**The Early History of the Weak Interaction**

Our history will begin with the first understanding of beta decay. Beta decay was one of three kinds of
radioactive decay that had been under investigation since the late 1800s. Early pioneers in this
field included Marie Curie,
William Roentgen, and
Henri Becquerel.
It was Rutherford
who first realized that there were at least two different types of radioactivity,
alpha and beta decay. Beta decay is what spurred the development of the theory
of the weak interaction.

In a beta
decay event, an atomic nucleus emits an electron (or a positron) and one of its neutrons is transformed into
a proton (or a proton into a neutron). In order to simplify things further we'll consider the
slightly more uncommon case of a decay of a lone neutron. All of the things we say here
will apply to the atomic case as well, it's just a bit more complicated.

The neutron was
discovered
in 1932 by James Chadwick. In the history to be discussed below people didn't know about quarks, but today we
know that a neutron
is a neutral particle made up of three quarks, two downs and an up. At the quark level,
what happens in a beta decay is that a down quark gets transformed into an up quark, changing the neutron
into a proton. In order to keep charge balanced an electron is emitted in this process.

In addition to the electron, an electron anti-neutrino is also emitted. As we discussed in the
first instalment this emission was postulated because it appeared that the decay to only the
electron did not respect the law of energy conservation. By assuming that a light, and
uncharged particle was also included in the decay the law of energy conservation could be
respected. The neutrino was eventually observed in the mid 1950s. Today neutrino physics
is a large, and rapidly expanding, subfield of particle physics (and one that will see
an exposition in a future instalment).

The name "weak interactions" comes from the assumed strength of the interactions which cause
these decays. One good measure of the strength of an interaction is decay times. For example
there is a particle known as
positronium.
It is a bound state of an electron and its antiparticle,
the positron. Positronium decays, via the electromagnetic interaction, in about 10^{-10}
second. This is in stark contrast to the neutron, which decays in about 15 minutes, or the muon
which decays in 10^{-6} second. The slower decay times indicate that the force causing
the decay is weaker. Hence the name weak interactions.

Theoretical attempts to understand the weak interactions began almost immediately after
their discovery. Shortly after the discovery of the neutron, in 1934,
Enrico Fermi presented
a comprehensive theory of beta decay. Fermi's theory treated the beta decay event as
a manifestation of a new force, separate from the forces of electromagnetism, gravitation or nuclear
binding. In Fermi's theory a neutron could disintegrate into a proton, electron, and anti-neutrino
with a prescribed strength. Other processes were possible depending on the situation. For
example, within an atomic nucleus it was possible for the proton to decay into
a neutron, positron and neutrino. Straightforward generalizations of Fermi's theory also quantified
the decays of newly discovered elementary particles, such as the muon. Fermi's theory also solved
the energy problem by postulating the neutrino.
It was, and remains, a powerful
tool.

Fermi's theory was not without some problems. The first was, though it used the same theoretical methods
as electrodynamics (quantum field theory) it did not explain the force in the same way. In
electrodynamics (the quantum version) the force is due to exchange of force carrier particles, known as
photons. Fermi's theory had no force carriers. This problem was more than conceptual, without
force carriers Fermi's theory had a mathematical inconsistency at extremely high energies.

The second problem with Fermi's theory was related to the angular momentum of the various particles involved in decays.
In Fermi's original theory the interaction was such that when the neutron decayed into proton the quantum spin was unchanged.
As a consequence of this when a nucleus beta decayed, the daughter nucleus had to have the same angular momentum
as the original. Roughly the total angular momentum of a nucleus is the sum of all the spins of its
constituent parts added to the angular momentum from the orbits of the various particles around each other.

The trouble was that there were beta decay transitions that were observed to change the angular
momentum of the nucleus by one unit. This is easily explained if the decaying neutron flips its spin when it
decays. Flipping its spin, in this context, would be like the Earth suddenly spinning in the other direction about
its axis of rotation. However the Fermi theory, as originally formulated, didn't allow for these types of transitions.

