Teaching with the
Contemporary Physics
Education Project chart on
particles and interactions
Gordon J. Aubrecht, II
IACPE, 1 (13:30), 2 (13:30), and 5 July (11:00)
2013
Part 1: Background (Monday)
Part 2: The Particle Adventure
exploration (Tuesday)
Part 3: the Higgs (Friday)
Part 1: Background
I like to quote Walter Michels in his 1964 Oersted
Lecture:
“we seem to be engaged in a conspiracy to prevent
elementary students from learning that imagination,
inventiveness, and intuition play any part in the growth
of physics, or from suspecting that anything in the
physical universe is not yet fully understood.”
Many school teachers who know little of science even
as they are assigned to teach it, have and transmit the
impression that all that can be known is already known.
What is known can be learned by rote and is boring. As
scientists, we know how wrong this view is, as Marco
Antonio Moreira pointed out this morning.
The Contemporary Physics Education Project, is
known as CPEP for short.
CPEP began as a way to bring particle physics
into high school (and college) classrooms. At that
time, twenty years ago, the Standard Model of
particles had jelled into something respectable.
We at CPEP thought that presentation of
cutting-edge physics and the knowledge that
there were still many open questions could lead
students to consider future careers as scientists.
I am the former chair of the
Contemporary Physics Education
Project (CPEP). We created this
chart in the late 1980s, as it became
clear to all of us that there was such
a thing as a “Standard Model.”
Experiments from 1898 to the 2000s led to
this “particle zoo.”
We do have a timeline in the
Particle Adventure (tomorrow)
Then, in the 1960s, Murray Gell-Mann,
George Zweig, and others invented ways to
categorize these many particles and the
result is called the quark model.
We’ll show quarks from the chart later.
Note: A proton is uud, a neutron is udd, etc.
The model also produces mesons—
hadrons that are made of quark-antiquark
pairs.
This was our original idea.
This was how we built on the idea. Notice
Gordon had a lot less gray in his hair!
This was the result of our first
attempt at a chart of particles and
interactions.
As you can see, there is a great deal of
information available backing up our charts that
can be used by both teachers and students. In
addition, as we saw for particles, kits are
available from Science Kit/Cenco that support
teaching with the charts and ancillary other
materials.
Let’s use an example. When forces are
introduced in many physics courses, they are
mysterious. Where does the force come from?
Actually, forces are really interactions, and
involve two bodies or agents. This is usually first
seen—and misunderstood—in discussions of
Newton’s Third Law. How does CPEP help?
The forces are introduced as interactions from the first:
gravitational interaction, electroweak interaction, strong
interaction. We show on what the interaction works, and
introduce the idea of exchange of particles as responsible
(emphasizing the two elements). Finally, we provide an
assessment of relative strength.
So, we prepare students to think of interactions
between particles as fundamental—a basic
physics concept that is in the context of current
physics research!
The Large Hadron Collider (LHC) is a place
where interactions can occur. The Higgs particle
was discovered there (later).
The current version is here.
There are materials available to help students and
teachers as well. CPEP thought that we needed to
assist serious study as well as providing visual
beauty and provoking curiosity through charts.
Amazon.com: The Charm of Strange Quarks: Mysteries
and Revolutions of Particle Physics: R Michael Barnett,
Henry Muehry, Helen R. Quinn, G. J. Aubrecht, ...
www.amazon.com/Charm-Strange-Quarks-MysteriesRevolutions/dp/0387988971 - 307k -
Part 2: The Particle Adventure
exploration
Teaching with the Contemporary
Physics Education Project chart on
particles and interactions
I hope we have enough laptops to
have us all be able to access the
Particle Adventure. We will then do
some searching and testing. Note
that the Particle Adventure is
available in many languages.
