switzerland. reason: fermions obey the Pauli exclusion principle, while bosons are not bound by it. The number of these type of fundamental particles is in the hundreds by the time this document was pre- Therefore, bosons can pile up in the quantum state pared. with lowest energy. 1 1.3 Hadron or Lepton We are going to study the bubble-chamber photo- graph of a moving antiproton p▯colliding with an sta- Another dimension that physicists use to classify tionary proton p. 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 A hadron is a particle most susceptible to strong forces. A lepton is a particle whose dominant forces are ei- In this new picture, we have identified all particles ther electromagnetic or weak. produced during the event. A meson is a particle that is both a lepton and a bo- son. A baryon 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 + ! + : This is the story: Scientist have been able to produce antihydrongen in Subevent 1. Proton-Antiproton Annihilation. The the lab. This is an atom with a positron orbiting an antiproton ▯collides with the stationary antiproton and is currently being produced at CERN. proton p. These new atoms receive the name of antimatter. Note that in the picture most particles are ejected in the traveling direction of 1.5 Typical Particle Events ▯. The energy involved in the interaction is When two particles interact in a laboratory, they usu- about 1,900 MeV, which is quite enough ally produce a great variety of particles as a product to produce eight particles, and is gov- of their interaction. erned by strong forces. 2 Conservation of Lepton Number p + ▯ ! 4▯ + 4▯ : (6) We will introduce a new quantum number called the Subevent 2. Pion Decay. Pions are unstable particles lepton number denoted by L. and decay in the order of 108 seconds. + If The decay produced an antimuon ▯ and a neutrino ▯. Note that ▯ leaves ▯ L = +1 the lepton is normal particle no track because is a uncharged particle ▯ L = ▯1 the lepton corresponds to an antiparti- and it does not interact with the mag- netic field confining the interaction. cle. ▯ L = 0 the particle is not a lepton. ▯+ ! ▯ + ▯: (7) Conservation of Lepton Number: This interaction is governed by weak forces, and ▯+ and ▯ must share about In all particle interactions, the net lepton 34 MeV of energy for motion. number is conserved. Subevent 3. Muon Decay. Muons and antimuons Note that there are three types of lepton numbers: are unstable particles, and they decay in ▯6 a lifetime on the order of 10 seconds. ▯ Le: electron lepton number, + + ▯ L▯: muon lepton number, ▯ ! e + ▯ + n▯u: (8) ▯ L▯: tau lepton number. The charge of the particles depends on the curvature of their trajectory: and each should be separately conserved. ▯ Clockwise curvature means negative charge 2.2 Hadrons (green lines) ▯ Counterclockwise curvature means positive A hadron (baryons and mesons) are particles whose charge (red lines). interaction is governed by strong forces. We will introduce the baryon number B with similar During the different subevents several conservation rules to the lepton number: laws are in play: ▯ B = +1 for a baryon. ▯ Electric charge conservation. ▯ B = ▯1 for an antibaryon. ▯ Spin angular moment conservation. ▯ B = 0 for any particle that is neither. ▯ Energy conservation. The baryon number also satisfies a conservation law 2 Leptons, Hadrons, and Strangeness A particle process cannot occur if it changes the net baryon number. 2.1 Leptons 2.3 Strangeness Conservation Law A lepton is a particle for whom the strong force is not dominant. We define the strangeness as the property that if par- We have seen a couple of examples where a particle ticle process produces most of the time a pair or par- decay produces a neutrino. But are they all the same? ticles, there is a change that they can be observed in- dividually. The answer is no. An electron decay produces a elec- tron neutrino, a muon decay produces a muon neu- The strangeness number S (not to be confused with trino and so on. spin) assigns the following values: 3 Family Particle Symbol Mass (MeV=c )2 Charge q Antiparticle ▯ + Electron electron e 0:511 -1 e electron neutrino ▯e ▯ 1 ▯ 10▯7 0 ▯e ▯ + Muon muon ▯ 105:7 -1 ▯ muon neutrino ▯▯ ▯ 1 ▯ 10▯7 0 ▯▯ ▯ + Tau tau ▯ 1777 -1 ▯ tau neutrino ▯▯ ▯ 1 ▯ 10▯7 0 ▯▯ ▯ S = 0 if the particles are not strange. There are nine spin-zero mesons as well: + ▯ S = +1 if the particle produced is a kaon K . 0 ▯ Pion ▯ ▯ S = ▯1 if the particle produced is a sigma ▯ . ▯ Pion ▯+ The conservation of strangeness: ▯ Pion ▯▯ Strangeness is conserved in interactions involving strong force. ▯ Kaon K + ▯ 2.4 Eightfold Way ▯ Kaon K There are eight spin-baryons: 0 2 ▯ Kaon K ▯ Proton p ▯ Kaon K▯0 ▯ Neutron n ▯ Eta ▯ ▯ Lambda ▯ 0 + 0 ▯ Sigma ▯ ▯ Eta ▯ ▯ Sigma ▯ 0 If we plot their strangeness we get the same pattern. ▯ ▯ Sigma ▯ ▯ Xi ▯+ ▯ ▯ Xi ▯ If we plot the strangeness of these eight baryons, they form an hexagon with two at the center. These and other related diagrams are called eight- fold patterns, and where proposed in 1961 by Gell- Mann and Ne’eman. These diagrams play a similar role to particle physi- cists than the periodic table does for chemists. 4 3 Quarks and Messenger Particles However, the mass of quarks at least one order of magnitude smaller than the combined particle. All the extra energy (mass) comes from strong force in- 3.1 Quark Model teraction between the quarks. In 1964 Zweig found an explanation for the eightfold patterns for baryons and mesons based on a building block called quark. Quarks and Mesons There are six quarks whose properties are summa- rized in Table 1.
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