It turned out that there were actually four distinct types of interactions one could construct in the same sort
of manner as Fermi's theory. Fermi had constructed one of them. For the curious their names were

Scalar and vector
interactions lead to transitions where the angular momentum doesn't change, called Fermi transitions. Axial vector
and tensor interactions give transitions where the angular momentum changes by one unit called
Gamow-Teller
transitions.
At the time the data on beta decays was not strong enough to uniquely determine
the types of interactions that were present. The best that could be done
was to rule out one of each. That is, for Fermi transitions, you had either
scalar or vector, not both. Likewise for the Gamow-Teller transitions, either
axial vector, or tensor. This situation persisted until 1956, when the next
big step was taken, the overthrow of parity.
**Parity and its Violation**

In order to discuss parity we need to get a grasp on what a symmetry of the laws of physics is. Symmetry is
a very important concept in modern physics, as we shall see when we discuss the unified electroweak theory.
The general idea behind symmetries is very simple. A symmetry of the laws of physics is an operation that
doesn't change the laws. For example, in particle physics most systems of interest are symmetric under translations.
This means that the laws of physics here in
Vancouver are the same as those translated to
Ulaanbaatar. Clearly this is an assumption, but it's one that serves to
powerfully constrain the possible set of laws you can write down.

Of particular interest are three symmetry operations of a special type called discrete symmetries.
The three discrete symmetries relevant here are those of charge
conjugation (C), parity (P) and
time reversal
(T). Time reversal symmetry is fairly obvious. It says that the laws of
physics ought to look the same if they're run backward (this obviously doesn't
hold on a large scale, but in the micro-world of particle physics it does
(at least sometimes)). Charge conjugation is equal simple, it says that
for every possible process you can have you can also have one with all the
charges of the various particles reversed (i.e. turn all the particles involved
into their antiparticles). Parity symmetry is also sometimes known as inversion
symmetry. Physical laws that are invariant under parity don't change when
you reflect them in a mirror. Another way of putting this is that the laws
don't care about particles spinning clockwise or anticlockwise.

Prior to 1956 it was assumed that all three of these discrete symmetries were conserved in all the fundamental interactions.
Certainly in the case of electrodynamics, each had been tested, and found to hold. Without realizing it, most physicists
simply carried the assumption that the same would be true in the weak interactions.
It took an experimental anomaly to shake that assumption.

The puzzle was the so-called "theta-tau" problem. Among the plethora of new particles discovered in the 1950s there
were two that were very strange. The theta particle and the tau particle (note to readers of part one, this is not the
same as the tau lepton, discovered in 1975) were both discovered in cosmic rays, and they had the same masses and spins.
However, they had one striking difference. The tau decayed into three pions
whereas the theta decayed into two pions. According to parity symmetry this meant that they had to be different
particles.

This requires a bit of a digression to make clear. Recall that the parity symmetry involved reflection in a mirror. We
can think of this like an operation. A **parity operation**
means "reflect all coordinates". Hopefully it is clear that if I do this
twice I have to get back to my starting point. That is if I make two reflections,
nothing changes. Let's represent this schematically. The state of a system
will be denoted by **STATE** and the parity
operation by **PARITY**. So by our reasoning we must have (X * Y means "do X to Y")

**PARITY * (PARITY * STATE)** = **STATE**

or, in a more abstract way,

**PARITY**^{2} = 1

Which is a handy way of saying two parity operations should do nothing.

The nice thing about the abstract "equation"
we have obtained is that we can "solve" it, by taking the square root of both sides. Now the square root of 1 is either
+1 or -1. So we've figured out the only two allowed possibilities for a **parity operation**. We can
have

**PARITY * STATE** = +**STATE**

or

**PARITY * STATE** = -**STATE**.

Now we can specialize this one last bit, and pretend that **STATE** represents a particle. This gives
use a useful classification tool. A particle is said to have **even parity** if it has the positive sign, and
**odd parity** if it has the negative sign. The pion, for example, has odd parity, the proton has even parity.

What if **STATE** was a multi-particle system? Well, it is possible to show that in this case
the overall behavior under **PARITY** is just given by the product of the single particle
states. That is if **STATE** consisted of a pion and a proton the total parity would be
the parity of the pion (-1) times the parity of the proton (+1), which is odd (-1).

