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Pi-Meson Decay

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 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. ...

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.

$2.19