Savchenko Problem 14.1.24

This is a relativistic kinematics problem about how decay products are distributed in angle when viewed from the lab frame. The key insight is that relativistic beaming—the Lorentz transformation of angles—concentrates photons preferentially in the forward direction. You need to find the critical angle in the lab frame where photons transition from moving "mostly forward" to "mostly backward," then use the relativistic angle transformation to determine what fraction of the isotropic decay (in the meson's rest frame) falls within angles less than $\pi/2$.

This is a relativistic kinematics problem about how decay products are distributed in angle when viewed from the lab frame. The key insight is that relativistic beaming—the Lorentz transformation of angles—concentrates photons preferentially in the forward direction. You need to find the critical angle in the lab frame where photons transition from moving "mostly forward" to "mostly backward," then use the relativistic angle transformation to determine what fraction of the isotropic decay (in the meson's rest frame) falls within angles less than $\pi/2$.