Part 3: The Higgs
Teaching with the Contemporary
Physics Education Project chart on
particles and interactions
The Higgs …
and CPEP’s poster
Sometime in the fall of 1967 that I attended a seminar by a
brash young physicist from MIT. From the way the senior
physicists at Princeton (where I was a graduate student at
the time) treated Steven Weinberg, it was clear that this was
someone who had a future in theoretical physics.
It wasn’t clear they thought he would go on to win the
Nobel Prize (in 1979, with Abdus Salam) for his
contributions to building what is now called the Standard
Model, but I and the other graduate students there knew he
was considered special.
That afternoon, I learned about spontaneous symmetry
breaking. I recall Weinberg talking about a scalar particle
and how this scalar particle could give mass to the vector
bosons. I remember him doing calculations on the
blackboard and coming out with a mass parameter μ from
the symmetry breaking. The idea is that the ground state
equilibrium is unstable, and any perturbation results in the
particle falling to the lower potential energy. It was my first
introduction to what has been called the “wine-bottle” or
“Mexican-hat” potential.
The frantic 1970s
Going back to the 1930s, there was a weak
interaction theory that was originally developed
by Enrico Fermi for beta decay. In fact, it is still
known to physics students as Fermi’s Golden
Rule: that the probability of a transition from
initial to final state depends on the density of
states and the square of the interaction matrix
element between initial and final states.
Of course, in 1934, people didn’t know the
matrix element; it would take until the 1950s to
develop the ideas that led to the proper betadecay spectrum. The Fermi model of weak
interactions had problems when applied beyond
relatively low energies—the prediction
extrapolated more generally led to a growing
transition probability because the 1950s constant
matrix element and the growing density of states.
The matrix element, as we have since learned, is
simply a low-energy approximation in the bigger
model.
Theorists showed that one could calculate real
values through a process of renormalization
reminiscent of Richard Feynman, Julian
Schwinger, and Sin-Itiro Tomonaga and many
others’ work on quantum electrodynamics
(QED).
The development of QED during the 1940s
showed how renormalization could work to
eliminate the infinities in electromagnetism.
Electromagnetism can be explained in terms of
exchange of photons. Of course, photons are
massless and their exchange—through matrix
elements that involved propagators that are the
inverse of the square of the four-momentum,
1/p2—led to calculations that found infinite
values for physical parameters.
The general idea of exchange of particles came
from what is known as gauge invariance in
electromagnetism, and the particles exchanged
could be referred to generally as gauge particles.
Photons are gauge particles for
electromagnetism.
A way to get rid of the pesky infinities in
theories of interactions is to realize that
interactions are mediated by gauge particles.
This is an old idea in particle physics. Nuclear
physicists considered exchange of virtual
(massive) pions and other virtual particles as the
way the strong interaction worked inside nuclei.
a) A neutron and a proton at time t1. b) At time t2 > t1, the proton
emits a virtual positively charged pion and becomes a neutron. c)
At time t3 > t2, the neutron absorbs the pion, becoming a proton.
d) At time t4 > t3, there is again a neutron and a proton.
Feynman developed a graphical method of calculation for QED.
The exchange on the last slide could be calculated from this
diagram (with appropriate rules).
The idea that interactions could
proceed by exchange of particles
that were massive was applied to
the weak interactions. Simplifying
the situation immensely, if there
were massive gauge particles
similar to the photon, the infinities
would go away.
If this idea were to work, for
example in the case of the 1930s
“poster child” for the weak
interaction, nuclear beta decay, this
would mean that nuclear beta decay
and scattering of a neutrino from a
neutron to produce a proton and an
electron would be related.
a) The Feynman diagram describing the process in which a neutron
(symbolized by d) and a neutrino scatter through the weak interaction
producing a proton and an electron.
b) The Feynman diagram for nucleon beta decay, in which a constituent of the
neutron (d) is changed by the weak interaction into a constituent of a proton
(u) and produces a W-, which then decays into an electron and an antineutrino
(note that the antineutrino line points to the right). The u and d are quark
constituents of the nucleons. There is a propagator for the W- and there are two
vertices (u-d-W- and e--e-W-) included in each of these Feynman diagrams.
