Lecture 2: Jan 26th 2012
Corrected web page: http://www.physics.wisc.edu/undergrads/courses/spring2012/535/
Homework: 1.1, 1.2, 1.3, 1.17(compare to particle data book online). Due Feb 2nd
Reading today: Griffiths Chapter 1
Reading next time: Chapter 2
1) Standard model of particle physics.
Two classes of particles, quarks and leptons, with three generations of each set of
particles.
Three forces, electromagnetic, weak and strong.
2) Standard model particles
Leptons: electron, electron neutrino and antiparticle versions positron and anti electron
and anti electron neutrino
Charges: q=1,0, weak lepton number = 1
Antiparticles are identical in most properties such as mass but opposite in charge. This
includes electric change and weak charge.
Interact electromagnetically (electron only) and weakly. Interaction means that they
carry the charge of this force and can interact via 3 prong vertices with the force carriers
of these forces.
Quarks, u and d quarks and antiparticle versions
Charges: q=2/3,-1/3, weak quark flavor u and d, color red, green and blue
Antiparticles have anti-charges such as anti-color charge, anti-red, anti-green anti-blue.
Interact electromagnetically, strongly and weakly
Three generations of particles. Need to be introduced to explain the observed particles.
Muon and tau versions for the letpons.
c,s and t,b versions for the quarks.
Second and third generation charged leptons can decay via lepton flavor conserving
decays involving the W boson.
Single second and third generation quarks can only decay via weak quark flavor changing
decays involving the W boson. Higher generation particles don’t typically exist in nature
they are produced in particle anti particle pairs to conserve lepton and weak charge
3) The standard model forces
Three forces. Introduced to explain why we saw interactions with substantially different
properties. For instance, their substantial differences in strength or probability.
The electromagnetic force carried by the photon.
The weak force carried by the W and Z boson
The strong force carried by the gluon.
(Gravity and the graviton?)
Question: Are the forces related? Can they be unified in some way?
The EM and weak forces are unified into the Electroweak force in the standard model.
Can gravity be included.
4) 3 generations and the quark model.
Lepton generations. We observed two particles that had the exact same electric charge
and thus types of electromagnetic interactions as the electron but with about 200 and
3500 times the mass respectively. The more massive leptons decayed weakly to the
lower mass particles. The neutrinos also had two sets of extra versions all will very small
masses.
Quark generations
The production of charged pions was high probability. Pion interacted strongly when sent
through dense quark matter. The decays of charged pinos had weak strength. They could
also interact electromagnetically if sent through a field.
The charged kaon was more massive than pion and seemed to involve a new charge since
they were produced in kaon anti-kaon pairs. The production was high probability. Kaons
interacted strongly when sent through dense quark matter. The decays had weak
strength. They could also interact electromagnetically if sent through a field.
Since we had added the muon to the electron why not add a second generation of
hadrons(or quarks) as well.
Understanding this was simpler if you adopted the quark model. There were compelling
reasons to adopt a quark model such as the presence of excited energy states that
otherwise had the same properties. Atoms could be in excited states as well because of
their structure involving a proton and an electron in quantized orbits. Even the nucleus
could be in excited states because of the structure of protons and neutrons. Therefore, it
was hypothesized that these particles were composed of multiple quarks that could be
excited into higher energy state orbits of each other.
Protons and neutrons were made up of uud and udd quarks respectively with charges u,
2/3, d -1/3. Pions were made up of uu+dd, ud or du quarks with the second quark being
and antiquark version to get charged and neutral pions. Kaons involved a strange quark
(charge -1/3) which was part of second generation of particles that was later rounded out
by the charm quark(charge 2/3). Excited states had considerable more energy(manifested
as mass) indicating a very strong binding. Free quarks were not observed. The sizes of
the composite particles were very small indicating a short range.
These particles could decay via the weak force so evidently the quarks and leptons both
had a weak or flavor charge. Though note that the strangeness or charmeness of the
second generation is not conserved in weak decays. Kaons were first seen in K->pipi
decays.
This zoo of particles soon expanded to include the tau lepton and neutrino and the bottom
and top particles. Top discovered in 1995 at the Tevatron.
5) The weak interaction
We knew that there were processes such as n->p+e- that happened over long time scales.
The free neutron lifetime is actually 15 minutes! These were long time scales compared
to for instance the time it takes for an atom in an excited state to decay to the ground state
electromagnetically emitting a photon. One way to explain this was with an interaction
that was extremely low probability or strength.
We also had a mystery in that the detectable momentum was not conserved in this
interaction and the electron energy could vary.
