I am taking a course where I have to solve the following problem related to the disintegration of a baryon in a proton and a pion $(\Lambda \to p^+ + \pi^-)$:
Assume that a $\Lambda$ particle with energy $10 ~GeV$ is produced. What mean distance will it travel before decaying? What is the range of possible values for the angle $\theta$ (where $\theta$ is the initial angle between the trajectories of the $p^+$ and $\pi^-$ particles) is the decaying is isotropic in the proper system?
As a data I have the masses of every particle and the half life of the baryon.
I have the solution of my professor to the problem but there is something that I don't understand when he's trying to calculate the range of values for $\theta$. He considers the system of the centre of inertia of and draws the following diagram:
This is what I don't understand. I understand the calculations that follow but I don't understand what is the meaning of the angle $\alpha$. What are the possible values that $\alpha$ can take? What is its physical meaning?