In this video, we will explain the so-called
OZI rule and why certain particle decays are
suppressed because of it.
The reason we know about the OZI rule is a
small particle called ϕ meson.
In the quark model, it is composed of a strange
antiquark and a strange quark, it is electrically
neutral and has spin-1, therefore it is called
a "vector meson".
It has a mean lifetime of about 1.5 times
10^-22 seconds, which is incredibly short.
After this time, the ϕ meson decays into
some other particles.
Let us consider two of such possible decay
products.
First, one possibility is that the ϕ meson
decays into two kaons, one K^+ and one K^-.
From the quark content we see that we are
creating an up-antiup pair in this reaction.
The corresponding Feynman diagram would look
like this, where the strange quark interacts
with a gluon which in turn creates an up–anti-up
pair.
The strange antiquark also interacts with
a gluon, which gets absorbed by the newly
created up quark and the up quark travels
on.
Due to the quark content, we see that this
yields a K^- and a K^+.
Another possibility is the decay into three
pions.
A pi^+, a pi^- and a pi^0.
If we look at the quark content, we see that
the strange quarks are annihilated somehow
and we create some up-antiup and down-antidown
pairs.
The Feynman diagram might look something like
this: Since we don't have strange quarks in
the final states, the strange and the anti-strange
must annihilate together.
This means, the strange quark travels in a
curve, and on the way, it interacts with three
gluons.
These three gluons create quark-antiquark
pairs, the first one a down-antidown, the
next one an up-antiup and the last one a down-antidown
again.
If we compare this with our quark content
above, we can identify the three pions.
Now do both processes happen with equal probability?
Or is one more likely to happen than the other?
Let's first do some theoretical considerations,
before we look at the experiment:
Theoretically, in order to say how likely
a decay process is going to happen, we look
at the so-called Q value.
In short, this is the amount of energy absorbed
or released during reaction.
We can calculate it as the difference of the
rest mass between the initial state and the
final state.
The ϕ meson has a mass of about 1020 MeV.
The charged kaons are at around 494 MeV and
the pions have a mass of approximately 140
MeV.
Therefore, the Q value of the first decay
process is around 32 MeV, whereas the Q value
of the second process is around 600 MeV.
Usually, the process with the higher Q value
is more likely to happen.
That is because the Q value is basically a
measure for how much phase space the final
state particles have.
In the case of the kaons, the phase space
is rather small, their kinetic energies do
not have a lot of room to move.
On the other side, the phase space for the
pions is 20 times larger, their kinetic energies
have a much larger range.
Therefore, the pionic decay should be more
likely to happen, by a factor of 20.
But here comes the experiment: If we measure
the decays of many, many ϕ mesons, we see
that around 84% of them decay into kaons!
How can that be?
This question occupied the minds of many physicists
in the 1960s.
Between 1963 and 1966, three physicists – independently
– came up with an explanation.
Their names are Susumu Okubo, George Zweig,
and Jugoro Iizuka, hence the name OZI.
They proposed the idea that if we can separate
the Feynman diagram of a certain decay into
initial and final states, just by cutting
gluon lines, this decay will be suppressed.
As you can see, if we cut the pion diagram
here, we only cut gluon lines, but then the
initial and final states are completely separated.
For the left diagram, we would also have to
cut quark lines.
The explanation of the OZI rule lies in the
asymptotic freedom of QCD's coupling parameter.
In the case of the pions, the gluons must
have a very large energy, since they alone
are responsible for the hadrons in the final
state.
In the left diagram, you can see that the
strange contributions to the kaons travel
all the way from the initial state.
Therefore, the gluons do not have to bring
such a high energy with them.
Now, asymptotic freedom states that the higher
the energy, the weaker the coupling between
quarks and gluons.
This means, that in the right diagram, where
the gluons have a really high energy, their
coupling strength to the quarks is really
small.
Therefore, this diagram does not contribute
as much as the left one does.
And therefore, the left process is much more
likely to occur.
The suppressing character of the OZI rule
is also the reason why the lifetimes of the
J/ψ and ϒ mesons are unusually long.
But that's pretty much it for this video,
thanks for watching!