In the 1970s, such an interaction
would be labeled a charged-current
interaction (the W- being charged
and being exchanged; we could
instead have drawn the diagrams
for electron plus proton to neutron
and electron neutrino and for
positron emission, which proceed
through exchange of the W+).
The exchanged virtual particles’
propagators would be of the form
1/(pp – m2), and the m2 term would
mean approximately constant matrix
elements at low energy (compared to
the m2), while the p2 part of term
would make them vanishingly small at
high energy by tending the
denominator toward zero.
There must also be indications not simply
of exchange of a charged gauge boson as in
nuclear beta decay. In other instances of
the weak interaction, there could possibly
be exchange of a neutral gauge boson,
similar to the photon in its lack of electric
charge, but having a nonzero mass. In the
parlance of the 1970s, the former would be
called a charged current interaction and the
latter a neutral-current interaction (the
currents form the matrix element).
Such a particle could be produced by sending electrons
and positrons colliding together and seeing, for
example, +-- pairs emerge or scattering an electron
neutrino from an electron and producing the same thing
or producing a - and . The first experimental
evidence for the electroweak theory was the discovery
of weak neutral currents, first seen in 1973 in by the
Gargamelle collaboration at CERN in –nucleon
scattering and anti-muon-neutrino-electron scattering,
and immediately thereafter by the Harvard-PennWisconsin collaboration at Fermilab. The exchanged
gauge particle is known as the Z.
Thus, the experimental result supported electroweak
theory, in which the photon, the W±, and the Z are the
gauge bosons.
The mystery was why the photon was massless, while
the W± and Z had masses.
This is where the spontaneous symmetry breaking
comes in. Massless particles have two states of
polarization, which we usually label clockwise and
counterclockwise. Massive particles also have a
longitudinal polarization, for a total of three states of
polarization.
The “extra” state is supplied through the acquisition of
mass by the Higgs mechanism.
This gives mass to the W± and Z particles.
To trust the model, the W± and Z would have to be
found experimentally.
They were found in experiments at the CERN SPS
(super proton synchrotron) in the early 1980s and the
1984 Nobel Prize was given for their discovery.
The “normal” massive particles’ masses arise largely
through the kinetic energy of the bound constituent
quarks. This is very different from the idea of the Higgs
mechanism.
Consider a field  for a particle whose original value
puts it on an extremum of the potential. We named
particles like these Higgs particles, which are
represented by the fields, spontaneously move away
from their original wavefunction to a new wavefunction
at  =  having a lower potential energy.
A three-dimensional vision of the potential.
V(ϕ) = λ(ϕ∗ϕ – μ2)2
In this process, known as the Higgs
mechanism, the fields disappear when
they “fall” into the lower potential and
through their disappearance become
responsible for creating the masses and
thus the longitudinal polarizations of
the gauge bosons. Thus, a key part of
verification of electroweak unification
is the appearance of Higgs bosons in
experiments.
A new field is made from the Higgs …
ϕ=H+μ
there is an interaction term
ϕ∗ϕA2 = μ2A2 + . . .
That acts like a mass term
(1/2 m2 = μ2).
Also, the Higgs field also has a mass
that comes from the potential V(ϕ).
From the 1970s to now, the Higgs
was a “holy grail” of experimental
searches. Up until Independence
Day 2012, no such scalar particle
had been found.
A particle accelerator (the LHC)
was built to try to find it.
LHC stands for Large Hadron
Collider.
What do we mean by the “hadron”
in the Large Hadron Collider?
There are two sorts of particles shown on the
chart I hope I gave you—leptons and hadrons.
They are completely different in their properties
from one another, but all leptons have spin
n + 1/2 and do not interact strongly.
All hadrons interact strongly and can have have
either integer spin or spin n + 1/2.
