 
Hi.
I'm Jenni Smillie.
And I'm a research fellow here
in the particle physics theory
group in Edinburgh.
We're now going to talk
about the weak force.
Like the strong
force, this is one
which is only really active
over tiny length scales, well
within the size of
an atom, for example.
So in everyday life,
we're really not
aware of feeling the weak force.
And this gave it its name, weak.
But in many ways
it's quite misleading
because it's responsible for
some very important effects
that we do see around
us all the time.
For example, it's
responsible for one
of the key steps in
the nuclear reactions
within the sun that give us
heat and light all around us.
And it's also responsible
for radioactive beta decay.
So today we're going
to start by looking
at radioactive beta decay and
the series of experiments which
taught us about the weak force.
And then we'll go on
to study the force
carriers of the weak
force in detail.
Like the photons and the
gluons that we've met before,
but the big difference is that
these have a non-zero mass.
And we'll see what
impact that has.
So beta decay is where a
neutron within an atomic nucleus
changes into a proton,
releasing energy.
So we met the last time
the neutron and the proton.
We know that the
neutron, for example,
consists of an up quark
and two down quarks.
 
And the proton is two up
quarks and one down quark.
 
So to change from
one to the other,
then one up quark
and one down quark
don't need to change at all.
However, between this down
and this up quark something
has to happen.
And this is the decay process.
 
And the energy, the radiation
that is produced here
is the beta radiation.
And already we know something
about this radiation
because the electric
charge on this side is 0.
The electric charge on
this side is plus 1.
And so this has to carry
negative electric charge
in order for charge
to be conserved.
As well as charge, we know
that energy must be conserved.
And so if we know the
energy on this side
and we know the energy of the
final system with the proton,
then we must know the energy of
this particle that is produced.
In fact, in 1900,
Henri Becquerel
was able to show that
this particle was
the same electron that was being
studied in other experiments.
And, therefore, we were
already piecing together
parts of the weak force.
But there was something
strange about the energy
of these electrons.
If you draw a graph
of the energy here,
and then the number of
electrons with that energy,
then given you know
energy before and after,
all of the electrons
produced should
have the same energy
at a particular value.
And you should get just one
discrete peak, as, indeed, you
see in other decay processes.
But, instead, what we saw was
a continuous spectrum that
went like this.
And it never exceeded this
value that was predicted.
But you can see from
the shape of the peak
here that most of the
time the electrons
were produced having lost
really a lot of the energy.
And it appeared that energy
was missing in this process.
And this caused a real problem
for physicists of the time.
And, indeed, led some
of them to question
whether energy was
really conserved at all.
But in 1930, Wolfgang Pauli
suggested that maybe there
was another solution, that
there wasn't energy missing.
We just had missed seeing it.
So the election
was being produced.
But if another particle was
produced at the same time,
it could carry away the energy.
And we wouldn't observe it.
And we'd see a spectrum
like this instead.
And he was right.
And the extra
particle produced is
one we now know as part
of a family of particles
called the neutrinos,
although it was 1956
before those particles were
actually officially discovered.
So this line here, actually,
is not just one beta radiation.
Instead, if you have your
down and your up quark,
then what is being
produced is your electron.
And this particular neutrino
is the antielectron neutrino
in this process.
Now when we looked at
both electromagnetism
and at the strong
force, there we
saw that these
forces were carried
by a type of particle
called bosons.
And it's exactly the
same for the weak force.
So we can actually do
better with this diagram
still and zoom in further.
And what you actually
see is that there's
a force carrier
here that is then
decaying to give you this
electron and this antineutrino.
And you'll notice here
that I deliberately
drew this with a W minus.
The W just stands for weak.
It's the name given to the
carrier of the weak force.
But the minus is
because it does, indeed,
carrier electric charge.
It must do to conserve charge at
each point in this interaction.
And this is exactly
the charge that
is carried by the electron.
And so it shows that
this W does actually
interact with the
electromagnetic force.
Now many times we talk about
four fundamental forces
as if they're
independent things.
But really they're not.
And, in fact, the
weak interaction
is completely coupled with
electromagnetic interactions.
And in 1956, the Nobel Prize
was given to Glashow, Salam,
and Weinberg for
precisely unifying
these different theories.
So now we see a
process like this.
There are, in fact, a
number of other processes
that are very similar.
Firstly, you can do
a kind of reverse,
where an up quark
becomes a down quark.
And there, instead,
you have a W plus.
The charge is now going
from plus to minus.
So it has to be
the opposite sign.
And here, for example,
you can have a positron.
And this becomes an
electron neutrino.
There's one last piece
in this puzzle, which
is that the weak
force does also have
a boson that is
electrically neutral.
There is a neutral one.
But it is slightly
different to the two W ones
entirely because
of this interaction
with the electromagnetic force.
And the fact that
they are so combined
means you will never
observe a W zero.
So in any physics process
you won't have a W zero.
And instead what you
see is a particle
that we call the Z.
It's also a heavy boson.
And, in fact, it's just
fractionally heavier
than the charge W
plus and W minus.
 
