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    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.

    © BrainMass Inc. brainmass.com October 9, 2019, 8:06 pm ad1c9bdddf
    https://brainmass.com/physics/decay-paths/pi-meson-decay-139582

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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