The updated CPEP particles chart:
adding the Higgs boson and possible
future discoveries
Gordon J. Aubrecht, II
Appalachian Section AAPT Meeting 2014
1 November 2014
I am the former chair of the
Contemporary Physics Education
Project (CPEP).
By the late 1980s, particle
physicists realized that an
established model of how particles
exist and interact—the Standard
Model—had come into being.
There were many streams
converging. One was development
of a model, QCD, that explained
how particle interactions work.
QED explained the electromagnetic
interaction, QCD the strong
interaction.
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.
Experiments from 1898 to the 2000s led to
this “particle zoo.”
This was our original idea.
This was how we built on the idea. Notice that I had a
lot less gray in my hair then!
This was the result of our first
attempt at a chart of particles and
interactions.
The current-minus-1 version is
here.
The current chart version (postHiggs) is here.
We support
all the
charts.
I want to
demonstrate
a little of the
Particle
Adventure.
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.
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).
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.
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.
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.
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.
What did ATLAS and CMS see? Here are the Atlas
data from 2013 (the Moriond Conference).
The gauge bosons in our previous chart.
The newest version.
The Higgs boson gives mass to the four colorless gauge
bosons (, W+, W-, Z) in the Standard Model.
New to the chart
New to the chart
New to the chart
New to the chart
New to the chart