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MARKUS KLUTE: Welcome
back to 8.701.

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So in this lecture,
we open a new chapter

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of weak interaction.

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So we are one by
one adding together

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the components we need
in order to describe

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all elementary particles
and their interactions.

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And I'll be adding the
third form of interaction.

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After the QED and QCD, we
enter into the discussion

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of the weak interaction.

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So let's have a look
at the standard model.

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So we discussed gluons and QCD.

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And we saw that gluons
couple to themselves and also

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to all quarks.

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Because they carry
a charge under the--

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on the QCD, a color charge.

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We have also
discussed the photon,

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and seen that the photon, they
do not couple to themselves,

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but they couple to all
charged elementary particles.

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Those are the meta
particles, the fermions.

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The photon also
couples to the W boson.

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We call it the
electrical charge.

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So now what we want to
do in this next chapter.

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We want to fully understand
the W and the Z boson.

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And we will see that they
couple to all meta particles.

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And we'll also discuss how they
might couple to themselves,

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or the Z boson couples
to the W boson.

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Well, that's the story
of this entire chapter,

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and we'll take it one by one.

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As an introduction, we start
with the Feynman Rules.

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So having the Feynman Rules
in place, and the cookbooks,

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the recipe, in order to
calculate decays and scattering

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processes.

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That is all we need in
order to get moving.

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You can, for example,
look at this vertex

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here, of this component
of the Feynman diagram.

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And what we need
to analyze this is

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the propagator for the W and Z
boson, and the vertex factor.

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This vertex factor
now looks a little bit

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more complicated
than for QED and QCD,

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because the W boson and the
Z boson, they carry mass.

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So we have some additional
factors. q squared minus M

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square.

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And this q squared over
M squared term as well.

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One interesting fact
about this vertex factor

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is what happens now, is q
squared is much, much smaller

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than M squared.

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We have to get rid of
those components here,

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and we find a
vertex factor which

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looks similar to the
one we have in QED.

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However, that's not one over
q squared term, but 1 over M

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squared term, which is constant.

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So we would see
that we can describe

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this in the context
of the Fermi theory,

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which is a lower
energy approximation

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of the full theory
of heat conduction.

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It's kind of an
interesting concept,

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and it extends to the
entire understanding

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of the standard model.

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It might be that
our standard model,

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you know, that we have
all the packages together,

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describes the lower
energy approximation

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of a more complicated-- more
holistic theory, which we then

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can discuss under the concept
of a grand unified theory.

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Maybe there's a
symmetry group which

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is embedding the symmetry
groups we need for QED, QCD,

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and the weak interaction.

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But that's a side remark.

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So we will look at the Fermi
Theory a little bit more later.

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The vertex factor itself,
describing the vertex here.

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It's given here.

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For the W boson, and
also for the Z boson.

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And it looks a little bit more
complicated than the vertex

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factors we have seen so far.

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What you notice that
there is the parameter,

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which is associated to the
strength of the interaction.

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And the gamma matrix.

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But there's also this term
here, which has two components.

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There's the one, and
the gamma 5 matrix.

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We have talked about
gamma 5 matrix already.

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And we can later identify
those as individual currents

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are coupling to vector current
and an [INAUDIBLE] current.

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So this looks even
more complicated

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now for the Z boson,
because here we

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have not just numbers of one,
but an additional factor.

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This factor cV is
a vector coupling,

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and it's specific
for each fermion.

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So each fermion has
one of those constants.

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And the second part of the
package or set of constants,

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for the axial current.

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You have a second
parameter here,

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which is the strength of
the coupling of the Z boson.

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So at this point, you
just take this axial,

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and you can do all
our calculation.

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On our next slide,
I'm going to explain

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to you what the corresponding
numbers and what d values are

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for those parameters cV and cA.

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Later, we will see how it
comes to this more complicated

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structure, and why
there is a vector,

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and why there is an
actual axial current

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in the weak interaction.

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But for now, we just
take this for granted,

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and we just take
this as a recipe.

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So now for the neutral.

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So we've just have seen that
this is the vertex factor.

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And here, for all
fermions, we list what

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these values are for cV and cA.

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What you can see is
for the neutrinos,

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the factor is one half,
both for cV and for cA.

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And for the charge
leptons and quarks,

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there is an even more
complicated term here,

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which includes a new parameter.

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Sine squared theta w.

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The value of this is 28 degrees.

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Sine squared theta w is 0.231.

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As a little bit of a
preview here already,

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the fact that there is this new
parameter and an angle involved

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leads to, or can
be explained later,

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by the fact that the weak
interaction is actually

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a result of a mixing between
an original weak interaction,

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and QED.

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So there's a mixed
thing going on.

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In other words,
the Z boson itself

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is a mixture between
the thing which

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couples to the weak
part of the particle,

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and the part, which
couples to the electrically

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charged part of the particle.

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When you see that,
that's why there

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is a simple factor for the
neutrinos who are electrically

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neutral, and a more complicated
term here for the electrically

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charged particle.

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And you see that this is
the electric charge here.

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Or two times the electric
charge of the particles.

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But for now, those are all
just constants and recipes

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to be used.

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One additional
word on the history

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of the neutral charge of
the neutral weak current

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is given here.

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So in the '60s and
'70s, the standard model

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was slowly developed.

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A little bit more slowly than
we do in this class here.

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And there was--
the hypothesis is

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that there have to be something
like a neutral current

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in there.

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But it has never been
observed in nature.

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And so this bubble chamber,
specifically the one

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Gargamelle at CERN, one was
able to actually see those, see

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virtual and really
see, those interactions

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for the first time.

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And the first pictures that have
been taken in the 1970s, 1973.

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And this picture
here illustrates--

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I will expand it in a second--

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illustrates the
interaction of a neutrino

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coming into the bubble
chamber, making an interaction

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with an electron, and then
scattering off, kicking off

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the electron.

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So what you see here
is this incoming--

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this is an anti-neutrino
kicking off an electron.

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See the electron here.

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The neutrino goes
off undetected.

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It just disappears.

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You see here, the electron.

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And then there's
also two protons.

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One proton here.

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Let's use a different color.

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And one photon here.

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Causing electron positron
pair, and the second photon

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here doing the very same thing.

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You can see those
particles here.

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See here and then
going on here as well.

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So this is a bubble
chamber picture.

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We'll talk about bubble
chambers very briefly

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later in the lecture as well.

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But they're very extremely
important and useful tools

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in order to illustrate--

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to visualize and measure
particle interaction.

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All right.

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So much to the
introduction, and we'll

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continue now with the
next lecture on talking

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about this mixture, this
electroweak mixture [INAUDIBLE]