This brings us back to the theta and the tau. Recall that these two particles looked exactly the same, same
mass, same spin, same charge, same everything, except parity. The tau decays into three pions. That means
that the parity of the final state (three pions) is odd. Therefore, if the parity were conserved in the
weak interactions, the tau should have odd parity. Likewise the the theta decays into two pions, implying
that it has even parity.

The nagging thing, of course, is that apart from this parity difference, the theta and tau particles
are identical. Despite searching for tiny differences, no experiment could detect any variation.

The solution to this puzzle emerged rapidly. Two theorists,
Tsung-Dao Lee and
Chen Ning Yang
published a landmark paper in which they showed that there was actually
not a shred of evidence available that the weak interactions had parity symmetry. For over
twenty years people had just assumed they did without checking. Lee and Yang argued that the
theta tau puzzle was evidence that, perhaps, the weak interactions didn't conserve
parity after all.

Prior to the publication of their paper, they had relayed their ideas to an experimentalist
Chien-Shiung Wu.
Aided by a team from the National Bureau of Standards she
observed the beta decays of a cobalt isotope when it was spinning up (clockwise) and down
(anticlockwise). The experiment confirmed that the two decays were different and parity was
not conserved in the weak interactions.

**Intermediate Vector Bosons and V-A**

We return now to the two problems with the Fermi theory that we discussed above.
We'll start with the second problem, the choice between the scalar (S),vector (V),axial (A) and tensor (T) interactions. To get
parity violation only certain combinations were allowed. Of these an experiment by
Hans Frauenfelder pointed at some combination of V and A type
interactions.

While it was sensitive to the *type* of interactions involved, Frauenfelder's experiment could not distinguish the relative sign
of the interactions. There were two possibilities, a V interaction
plus an A interaction, or V interaction
minus A interaction. Recall that V interactions do not change spin (Fermi transitions)
whereas A interactions do (Gamow-Teller transitions).

It was a remarkable experiment by
Maurice Goldhaber,
Lee Grodzins and
Andrew Sunyar that decided the issue. The conclusion of this experiment is very interesting,
imagine you were looking at a neutrino as it flew away from you. If you could see
the spin of the neutrino you would **always** see it spinning
clockwise. That is neutrinos always "spin" in the same direction.
To the level of precision available to them this is what
Goldhaber's experiment indicated.

The Goldhaber experiment was preformed in 1958. Its conclusion, along with a growing body of
secondary evidence, strongly supported the V **minus** A theory.
A full version of this theory had been proposed earlier in the year by two pairs of theorists.
The first pair was Robert Marshak and
George Sudarshan. The
second pair was the (more famous)
Richard Feynman
and Murray Gell-Mann.

Initially this theory still involved Fermi type interactions, that is all the weak interactions
occurred at a single point in space. There was no mediation by massive force carriers. This
was the cause of the problem that the theory is mathematically
inconsistent at high enough energies. Feynman and Gell-Mann "patched" this up
by simply postulating force carriers. As we shall discuss below, this led
to almost as many problems, but in the late fifties it was an advance.

There was, and still is in some cases, a troubling problem. The V-A theory worked
really well when describing truly fundamental particles. The prime example
was the decay of the muon, which V-A was very good for. However, for hadronic
particles (like protons, pions, kaons, etc.) there was a snag.

The problem was that the strength of the interaction varied from particle to
particle. This is because hadronic particles, which we now know are made up
of quarks, are also affected by the strong interactions. As discussed
in the last instalment, at low energies, the effects of strong
interactions are hard to compute. For weak interactions of hadrons this
has the effect of modifying the strength of the force on the various particles.

To appreciate the partial solution that was found, it's useful to have a schematic idea
of the weak interaction. The interaction can be represented as the product of
two things. For hadronic particles theres the hadron part H and the electron-neutrino
part J (J is historical). So the interaction is H*J. Each piece has the V-A part. Indeed
if we were dealing with muons instead of hadrons we'd have J'*J, where J' and J are identical
apart from the different masses.

The interesting thing about J is that the vector (V) part of it looks very similar
to the electromagnetic interaction. In the weak case there are two things that J
causes, electron-antineutrino interactions, or positron (antielectron)-neutrino
interactions. The first interaction raises the charge by one unit - electrons have a
charge of -1, neutrinos are chargeless - and the second lowers the charge by one.

