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I was reading about Regge radial trajectories for $\rho$ meson and I found that we have two given by the values of the orbital angular momentum, $L=0$ and $L=2$. With this part, I feel OK. But, when I try to understand how they know that $\rho(1450)$ is $2^3\,S_1$ and the next mass state $\rho(1700)$ is associated to $1^3\,D_1$, the first state in the $L=2$ trajectory, I become a mess!. So, please, anyone could tell me how they do the categorization?. Was it make on experimental parameters?

I'm not so familiar with the standard technics of characterization used in meson physics, so could you give some references. Thanks in advance!

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We can obtain the angular momentum of the meson under consideration by measuring the angular distribution of its decay products.

$\rho(1700)$ has a dominant decay mode into

$\pi^{+}\pi^{-}\pi^{+}\pi^{-}$

This also happens to be the dominant decay mode for $\rho(1450)$

So, from the angular distribution of these final states we can classify the observed resonance into either of these two states.

If we draw Chew-Frautschi plot for these states we will observe that the angular momentum and the squared mass of the meson follow a linear Regge trajectory, although this is done with hindsight.

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