Probability decay for rho meson I have the following putative set of decays for the $\rho^0$ meson:
$$\begin{array}{l}
\rho^{0} \rightarrow \pi^{0} \pi^{0}:\text{STRONG} \\
\rho^{0} \rightarrow \pi^{-} \pi^{+}:\text{STRONG} \\
\rho^{0} \rightarrow \pi^{-} \pi^{+} \pi^{0}:\text{STRONG} \\
\rho^{0} \rightarrow K^{-} \pi^{+}:\text{WEAK}\\
\rho^{0} \rightarrow \pi^{0} \gamma:\text{EM}
\end{array}$$
What criteria do I have to follow to order the reactions according to their probability? that is, is it enough to know the type of interaction to establish its probability? How does it relate to the nuclear cross section?
 A: All else being equal, when all three decays are allowed, and with a few exceptions, the probability of a strong decay is higher than an electromagnetic decay or a weak decay. Electromagnetic decays also tend to be more likely than weak decays, except when the mass of the decaying particle is greater than the mass of the Z and/or W bosons.
Additionally, all else being equal, final states with more particles are less likely than final states with fewer particles.
Note that this is just a general rule, and does not apply in 100% of cases. It does apply here for the primary decay- the probability for $\rm\rho^0\to\pi^+\pi^-$ is overwhelmingly higher than any of the others. But for instance the decay $\rho\to\pi^0\pi^0$ is just straight up forbidden by exchange symmetry- from conservation of angular momentum, the angular momentum of the final state implies that the state must be antisymmetric, but the fact that the final state is two identical bosons implies that the state must be symmetric. This is a contradiction, so the decay cannot occur at all.
The general process for analyzing these sorts of things qualitatively is checking for symmetry violations. Processes that violate strict symmetries are forbidden and can be ignored, while processes that violate approximate symmetries are suppressed and therefore much less likely than processes that don't violate any symmetries. Beyond that, you have to at least be comfortable drawing Feynman diagrams, where you can look for additional factors that can suppress decays, such as decays that can only occur via loops (e.g. $\rm H\to\gamma\gamma$), where the OZI rule applies (e.g. $\rm\phi\to\pi^+\pi^-\pi^0$), or extra vertices required in the decay at tree level.