What Feynman and Gell-Mann proposed in their theory is that this raising and lowering
is part of a **triplet** of interactions, the third being
**no change**. And no change in charge is the electromagnetic interaction.
They proposed that the V part of the weak interaction for both the hadrons and leptons
was merely a part of a larger structure that included the electromagnetic current.

The useful thing about this is that it allows one to use all the information
acquired about the electromagnetic interactions of hadrons (which is a lot
of information) to make statements about the V part of their weak interactions.
Of course the A part still was a problem, but this was major progress nonetheless.
This notion, of the V part of the weak interaction being somehow related
to electromagnetism goes by the name
conserved
vector current hypothesis, or CVC. CVC was the first
step toward a fully unified theory of the weak and electromagnetic interactions.

A proper unified theory of the electromagnetic and weak forces was first
constructed by
Sheldon Glashow
in 1961. Using the CVC idea as a starting point Glashow wrote
down a theory which had a unified electroweak force. Glashow's theory
had four force carrier particles. There was the familiar photon, which
carried the electromagnetic force, as well as two massive charged bosons
the W^{+} and W^{-} which were responsible for the
charge changing portions of the weak interactions.

The final particle, which was a new proposal, was called the Z^{0} boson. Like the photon it had no electric charge, so it didn't change the charges
of particles it interacted with. Unlike the photon, however, it was very massive.
As well, it could interact with neutrinos. This was the proposed experimental
signature for the Z. When colliding and electron and positron typically produced
other visible particles as end products. Either another lepton-antilepton pair
or a pair of hadronic jets. Each of these outcomes
would be possible with a photon or a Z mediated force. However, the Z mediated force
could also give rise to an neutrino-antineutrino pair as a final state. This
would be a unique signature. A process like this was said to be mediated by
a "weak neutral current".

The problem with Glashow's theory was that he didn't have a mechanism for
giving these particles - the W and Z at least - masses. Instead he added the mass
in an *ad hoc* way. Essentially he mutilated the theory by adding the
appropriate terms by hand. It was clear that this procedure would not
produce a fully consistent theory. In technical jargon, the theory was
said to be non-renormalizable, which basically means that it wasn't fully
predictive. It would take two more big breakthroughs to get to the
final electroweak theory.

**Spontaneous Symmetry Breaking and Gauge Boson Masses**

To understand the first breakthrough we need to go back to 1954, when Yang
(the same guy who proposed parity violation) and his colleague Robert Mills showed
how to construct fairly arbitrary generalizations of electromagnetism. In fact we saw in the
last instalment that the strong interactions are described by a Yang-Mills theory.
The same is true of the electroweak interactions, but it is much more complicated.

In their original work Yang and Mills tried to give the force carriers masses. They could not
find a way to do so, apart
from the method Glashow would use putting them in by hand. However, putting them
in by hand destroys a number of nice things about the theory. The most
notable is the the symmetries of the theory. If you try to compute something
accurately you'll end up with processes that should be forbidden (for example, violations of conservation rules)
actually being allowed. Then you have to go in and patch this up, only to find
that at the next level of accuracy, more forbidden stuff crops up again.

This problem became the focus of people trying to find a solution to the
weak interactions. It was in collaboration with workers in other fields
of physics that the problem was solved.

The first portion of the solution involved spontaneous symmetry
breaking. Above we talked about the importance of symmetries in
physical laws. However, the symmetries that particle physicists
are enamored about rarely manifest themselves in the real world.
The macroscopic world is clearly not time reversal symmetric, or
to use a more famous example, a chair is not rotationally symmetric,
despite the fact that the laws describing it are.

Given this situation, there are two ways of resolving it. The first is
to simply write the laws of physics such that they don't respect the
symmetry. This is known as explicit symmetry breaking. This is generally
regarded as an unpleasant thing to do, because it's hard to explain.
The other option is to look for theories which break
the symmetries on their own as some physical variable is changed.

This sort of symmetry breaking is common in condensed matter physics.
A familiar example is the freezing of water. At room temperature
water is in its liquid form. If you picked any point in the water
it would look **on average** the same as any other point.
This is a manifestation of translational symmetry. As the temperature is
lowered, not much changes until zero degrees is reached. Then the system
changes, essentially spontaneously, into solid form. Here the system
is not symmetric under an arbitrary translation. The water molecules are
now bound in a crystal form, each is a specific distance away from the next.
In this case, only a translation by the distance will get you to a place
in the crystal that looks the same. This is an example
of a large symmetry - arbitrary translations - being broken spontaneously
into a smaller symmetry - translations by a specific distance.

