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MARKUS KLUTE: Welcome
back to 8.701.

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In the previous
lecture, we have seen

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how the gauge bosons, the W,
and the Z boson acquire mass,

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while the photon
remains massless,

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through the Higgs mechanism.

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We introduced a new field,
a new complex doublet field,

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the Higgs field,
which then broke,

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through its vacuum expectation
value, the symmetry.

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And then through the
coupling to the gauge bosons,

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they acquired mass.

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Right.

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But we also have to find a
solution for the fermions.

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You cannot simply add a fermion
mass onto the Lagrangian.

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That would change, or
that could violate, break,

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the gauge invariant.

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So how do we do this?

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We do this in a
very similar way--

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even easier.

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But before we look
into how this is done,

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let's have a look at
the masses itself.

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It's spectacular.

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The top quark is our
heaviest known fermion.

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It has a mass of about 172 GeV.

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The tau has a mass of 1.7 GeV.

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The muon is an
order of magnitude

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lighter, with 0.1 GeV.

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And for the electron, we
have to go to 0.51 MeV.

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OK?

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And we haven't even
tried to understand,

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or we were not able
to measure, actually,

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the masses of neutrinos.

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We will talk about neutrinos in
one of the following lectures.

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So here you have six
orders of magnitude.

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And you have to go
further down here in order

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to find the neutrinos
on this mass scale.

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So we have to have a
mass-giving mechanism which

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allows this broad spectrum
of masses to occur.

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And the very simple
ad hoc mechanism

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which was introduced
to the standard model

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is one where the particle simply
interacts with the Higgs field.

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So we have our Higgs field here.

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Let's say we have a
left-handed particle coming in.

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And the interaction
with the Higgs field

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turns it into a
right-handed particle.

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This is a little bit
simplified, but what

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we do there here is
simply introducing terms

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into the Lagrangian
which do nothing else.

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We turn our
left-handed particles,

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via the interaction
with the Higgs field,

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into right-handed, and
the other way around.

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And we have to do this
for up-type particles

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and for down-type particles.

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So here is another view of this.

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The strength here is the mass
of the particle over the vacuum

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expectation value.

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This number here, this
number, this lambda d,

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it's the so-called
Yukawa coupling.

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And those Yukawa couplings now
change from fermion to fermion.

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Each fermion comes with
their own Yukawa coupling.

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It's basically a free
parameter in our theory

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in the standard model.

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So instead of talking about the
masses being free parameters,

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we talk about the coupling
to the Higgs field

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as free parameter.

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But they are one and the same.

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All right.

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So this was rather
straightforward.

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It's a simple coupling; you
introduce this term ad hoc,

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and then hope for the
best that it's actually

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realized in nature.

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And you'll see
that this is indeed

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the case for some of
the fermions later.