Question

Show that the energy of the neutrino in the pion rest frame, E'ν, can be written in natural units as

E'ν = (m2π − m2μ)/2mπ

where mπ and mμ are the masses of the charged pion and the muon, respectively. (You may assume here that the neutrino mass is negligible)

Answer 1

In the decay A → B + C,

EB = ( mA2 + mB2 − mC2)/2mA

Here B = ν, A = π, C = μ. It follows that

E'ν = (m2π − m2μ)/2mπ (because mν = 0)