# 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.

© BrainMass Inc. brainmass.com October 9, 2019, 8:06 pm ad1c9bdddfhttps://brainmass.com/physics/decay-paths/pi-meson-decay-139582

#### 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.