if that's even the right word.

My favorite tree and flower in the entire world is the Mimosa. Today, I saw one growing near the interstate so I pulled over and broke off one of the branches which had flowers and buds on it.
Someone told me, if I stick that in the ground and baby it, it could start growing and become a tree. But isn't that sort of like chopping off someone's arm and then expecting a body to grow?
I also planted one of the buds, being optimistic.

In either the fall or spring the tree grows brown pods (imagine a pea pod), so perhaps my best bet would be to wait for those and plant a couple instead? When I was a kid and knew nothing about seeds and flowers and such, there was a mimosa in the neighborhood. I picked every single pod that was on it one year and it never did flower again.

Any gardeners here who could help?

Many thanks.