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MARKUS KLUTE: Welcome back
to 8.20, Special Relativity.

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In this section, we want to
study the decay of a particle,

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in this case, the
decay of a pion.

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The pion is a particle
which consists

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of quarks and antiquarks, which
are bound together by gluons.

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They're part of a
family of particles

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which are called mesons.

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And they can be
charged and neutral.

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So we have positively-charged,
negatively-charged, and neutral

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pions.

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In this example, we
look at a neutral pion

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decay and the specific
decay into an electron

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and a positron.

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Mostly, neutral pions and
decay into a pair of photons.

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But we study this effect
here because it's more fun.

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The lifetime or the
mean lifetime over pi 0

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is 8 times 10 to the
minus 17 seconds.

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So when we produce neutral
pions in our detector,

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they immediately
decay, as I said,

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mostly into a pair of photons.

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That we discovered in the 1940s.

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So let's get to it.

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So the mass of a pion--

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of neutral pion is 135 MeV.

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So it's much heavier than
an electron, which is 500--

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has a mass of 511 KeV.

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So we're looking
at this decay here.

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We have a pion a rest into
an electron and a positron.

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And so the charge for you
now is to find the gamma

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factor of the electron
or the positron

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or, [? with ?] that, the
velocity of those particles

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and the decay of a pion at rest.

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So again, as usual,
stop the video,

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and try to work this out.

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And again, what we want to do is
just write down the four-vector

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of the particles involved.

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We start with the
pion, which has

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an energy of the pion
mass times c square.

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And it's at rest in
this example here,

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which means that
the momentum is 0.

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And so then the
outgoing particles

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are the electron and
positron with their energy

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and their momentum.

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And then just from
this first line

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here from the energy
relation, you can--

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by knowing that the mass of
the electron and a positron

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are the same, by knowing
that the gamma factor is

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the same that comes out of
the momentum relation here,

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that they have
the same velocity,

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you can just simply
find gamma as

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equal to the pion mass divided
by 2 times the electron mass.

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And that is about 132.

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So again, we studied
the decay of a pion.

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And as a general
example of the decay

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of a particle into
two new particles,

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we used the energy
momentum relation.

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We make sure use of the
[? effect, ?] in this case,

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that we are in the
rest frame of the pion.

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And then we are able to get
to the velocity or the gamma

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factor of the
outgoing particles.