MARKUS KLUTE: Hello.
MARKUS KLUTE: Hello.

So with this recording I'd like to introduce
So with this recording I'd like to introduce

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

So when the neutron was discovered,
So when the neutron was discovered,

it was noted that the mass of the neutron
it was noted that the mass of the neutron

is very close to the mass of the proton.
is very close to the mass of the proton.

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

Even so, the electric charge is different.
Even so, the electric charge is different.

The proton is charged, the neutron is neutral.
The proton is charged, the neutron is neutral.

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

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

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

to regard them as two states of the same particle.
to regard them as two states of the same particle.

They were really so different that you
They were really so different that you

could think that they are basically the same, just
could think that they are basically the same, just

a rotation from one end to the other.
a rotation from one end to the other.

And that's exactly what he did, considering them
And that's exactly what he did, considering them

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

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

as a down doublet, similar to an up
as a down doublet, similar to an up

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

Those particles were not known at the time.
Those particles were not known at the time.

So he introduces a new concept, so-called isospin
So he introduces a new concept, so-called isospin

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

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

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

but introduce new labels for new particles or particles,
but introduce new labels for new particles or particles,

new particles at the time.
new particles at the time.

But now if you assume that the strong force is invariant
But now if you assume that the strong force is invariant

under rotations in this isospin space,
under rotations in this isospin space,

meaning when you flip the neutron into a proton and vice
meaning when you flip the neutron into a proton and vice

versa, those rotations are invariant.
versa, those rotations are invariant.

The strong force is invariant under those rotations.
The strong force is invariant under those rotations.

That means or it follows directly
That means or it follows directly

that the isospin is conserved in all strong interactions.
that the isospin is conserved in all strong interactions.

So that is what really the conclusion
So that is what really the conclusion

is of this introduction of those new labels
is of this introduction of those new labels

is that isospin is conserved under strong interactions.
is that isospin is conserved under strong interactions.

So this was proposed in the 1930s.
So this was proposed in the 1930s.

Again, we noticed the symmetry in nature.
Again, we noticed the symmetry in nature.

And from that symmetry, a conservation follows.
And from that symmetry, a conservation follows.

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

or ratios of cross-sections from it,
or ratios of cross-sections from it,

without understanding in this case,
without understanding in this case,

QCDs a strong interaction.
QCDs a strong interaction.

So this is very fascinating.
So this is very fascinating.

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

for example, the pion.
for example, the pion.

The pion has an isospin of 1.
The pion has an isospin of 1.

And there are three pions or three states--
And there are three pions or three states--

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

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

In general, you can conclude that the multiplicity
In general, you can conclude that the multiplicity

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

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

is 2 times the isospin plus 1.
is 2 times the isospin plus 1.

Isospin equals 1 means that the three particles
Isospin equals 1 means that the three particles

as part of the representation.
as part of the representation.

So far so good.
So far so good.

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

Many new particles were introduced and produced
Many new particles were introduced and produced

in the emerging accelerators and experiments on the market.
in the emerging accelerators and experiments on the market.

And people tried to classify them by the isospin.
And people tried to classify them by the isospin.

Gell, Mann, and Nishijima empirically
Gell, Mann, and Nishijima empirically

observed that there's a relation which holds,
observed that there's a relation which holds,

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

assigned the maximum value, I3, the third component
assigned the maximum value, I3, the third component

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

charge--
charge--

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

Then the charge of this particle follows
Then the charge of this particle follows

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

We looked at baryon number and strangeness before.
We looked at baryon number and strangeness before.

As a reminder, strangeness is the number
As a reminder, strangeness is the number

of strange quarks in the baryon or the meson,
of strange quarks in the baryon or the meson,

and the baryon number is simply the number of baryons.
and the baryon number is simply the number of baryons.

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

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

strangeness equals 0, which follows
strangeness equals 0, which follows

that the maximum charge involved is
that the maximum charge involved is

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

So far so good.
So far so good.

This was empirically observed.
This was empirically observed.

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

this is then in the 1970s--
this is then in the 1970s--

you can deduce this equation directly from the assignment
you can deduce this equation directly from the assignment

of isospin to quarks, which is rather fascinating.
of isospin to quarks, which is rather fascinating.

Again, we don't understand the physics fully.
Again, we don't understand the physics fully.

But just from the symmetry you can,
But just from the symmetry you can,

and empirically you can deduce information
and empirically you can deduce information

about physical systems.
about physical systems.

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

to the complete quark model, you find that the symmetry
to the complete quark model, you find that the symmetry

starts to be broken.
starts to be broken.

It already starts to be broken slightly,
It already starts to be broken slightly,

when you include strangeness or strange quarks.
when you include strangeness or strange quarks.

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

And the reason can be seen here.
And the reason can be seen here.

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

making up ions and the neutron and the proton.
making up ions and the neutron and the proton.

And even if you include strangeness,
And even if you include strangeness,

the different in mass is not very large.
the different in mass is not very large.

So the symmetry, the particles really
So the symmetry, the particles really

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

of the same particle.
of the same particle.

But when you introduce other quarks, heavier quarks, charm
But when you introduce other quarks, heavier quarks, charm

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

that the symmetries are broken.
that the symmetries are broken.

So this concept starts failing because
So this concept starts failing because

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

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

And again, from the observation of those symmetries,
And again, from the observation of those symmetries,

we can deduce physics without fully understanding
we can deduce physics without fully understanding

the underlying physics.
the underlying physics.