So we've seen that for the
weak force the Ws and the Zs
play the same role as
the photons and gluons
that we've seen before.
But the difference is that
now they have nonzero mass.
In fact, they really
are very heavy.
The mass of a W is
80.4 gigaelectronvolts
over c squared,
where, again, we're
using these strange particle
physics units for masses.
But if you compare these
to the mass of, say,
the proton or the neutron, which
are about 0.9 gigaelectronvolts
over c squared, then that really
is very heavy, 80 times as
heavy, in fact.
And it's actually
quite surprising
that in a reaction which just
changes one of these particles
to the other you can
produce something
that is as massive as this.
And the only reason
that we can do that,
actually, is because
of quantum mechanics.
It's a quantum effect that
allows you to borrow energy,
provided you do it only for
a very short amount of time.
But now, what is
the real difference
to having a massive force
carrier to a massless one?
If we return to
electromagnetism for a bit,
there we saw that you have
a Coulomb potential where,
if you have two
charges with a charge
q1 and q2 separated
by a distance r,
then the potential
is just the product
of these charges, some
constants, and then
the distance between
the two particles.
So that was the
Coulomb potential.
If now you have a
massive particle,
then this potential changes.
It takes the form known
as a Yukawa potential,
where now the v of r still
has some constants that
depend on the exact
particles involved.
But there's extra
dependence on the distance.
And it has this
exponential factor of e
to the minus r over r.
So the first sanity check is
that if we put m equals 0,
we do, indeed, recover something
of the form of a Coulomb
potential.
But the effects of
this exponential
is actually very strong.
If you think of sketching
these two potentials,
then both become very large
when r becomes very small.
And both will become very small
when r becomes very large.
So you get a distribution
that's something like that.
But the effect of this
extra exponential term,
compared to just straight 1 over
r, is to cause this to decay
much, much faster.
So you will get curves
that go like this
or that actually drop
in a way that you simply
can't see by eye.
And, in fact, it's
exactly this which
makes the weak force
such a short-range force.
If you put the mass of the
W boson into this formula,
a typical length scale
for the weak force
is 10 to the minus
18 metres, which
really is a tiny distance.
It's about a thousandth
of the radius of a proton.
And that's why
everyday length scales
you would never actually
see this force at all.
But this presents us
with a bit of a problem
because we want to
test the weak force.
We want to test that
we understand it.
And so we need to be able
to probe these tiny scales.
And we can do this by
supplying particles
with a large amount of energy.
This counteracts the need
to borrow energy at all.
And as you increase
the energy, you
probe shorter and
shorter length scales.
And this image here
is actually one
of the first collisions
that produced a W boson.
This was an experiment
which was conducted
at CERN many, many years before
the LHC, which collided protons
and antiprotons and exactly
overcame this lack of energy
and was able to discover
the W plus and the W minus.
Later, their heavier
cousin, the Z
were also discovered
at the same experiment.
For now, we'll return to looking
at the effect of the mass.
So when we first
discussed the photon,
we discussed that it has
these different independent
polarizations.
And if your photon is travelling
in a particular direction,
then these polarizations have
to be at right angles to that
direction.
And, therefore, there were these
two independent polarizations
for the photon.
But when there's a mass,
there's a very big difference
to the behaviour of a particle.
From special relativity,
you know that whatever speed
you're travelling at, whatever
speed a light source is
travelling at, then a photon,
light will always travel
at the speed of light, at c.
Its speed is always fixed.
And it's always moving.
But the same is not true
for a massive particle.
For a massive particle,
you can even stop it.
You can have it
completely at rest.
And that, then, means that
if you impose this condition
that you want the polarizations
to be at right angles
to the direction, that becomes
a meaningless statement
because there is no direction if
something isn't moving at all.
And so that doesn't
give you any constraint.
You can have polarizations
in any one of the three
directions.
You call them x, y, and z.
And, indeed, for the
massive gauge bosons,
they do have these three
independent polarisation
states, which makes
them very different,
then, to the massless
force carriers.
But this is, so far,
working quite well
because we have a force
that we understand
with massive particles which
are predicted and observed.
And we have to allow an
extra polarisation state.
But that's OK.
However, there is a
very, very big problem
when we try to develop
a theory to describe
these massive bosons.
We want to write down equations
of motion and equations
which really describe these
bosons in the same way
as the Klein-Gordon equation
and the Dirac equation
that you saw last week.
But if you have a massive
particle, you need a mass term.
But you still have all
the same requirements
that your theory must
have certain symmetries.
It must obey certain laws.
You can't write down
arbitrary terms.
And there is simply
no way to combine
a term for the mass of a
boson with these rules,
with these requirements
of symmetry.
And so no theory that
anybody could write
could describe this theory
which had been beautifully
experimentally observed.
And it is precisely
this problem of how
you reconcile a mass with
the symmetries of the theory
that Peter Higgs solved in
his groundbreaking work.
 