Leptons interact gravitationally,
electromagnetically, and via the weak interaction.
Hadrons are the only particles that interact via
the strong interaction. Quarks are hadrons.
This is important: the hadrons act over really
short distances—
distances of a femtometer (10-15 m).
The Large Hadron Collider (LHC) is a place
where interactions can occur through particle
collisions.
According to Wikipedia,
“The Large Hadron Collider (LHC) is the world’s largest
and highest-energy particle accelerator, intended to collide
opposing particle beams, protons at an energy of 7
TeV/particle or lead nuclei at 574 TeV/particle.”
The LHC is a circular accelerator ring 27 km
around. Particles are steered in both directions
using superconducting magnets and made to
collide in several regions loaded with detectors
like the Atlas detector.
Because the ring is so big, the particles’
energies are immense—10 TeV—and the
particles are traveling at essentially the speed of
light: E =  mc2 =  1 GeV, so
 10 TeV/(1 GeV) = 10,000, giving
v = c - 1.5 m/s.
Let’s think a bit.
The resolution of objects depends on the
wavelength of the probing object. A
wave of wavelength  bends around
objects of size d. Waves and particles are
not more than different evocations of
some underlying reality. Particles have
momentum p that is related to the
wavelength : p = h/.
Because
p = h/,
 is comparable in size to the object (d),
and the energy of a particle is given by
E = (p2c2 + m2c4)1/2 = mc2,
we see that to “see” a small object (d
very small), p must be very large, and so
in turn E must be very large.
This means that particle physicists are
always searching to increase the energy
of collisions. They do this by
accelerating the particles in an
accelerator.
The first accelerators were designed in
the 1920s—Cockroft and Walton
designed a linear accelerator (linac), and
E. O. Lawrence designed a circular
accelerator (cyclotron).
Lawrence’s machine was called a
cyclotron (not prefix), and today particle
physicists use both linacs and
synchrocyclotrons to study particle
physics.
The synchronization is necessary due to
the effects of special relativity.
LHC preaccelerators
p and Pb: Linear accelerators for protons (Linac 2) and Lead (Linac 3)
(not marked) Proton Synchrotron Booster
PS: Proton Synchrotron
SPS: Super Proton Synchrotron
LHC experiments
ATLAS
A Toroidal LHC Apparatus
CMS Compact Muon Solenoid
LHCb
LHC-beauty
ALICE
A Large Ion Collider Experiment
TOTEM
Total Cross Section, Elastic Scattering and Diffraction Dissociation
LHCf
LHC-forward
ATLAS is about 45 meters long,
more than 25 meters high, and
has a mass of about 7,000
tonnes.
The Compact Muon Solenoid (CMS) is
21 meters long and 15 meters wide and
high. It has a mass of 12,500 tonnes.
ALICE is about 26
meters long, and 12
meters high and wide,
and has a mass of
about 10,000 tonnes.
This experiment
is a collaboration
of over 1000
physicists.
LHCb (Large Hadron Collider beauty) is
21 meters long, 10 meters high, and
13 meters wide, with a mass of 5600
tonnes.
650 physicists belong to
this experimental
collaboration.
TOTEM is 440 meters long, 5 meters
high and 5 meters wide. It has a mass
of 20 tonnes. Fifty physicists work on
this experiment.
<-- This is CMS.
The long red thing is TOTEM.
View of one quarter of the CMS detector with the TOTEM forward trackers T1 and T2. The CMS calorimeters, the
solenoid and the muon chambers are visible. Note also the forward calorimeter CASTOR.
LHCf (Large Hadron
Collider forward)
LHCf has two
detectors, each
measuring 30 cm long,
80 cm high, 10 cm
wide, with a mass of 40
kg each. Twenty-two
physicists work on this
experiment, which uses
the LHC to simulate
cosmic rays.
