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MARKUS KLUTE: Welcome
back to 8.701.

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In this section we want to look
at how we can theoretically

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describe masses of neutrinos.

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There is not just
one way to do this

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and the judge is still out
there which one is actually

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realized in nature, or perhaps
both are realized in nature.

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So mass terms can be
constructed by introducing

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so-called sterile neutrinos.

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The first way, and it's
shown here in the Lagrangian,

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is very familiar
to you where you

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have a left-handed
component of a particle

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coupling via the Higgs boson
to a right-handed component.

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Now, if we now have a
right-handed component

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or right-handed neutrino,
that neutrino does not

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interact with the
weak interaction

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and doesn't interact with any
other interaction we know.

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Hence, this neutrino,
this right-handed particle

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is a sterile neutrino.

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It's not interacting in
any of known ways other

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than with the Higgs field with
the rest of the standard model.

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The second part, the second way
the mechanism is using Majorana

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particles, particles which
are their own antiparticles,

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and we'll look in how
this is being implemented.

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So again, the first,
the Dirac term

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is generated after
electroweak symmetry breaking

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from Yukawa interactions.

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We have seen the very same
thing for our charged leptons.

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What we see here is that the
lepton number is conserved.

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Before and after
the interaction we

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have the same number of leptons,
but the lepton flavor is not

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conserved in this interaction.

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We can rewrite this.

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We identify the sterile neutrino
as the right-handed component

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of the spinor.

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I mentioned this
already, and we basically

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couple the
weak-doublet components

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as you would just
expect that to appear.

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The second term, the
Majorana mass term,

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is interesting as we
introduce another singlet

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into the standard model.

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So this then can
appear as a bare mass

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term with some consequences.

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So here what we
are trying to do is

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we are involved two neutrinos,
right-handed fields.

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Those break the lepton number.

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So if those neutrinos
are realized in nature,

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we have to observe lepton--

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we should observe lepton
number-violating processes.

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And so the search for the
specific kind of neutrino

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is through searching for lepton
number-violating processes.

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So we can rewrite this
part of the Lagrangian,

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this part of the math term
here using this matrix.

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Let's see how this unfolds.

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If the math term now is
much, much larger, or larger

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than the electroweak
scale, you can

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try to diagonalize
the master and it

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leads to three neutrinos,
three light neutrinos,

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three light neutrinos
you would expect,

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and one potentially--
one potential, or maybe

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multiple potential
heavy neutrinos.

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If you then rewrite
the math term

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you find for the light
ones, the term which goes

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is 1 over the scale of
this [? known ?] neutrino.

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That is a nice motivation
for this kind of physics

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as it automatically reduces
the amount of the neutrino

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as we observe the math is
to be very small in nature.

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And then the mass of
the heavy neutrino

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is proportional to the mass.

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This mechanism is called see-saw
because it automatically moves

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the scales of those
two neutrinos,

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the heavy ones and the light one
apart so you happen to observe

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the heavy one, maybe because
they're very, very heavy,

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and the light ones have light
mass because of this mechanism

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of being proportional to
1 over the mass scale--

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the mass eigenstate
of those neutrinos.

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However, if the mass scale of
those eigenvalues is much--

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not higher than the
electroweak scale,

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the low energy spectrum contains
these additional light states.

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So you have not just the
three light neutrinos but you

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have additional light scales--

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states which mix with these
three light neutrinos.

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And that is kind of
an interesting area

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to look for these particles
as they would lead

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to small deviations in
observed electroweak

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efficient properties,
and they might

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yield to some interesting
decays in nuclear physics,

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and we'll come to
those specifics later.

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We have seen in this
lecture two different ways

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to generate masses.

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One's to recover
interactions, same

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as the interaction with
the Higgs field, and one,

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we have the see-saw mechanism
introducing Majorana neutrinos.