- #1

RyanP

- 17

- 0

## Homework Statement

A charged

**π**meson (rest mass = 273m

_{e}) decays into a neutrino (zero rest mass) and a

**μ**meson (rest mass = 207m

_{e}). Find the kinetic energies of the neutrino and the mu meson.

## Homework Equations

E = m

_{o}γc

^{2}

K = m

_{o}(γ-1)c

^{2}

v = pc

^{2}/E

p = m

_{o}γv

## The Attempt at a Solution

In the rest frame of the pi meson (S frame),

E

_{i}= 273m

_{e}c

^{2}

E

_{f}= 207m

_{e}γc

^{2}+ K where γ is the gamma factor of the mu meson and K is the energy (kinetic) of the neutrino.

Since the neutrino has no rest mass, it travels at c, so p

_{v}= E

_{v}/c = K/c.

I couldn't figure out how to carry on in this frame, so I switched to an S' frame where the mu meson is at rest.

In this frame,

p'

_{i}= -273m

_{e}γv where v is the speed of the pi meson initially (equal to the speed of the mu meson in the pi rest frame).

p'

_{f}= -E'

_{nu}/c since the neutrino is the only thing moving after the collision in this frame.

E'

_{i}= 273m

_{e}γc

^{2}

E'

_{f}= 207m

_{e}+ E'

_{nu}

How do I proceed from here?