The experiments ALICE, ATLAS, LHCb, etc.,
will be looking for traces of the Higgs particle(s),
and we know that the Tevatron at Fermilab has
already constrained the Higgs mass to be above
100 GeV. We need to get to those high energies
the LHC promises to see what’s what.
We need to look for evidence of what lies beyond
the Standard Model …
… such as supersymmetry (colloquially known
as SUSY) or some more exotic things (whatever
they might be). SUSY might be able to explain
dark matter, the mysterious extra mass that helps
hold galaxies together. As in the Pauli joke
explanation, the lowest-mass object is stable; it
doesn’t decay. The lowest-mass SUSY particle
could be the source of this dark matter.
SUSY might tell us that grand unification is
correct (the couplings are the same at high
enough temperature [energy]).
The Standard Model (the chart I showed) has
been the most successful model ever in
describing the actions of particles.
The Standard Model explains all the particle
physics of the past 30 years.
Explorations of the Standard Model have been
responsible for 32 Nobel Prizes over the last 30
years.
The Higgs boson gives mass to the four colorless gauge
bosons (, W+, W-, Z) in the Standard Model.
In the Standard Model chart, we now have the Higgs.
There are other bosons besides the
gauge bosons. In the standard
model, they are made of quarkantiquark pairs.
As already noted, constituent
mesons get their masses mainly
from their enclosed constituents’
kinetic energy.
(Note the smallness of the quark
masses.)
The protons, neutrons, and other
ordinary constituent fermions in
matter are made up of three quarks.
The protons, neutrons, and the
other ordinary constituent fermions,
get their masses through a similar
mechanism to the constituent
bosons. Their masses also come
mainly from enclosed constituents’
kinetic energy.
The quarks, basic fermions, get
their masses through still a different
mechanism. Their masses come
mainly from entrained kinetic
energy, perhaps vibrating strings.
So the Higgs particle is central to
the Standard Model in that it makes
the gauge bosons.
Did the LHC experiments see the
Higgs particle?
Two experiments, Atlas and CMS,
reported “5  results.
What did ATLAS and CMS see? Here are some
Atlas data from December 2011.
What did ATLAS and CMS see? Here are the Atlas
data updated to early March 2013 (Moriond).
Here is where they both see the the
possibility of the Higgs—between
120 and 130 GeV/c2.
Atlas Moriond Conference result,
06/03/13
Atlas Moriond Conference result,
06/03/13
CMS Moriond Conference result,
06/03/13
HIG-13-004 Figure 1: The data in the τ channel (black curve) and the expectation
for a Standard Model Higgs boson of mass 125 GeV decaying into two τ leptons
(blue). The observed result gives a best fit for the SM Higgs boson of mH = 120 ±9
Moriond Conference results, 06/03/13, as reported in a CERN
press release:
Whether or not it is a Higgs boson is demonstrated by how it
interacts with other particles, and its quantum properties. For
example, a Higgs boson is postulated to have no spin, and in the
Standard Model its parity – a measure of how its mirror image
behaves – should be positive. CMS and ATLAS have compared a
number of options for the spin-parity of this particle, and these all
prefer no spin and positive parity. This, coupled with the
measured interactions of the new particle with other particles,
strongly indicates that it is a Higgs boson.
“The preliminary results with the full 2012 data set are
magnificent and to me it is clear that we are dealing with a Higgs
boson though we still have a long way to go to know what kind
of Higgs boson it is,” says CMS spokesperson Joe Incandela.
