If we consider the decay of a spin-1 particle with spin projection $m_s=1$ into two (distinguishable) spin-0 particles, what are the possible values of the orbital angular momenta $l$ of the resultant particles?
Using the rules for addition of angular momentum, $m_s=m_1+m_2$ so for $(m_1, m_2)$ we have $(1,0)$ or $(0,1)$.
But the total angular momentum is initially $j=1$ so $|l_1-l_2|\leq j\leq l_1+l_2$. So naively, I'm thinking that $l_1$ and $l_2$ can be arbitrarily large.
I don't think this is right, but I can't figure out what I'm missing.