How can I differentiate ground state and excited state hadrons?

Hadronic states do not work like the hydrogen atom, mainly because the strong interaction is so attractive that stable solutions depend on calculations with Lattice QCD, whose solutions are not as simple as the hydrogen atom energy levels.

Look at how complicated a proton is, due to the gluon interactions between quarks :

The same picture is true for mesons, pairs of quark antiquark.

What organizes the hadrons into "families" are the quantum numbers, representations of the group structure of weak SU(3), example:

The octets for spin 0 (pseudoscalar) meson (plotted in the I3--Y plane). The valence quark content is displayed in the figure

If one goes to the resonances with the same quark content but higher masses, one sees:

The vector meson nonet

The vector meson nonet has higher masses, but calling it an excited state, and the pseudoscalar one a ground state is qualitative statement, due to the quantum chromodynamics complexity indicated by the proton image.

I did find this paper:

Ground-state pseudoscalar nonet and the generalized MIT bag model

Abstract:Some properties, such as masses and charge radii, of the (π,K,η,η’,) mesons are analyzed in the framework of a generalized MIT bag model. A suggestion is made about the η’ problem.

So the term "ground state" seems to be in use.