Pi-Meson Decay
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I am confused as to how to apply the 10% accuracy in the attached problem. Also, I am not sure how to set up the problem just to get the minimum value.
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Solution Summary
I am confused as to how to apply the 10% accuracy in the attached problem. Also, I am not sure how to set up the problem just to get the minimum value.
Solution Preview
The explanations are written in the attached pdf file.
The web pages referenced there are
http://en.wikipedia.org/wiki/Pion
http://en.wikipedia.org/wiki/Time_dilation
http://en.wikipedia.org/wiki/Lorentz_transformation
Here is the plain TEX source:
centerline{bf $pi^0to gammagamma$ decay}
As the $pi^0$ rest mass is $135~MeV/c^2$ (see e.g. http://en.wikipedia.org/wiki/Pion),
a $pi^0$ with momentum $135~GeV/c$ has $gamma$-factor
$$
gamma = {1oversqrt{1-beta^2}} approx 1000,
eqno(1.1)
$$
where $beta = v/c$, $vapprox c$ is its velocity, and $capprox 3times 10^8~m/s$ is the
speed of light.
Given rest-frame mean life $tau_0 = 8.5times 10^{-17}~s$,
the Lorentz time dilation results in mean decay path of
$$
lambda = cgammatau_0
eqno(1.2)
$$
(see e.g. ...
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