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MARKUS KLUTE: Hello.

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So with this recording
I'd like to introduce

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the topic of flavor symmetry,
what we mean by that.

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So when the neutron
was discovered,

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it was noted that the
mass of the neutron

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is very close to the
mass of the proton.

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And so it seems like those two
particles are somehow related.

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Even so, the electric
charge is different.

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The proton is charged,
the neutron is neutral.

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And you can see here that the
masses are really very, very

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close, about 1 MeV or about
1% difference in mass.

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So Heisenberg proposed,
and that was in the 1930s,

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to regard them as two
states of the same particle.

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They were really so
different that you

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could think that they are
basically the same, just

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a rotation from one
end to the other.

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And that's exactly what
he did, considering them

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as one particle, a nucleon,
where the proton is described

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as a doublet, with an up
doublet, and the neutron

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as a down doublet,
similar to an up

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quark and a down quark in
electron and neutrino later on.

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Those particles were
not known at the time.

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So he introduces a new
concept, so-called isospin

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or strong isospin, where
he's doing exactly the this.

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He labels the proton up, and
he labels the neutron down.

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So, so far, we
haven't done anything,

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but introduce new labels for
new particles or particles,

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new particles at the time.

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But now if you assume that
the strong force is invariant

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under rotations in
this isospin space,

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meaning when you flip the
neutron into a proton and vice

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versa, those rotations
are invariant.

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The strong force is invariant
under those rotations.

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That means or it
follows directly

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that the isospin is conserved
in all strong interactions.

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So that is what
really the conclusion

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is of this introduction
of those new labels

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is that isospin is conserved
under strong interactions.

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So this was proposed
in the 1930s.

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Again, we noticed the
symmetry in nature.

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And from that symmetry,
a conservation follows.

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Even so, and we can conclude
in physics cross-sections

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or ratios of
cross-sections from it,

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without understanding
in this case,

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QCDs a strong interaction.

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So this is very fascinating.

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And you can just apply this
concept now to other particles,

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for example, the pion.

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The pion has an isospin of 1.

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And there are three
pions or three states--

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the 0 state, the up
state, and the down state,

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which is pi plus, the
pi 0, and the pi minus.

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In general, you can conclude
that the multiplicity

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of your particles, as you see
the neutron and the proton,

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the pi plus, the pi 0, and
the pi minus, the multiplicity

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is 2 times the isospin plus 1.

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Isospin equals 1 means
that the three particles

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as part of the representation.

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So far so good.

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So later, this concept was
moved to other new particles.

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Many new particles were
introduced and produced

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in the emerging accelerators
and experiments on the market.

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And people tried to classify
them by the isospin.

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Gell, Mann, and
Nishijima empirically

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observed that there's
a relation which holds,

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this equation here, which
is that the charge, if you

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assigned the maximum value,
I3, the third component

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of the isospin, to the member of
the multiplet with the highest

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charge--

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in the previous example it
was the proton or the pi plus.

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Then the charge of
this particle follows

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from the isospin, the baryon
number, and the strangeness.

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We looked at baryon number
and strangeness before.

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As a reminder,
strangeness is the number

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of strange quarks in
the baryon or the meson,

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and the baryon number is
simply the number of baryons.

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So if you just look at this,
for example, for this pion case,

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we had the isospin equals
1, baryon number equals 0,

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strangeness equals
0, which follows

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that the maximum
charge involved is

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1, which is a charge of a
positively charged proton.

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So far so good.

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This was empirically observed.

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But once you then later discover
and develop a quark model--

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this is then in the 1970s--

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you can deduce this equation
directly from the assignment

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of isospin to quarks, which
is rather fascinating.

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Again, we don't understand
the physics fully.

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But just from the
symmetry you can,

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and empirically you
can deduce information

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about physical systems.

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However, if you try to now
extend this idea of isospin

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to the complete quark model,
you find that the symmetry

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starts to be broken.

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It already starts to
be broken slightly,

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when you include strangeness
or strange quarks.

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But it's badly broken when you
include charm, bottom, and top.

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And the reason can be seen here.

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The up quark and the down
quark, both of the particles

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making up ions and the
neutron and the proton.

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And even if you
include strangeness,

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the different in mass
is not very large.

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So the symmetry,
the particles really

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look like they're the same
particle in a different state

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of the same particle.

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But when you introduce other
quarks, heavier quarks, charm

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and bottom, you find that the
mass difference is so large,

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that the symmetries are broken.

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So this concept
starts failing because

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of the large mass differences,
because the symmetry is broken.

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All right, so from here, we
now go to discrete symmetries.

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And again, from the observation
of those symmetries,

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we can deduce physics
without fully understanding

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the underlying physics.