A journey through time
with the Higgs particle
Gordon J. Aubrecht, II
Columbus Science Pub, 2 October 2012
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.
First, I’d like to look ahead to the
Standard Model. This is the chart from
CPEP.
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.”
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.
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.
Here is where they both see the the
possibility of the Higgs—between
120 and 130 GeV/c2.
The combined upper limit on the Standard Model Higgs
boson production cross section divided by the Standard
Model expectation as a function of mH is indicated by the
solid line. This is a 95% CL limit using the CLs method in
in the low mass range. The dotted line shows the median
expected limit in the absence of a signal and the green and
yellow bands reflect the corresponding 68% and 95%
expected regions. At that time it was over 2 .
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 (or something very
like it).
It took from the 1960s to the 2010s, but theory was
vindicated.
There are more problems lurking—beyond the Standard
Model.