A charged π meson (rest mass = 273me) decays into a neutrino (zero rest mass) and a μ meson (rest mass = 207me). Find the kinetic energies of the neutrino and the mu meson.
E = moγc2
K = mo(γ-1)c2
v = pc2/E
p = moγv
The Attempt at a Solution
In the rest frame of the pi meson (S frame),
Ei = 273mec2
Ef = 207meγc2 + 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 pv = Ev/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 = -273meγv 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 = 273meγc2
E'f = 207me + E'nu
How do I proceed from here?