Also there didn’t appear to be any weak field that particles with weak charge were
repelled or attracted by.
The answer to these puzzles was to propose a new qualitatively different weak
interaction. The weak interaction involved a massive force carrier that when produced
virtually could only exist for a very short time. This limited the strength and range of the
interaction. Also as part of the decay there had to be another particle that was produced.
This particle was massless (or almost massless!) and only interacted weakly. Finally, the
weak force carriers for nuclear beta decay carry electric charge and change the nature of
the object they are emitted from which precludes having a weak bound state as you do in
the EM force. There is also a neutral massive weak force carrier like the photon but you
would still not expect weak bound states because of the extremely low probability of the
weak interactions.
The n->p+e- interaction involved the neutron emitting a negatively charged Wintermediate boson which then split into the electron and antineutrino. Intermediate since
it was a virtual particle only produced for a short time within the interaction. In fact the
W- is 81 times more massive than the proton.
Why a massive boson? Again consider tE~hbar. Or tmc2~hbar and range R = ct =
hbar/mc. The time or range of this force are going to be extremely limited. The force
and potential are difficult to calculate. You have to solve the wave equation for a
massive relativistic particle. Approximately at low energy F = C/m2.
The neutrino hypothesis and the strength of the weak interaction were convincingly
demonstrated when the crossed interaction n->p+e- was observed using a source of
electron neutrinos. The interaction took a flux of 5x1013 neutrinos to observe with
detectable rate demonstrating the weak nature of the force due to it’s short range and thus
small cross section. Similar interaction with and antineutrino in the initial state or a
muon in the final state were not observed which suggested the idea of lepton number
conservation where the leptons and neutrinos or antiparticles each had a conserved lepton
or anti-lepton quantum number.
For the muon you could observe the weak decay ->e- where the neutrinos were muon
and anti-electron types.
We could tell there where a electron and muon type of antineutrinos from observing p+
-> +n and p+ -> e+n.
So the rules of the weak interaction were that it conserved lepton number (separately for
electrons and muons and their neutrinos)(and electric charge) and relativistic momentum
and energy. The interacting was short range, low probability or strength, decays had long
time scales and the force was too weak to form bound states.
6) The strong force and the SM
However what bound the quarks together? They were charged and even closer together
so should experience massive electromagnetic attractive and repulsive forces.
The quantum field theory with these features was Quantum cromodynamics and the
gluon carried the strong force, which interacts with things that have strong or color
charge. Note that all three forces involve a charge and fundamental particles with the
proper charge can interact via that force.
A proof of the color charge is the existence of the Delta uuu fermion, where all three
quarks are spin up, which to obey Fermi statistics must have each quark in a different
color state.
Convincing proof of this theory comes from very high energy scattering experiments.
Deep inelastic scattering experiments have probed the structure of the proton and see the
quarks and infer gluons. Inelastic because the energy is high enough that we tend to blow
apart the proton.
The strong force was also limited in range, but by a difference mechanism. Instead of
having a massive force carrier the gluon carries color charge itself and can interact with
itself, which has the end result of limiting the range of the force. It also gives us other
features such as confinement of the quarks to groups of 2 or 3.
Calculating the potential you get V=-C/r +kr with the constant being near 1! This leads
to the interesting effect that it’s more probable to have interactions with lots of gluons
that with just one.
Because of the linear term as quarks separate they build up so much potential energy
when quarks separate that either they are “confined” by being attracted back together, or
that energy is large enough eventually that you “pop” new quark-antiquark pairs out of
the vacuum converting the energy of the potential to mass. The linear term physically
can be thought of as a string of gluons stretching between the quarks. When the string
breaks it’s energy goes into making two new quarks which will be near the old quarks. If
it doesn’t break the quarks are pulled back into the hadron, or confined.
So the rules of the strong interactions were that it conserved color charge number(and the
other charges) and relativistic momentum between the initial and final products. Also the
interaction was very short, high enough probability to be easily observed and result in
decays of extremely short time scales and also strong enough to form bound states
between particles like quark(or protons) and exceed the EM repulsion between those
objects. The short range we due to the fact that the force carrier had charge not an
intrinsic property of individual interaction, which should be long range since the gluon is
mass less.
7) Questions that led to the unification of the field theories into the SM.
Why did we have three quantum field theories have such different features such as:
differing strength or probability of the interactions, the massiveness of some of the force
carrying bosons, and the ability of some of the bosons to interact with each other.
Next week: Putting it together, the SM in detail.