The CMS Collaboration, “A new boson with a mass of 125
GeV observed with the CMS experiment at the Large
Hadron Collider,” Science 338, 1569-1575 (2012)
The CMS Collaboration, “A new boson with a mass of 125
GeV observed with the CMS experiment at the Large
Hadron Collider,” Science 338, 1569-1575 (2012)
5  as explained by BBC News
Statistics of a ‘discovery’
Particle physics has an accepted definition for a “discovery”: a fivesigma level of certainty
The number of standard deviations, or sigmas, is a measure of how
unlikely it is that an experimental result is simply down to chance
rather than a real effect
Similarly, tossing a coin and getting a number of heads in a row may
just be chance, rather than a sign of a “loaded” coin
The “three sigma” level represents about the same likelihood of tossing
more than eight heads in a row
Five sigma, on the other hand, would correspond to tossing more than
20 in a row
Unlikely results can occur if several experiments are being carried out
at once - equivalent to several people flipping coins at the same time
With independent confirmation by other experiments, five-sigma
findings become accepted discoveries
More CMS results.
More CMS results.
World Conference on Physics Education, Bahçeşehir Üniversitesi,
İstanbul, July 2012
Fast forward to Wednesday, 4 July 2012. I was sitting in sessions of the
World Conference on Physics Education in Istanbul. Because I was
listening to talks, I couldn’t watch the seminars at CERN describing the
discovery of “a Higgslike particle,” but I could surreptitiously keep
following the live blog at the Guardian newspaper website.
At around 9:30 Istanbul time, I read a posting of a tweet from Brian
Cox was posted on the blog: “And combined - 5 sigma. Round of
applause. That’s a discovery of a Higgs - like particle at CMS. They
thank LHC for the data!”
“9.44am: Rolf Heuer, Director General of CERN, offers this verdict:
As a layman I would say: I think we have it. You agree?
The audience claps. I think that’s a yes.
ATLAS: The observed (full line) and expected (dashed line) 95%
CL combined upper limits on the SM Higgs boson production
cross section divided by the Standard Model expectation as a
function of mH in the full mass range considered in this analysis
(a) and in the low mass range (b). The dashed curves show the
median expected limit in the absence of a signal and the green
and yellow bands indicate the corresponding 68% and 95%
intervals.
One standard deviation from the center would give a probability
of 68% of all data (~ 1 in 3). About 95.5% of the data will be
inside two standard deviations (~ 1 in 22); about 99.7% lie within
three standard deviations (~ 1 in 370), four standard deviation
events occur 1 in 15,787 times; and five standard deviation events
occur 1 in every 1,744, 278 times.
So a five sigma effect, which they both now have, means that
such a thing would be observed by chance with a probability of
1/1,744, 278 = 5.7 x 10-7. This is so unlikely that this is the
criterion for accepting an effect as real in particle physics, when it
is corroborated by another experiment as in this case.
There you have it. There is a Higgs (it seems that there
is little doubt of this as of today).
It took from the 1960s to the 2010s, but theory was
vindicated.
There are more problems lurking—beyond the Standard
Model. The biggest problem is that the Higgs seems to
be “business as usual,” no problems arise.
Isaac Asimov has said the most important words uttered
by a scientist is “that’s funny …”
Unfortunately, there seems to be no funny business in
attendance on the Higgs found at CERN.
The “very nature of being a Standard Model Higgs may
be the reason our universe is ultimately unstable. It has
to do with the so-called vacuum stability in the Standard
Model.
“According to the description currently favored by
physicists, a vacuum is not completely devoid of matter
but instead teems with particles and antiparticles that
pop into existence and then run into one another and
annihilate themselves, all in very short times. The
inherent uncertainty embodied in quantum mechanics
permits these spontaneous fluctuations—as long as the
particles don't live for more than a fleeting instant, the
process violates no laws of physics.”
“The observed 126 GeV mass seems to imply the universe does
not exist in the lowest possible energy state but is in fact
positioned in a slightly unusual place. ‘It turns out that for a
Higgs boson of 126 GeV, we might be in the gray area where the
universe is at a local minimum that is not the global minimum,’
says physicist Matthew Strassler of Rutgers University.”
“There is a tiny sliver of metastability. Why is the universe just at
this point? Is this actually a profound thing we have to
understand?”
—Paul Steinhardt
(This tunneling to the lowest state would have a lifetimes of
billions of billions of years if the universe is metastable.)