In particle physics, you can play a similar game, except instead of
temperature, you think in terms of energy. With the weak interactions, one
expected that at high energies - above the mass of the force carriers - the
symmetry was full, and at low energies, the symmetry was broken.

The idea was to start with a Yang-Mills type of theory and break the
symmetry in such a way that you would get Glashow's theory. However there
seemed to be a serious problem with this. According to something
known as
Goldstone's theorem
anytime you spontaneously broke a symmetry you ended up with a massless
particle with spin zero. In our water-ice example the massless particles
are related to vibrations in the ice crystal. However
with the weak interactions, no such particles had been observed to exist.
And massless particles with spin zero should have been fairly easy to spot.

The final piece in this unification puzzle was discovered
by
Peter Higgs.
His discovery, known as "the Higgs mechanism" showed people how
to break the symmetries of Yang Mills theories in such a way that the both the force
carriers and the spin zero particle became massive. The massive spin zero particles are
known as Higgs particles.

To understand this we need to think in a bit more detail about the spin zero particle.
In many ways, "Particle Physics" is a bad name for the field. If you hear a particle physicist
say "particle" they really mean "quantum particle". This is an important distinction, as the
unadorned word "particle" makes people think of billiard balls, classical things. A quantum
particle is a much more subtle thing, because it has a wavelike nature as well as a particle nature.

Typically when one talks about quantum particles one thinks about creating them out
of a vacuum state. That's how interactions are thought of. First you annihilate all
the particles into the vacuum, then you create the new ones out of the vacuum.
Normally one assigns the vacuum state zero energy. This is the case for things
like electrons and photons. However this isn't necessary. For Higgs particles
the vacuum is assigned a finite amount of energy. This is called the vacuum
Higgs field.

When the massless Yang Mills force carriers move through the vacuum Higgs field
they acquire mass. This is similar to what happens if you through a baseball
underwater. It moves much slower due to the resistance of the water. It
looks as if it is more massive than it really is. The same applies for
the Yang Mills force carriers. The end up looking more massive than they really are.

**The Weinberg-Salam Theory**

These ideas were put together in their final form, in 1967, by
Steven Weinberg and
Abdus Salam.
By postulating a trio of Higgs particles, they started with a fairly simple
unified theory at high energies, and showed how, via the Higgs mechanism, the
low energy Glashow theory emerged. All of the essential ingredients were
in place, Weinberg and Salam synthesized them into the final theory.

The Salam-Weinberg theory included the W and Z bosons of the Glashow theory,
along with the photon of electromagnetism. There was also a Higgs particle,
with its funny vacuum. At low energies, the Higgs particle would not been seen.
Only its vacuum value would have an effect on the W and Z, giving them mass, which
is what makes the weak interaction weak at low energies. The photon at
low energy gives the electromagnetic force. At high energy all of these
things are unified. There are four force carriers, which are massless, along
with a spin zero particle. This high energy region will be probed
by the
Large
Hadron Collider in 2008.

There were a number of lingering issues with the Weinberg-Salam theory.
The most problematic was the issue of renormalization. Recall that
if a theory is not renormalizable, it is not fully predictive.
Although it was widely believed that Yang Mills theories were renormalizable
a proof was lacking. Another problem was incorporating quarks into the theory.
A final problem was the lack of evidence for the Z bosons effects discussed
above.

As one might suspect, all of these problems were resolved. In fact, the eight
years, from 1967 through 1975 provided the crucial data, and theoretical
developments to finalize the standard model of particle physics in the form
we use it today. These final developments will be the subject of
the second part of this instalment.

*
Matthew Nobes is a PhD student in theoretical particle physics. He studies at
Simon Fraser University, in British Columbia, Canada. He has been working on
a PhD for about three years, prior to that he spent two years doing a masters
degree. He has a web page here
where you can go to find some links relating
to particle physics. He also would like to thank Peter Whysall for his
editorial assistance.
*