I have to answer the following question:
Consider the decay $\rho^0\to\pi^+\pi^-$. The rho meson has angular momentum 1, what must the orbital angular momenta of the pions be, given that they are both spin-zero?
I know this question has been asked before, but I am only marginally interested in the numerical result itself (which I believe to be 1).
I believe angular momentum must be defined with respect to something -- e.g. a reference point, another particle, and so on. Therefore, 1) in "the rho meson has angular momentum 1", am I correct in assuming that it's entirely spin angular momentum? My reasoning is that it would not make sense to talk about the angular momentum of a single particle without a reference point, so I assume it's all spin. Following-up: every time I hear "particle X has angular momentum y", 2) can I assume it is the spin that is being mentioned?
3) is "the orbital angular momenta of the pions" the orbital angular momentum shared by the pions? In this case, with two particles, I believe it makes sense to talk about orbital angular momentum, if we implicitly refer to the angular momentum between them.
UPDATE Actually, in a later question I just read "Both the ground state $D^0$ meson and the excited state $D^{0*}$ have zero orbital angular momentum". I interpret this as saying that the orbital angular momentum is a well-defined quantity -- in this case it is zero, but it needn't be. How can you talk about the orbital angular momentum of a single particle? Without mentioning a reference point? For example, when in atomic physics I used to read about the orbital angular momentum of the electron, I always assumed that implicitly they meant the orbital angular momentum with respect to the nucleus.