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MARKUS KLUTE: Welcome back to 8.701.
So in this lecture, we open a new chapter
of weak interaction.
So we are one by one adding together
the components we need in order to describe
all elementary particles and their interactions.
And I'll be adding the third form of interaction.
After the QED and QCD, we enter into the discussion
of the weak interaction.
So let's have a look at the standard model.
So we discussed gluons and QCD.
And we saw that gluons couple to themselves and also
to all quarks.
Because they carry a charge under the--
on the QCD, a color charge.
We have also discussed the photon,
and seen that the photon, they do not couple to themselves,
but they couple to all charged elementary particles.
Those are the meta particles, the fermions.
The photon also couples to the W boson.
We call it the electrical charge.
So now what we want to do in this next chapter.
We want to fully understand the W and the Z boson.
And we will see that they couple to all meta particles.
And we'll also discuss how they might couple to themselves,
or the Z boson couples to the W boson.
Well, that's the story of this entire chapter,
and we'll take it one by one.
As an introduction, we start with the Feynman Rules.
So having the Feynman Rules in place, and the cookbooks,
the recipe, in order to calculate decays and scattering
processes.
That is all we need in order to get moving.
You can, for example, look at this vertex
here, of this component of the Feynman diagram.
And what we need to analyze this is
the propagator for the W and Z boson, and the vertex factor.
This vertex factor now looks a little bit
more complicated than for QED and QCD,
because the W boson and the Z boson, they carry mass.
So we have some additional factors. q squared minus M
square.
And this q squared over M squared term as well.
One interesting fact about this vertex factor
is what happens now, is q squared is much, much smaller
than M squared.
We have to get rid of those components here,
and we find a vertex factor which
looks similar to the one we have in QED.
However, that's not one over q squared term, but 1 over M
squared term, which is constant.
So we would see that we can describe
this in the context of the Fermi theory,
which is a lower energy approximation
of the full theory of heat conduction.
It's kind of an interesting concept,
and it extends to the entire understanding
of the standard model.
It might be that our standard model,
you know, that we have all the packages together,
describes the lower energy approximation
of a more complicated-- more holistic theory, which we then
can discuss under the concept of a grand unified theory.
Maybe there's a symmetry group which
is embedding the symmetry groups we need for QED, QCD,
and the weak interaction.
But that's a side remark.
So we will look at the Fermi Theory a little bit more later.
The vertex factor itself, describing the vertex here.
It's given here.
For the W boson, and also for the Z boson.
And it looks a little bit more complicated than the vertex
factors we have seen so far.
What you notice that there is the parameter,
which is associated to the strength of the interaction.
And the gamma matrix.
But there's also this term here, which has two components.
There's the one, and the gamma 5 matrix.
We have talked about gamma 5 matrix already.
And we can later identify those as individual currents
are coupling to vector current and an [INAUDIBLE] current.
So this looks even more complicated
now for the Z boson, because here we
have not just numbers of one, but an additional factor.
This factor cV is a vector coupling,
and it's specific for each fermion.
So each fermion has one of those constants.
And the second part of the package or set of constants,
for the axial current.
You have a second parameter here,
which is the strength of the coupling of the Z boson.
So at this point, you just take this axial,
and you can do all our calculation.
On our next slide, I'm going to explain
to you what the corresponding numbers and what d values are
for those parameters cV and cA.
Later, we will see how it comes to this more complicated
structure, and why there is a vector,
and why there is an actual axial current
in the weak interaction.
But for now, we just take this for granted,
and we just take this as a recipe.
So now for the neutral.
So we've just have seen that this is the vertex factor.
And here, for all fermions, we list what
these values are for cV and cA.
What you can see is for the neutrinos,
the factor is one half, both for cV and for cA.
And for the charge leptons and quarks,
there is an even more complicated term here,
which includes a new parameter.
Sine squared theta w.
The value of this is 28 degrees.
Sine squared theta w is 0.231.
As a little bit of a preview here already,
the fact that there is this new parameter and an angle involved
leads to, or can be explained later,
by the fact that the weak interaction is actually
a result of a mixing between an original weak interaction,
and QED.
So there's a mixed thing going on.
In other words, the Z boson itself
is a mixture between the thing which
couples to the weak part of the particle,
and the part, which couples to the electrically
charged part of the particle.
When you see that, that's why there
is a simple factor for the neutrinos who are electrically
neutral, and a more complicated term here for the electrically
charged particle.
And you see that this is the electric charge here.
Or two times the electric charge of the particles.
But for now, those are all just constants and recipes
to be used.
One additional word on the history
of the neutral charge of the neutral weak current
is given here.
So in the '60s and '70s, the standard model
was slowly developed.
A little bit more slowly than we do in this class here.
And there was-- the hypothesis is
that there have to be something like a neutral current
in there.
But it has never been observed in nature.
And so this bubble chamber, specifically the one
Gargamelle at CERN, one was able to actually see those, see
virtual and really see, those interactions
for the first time.
And the first pictures that have been taken in the 1970s, 1973.
And this picture here illustrates--
I will expand it in a second--
illustrates the interaction of a neutrino
coming into the bubble chamber, making an interaction
with an electron, and then scattering off, kicking off
the electron.
So what you see here is this incoming--
this is an anti-neutrino kicking off an electron.
See the electron here.
The neutrino goes off undetected.
It just disappears.
You see here, the electron.
And then there's also two protons.
One proton here.
Let's use a different color.
And one photon here.
Causing electron positron pair, and the second photon
here doing the very same thing.
You can see those particles here.
See here and then going on here as well.
So this is a bubble chamber picture.
We'll talk about bubble chambers very briefly
later in the lecture as well.
But they're very extremely important and useful tools
in order to illustrate--
to visualize and measure particle interaction.
All right.
So much to the introduction, and we'll
continue now with the next lecture on talking
about this mixture, this electroweak mixture [INAUDIBLE]