Why the mesons $\pi^0$ and $\eta$ are "degenerate"

Question

I don't know anything about elementary particles, but reading the book by Zeidler on p158, table 2.8 one can observe the quark content of baryons and mesons. It is strange that the $\pi^0$ meson has either(?) quark components $u\overline{u}$ and $d\overline{d}$ and similarly $\eta$ has components $u\overline{u}$, $d\overline{d}$ and $s\overline{s}$.

Why these hadrons appear to be "degenerate", i.e. there are two/three possible options in which the particle can be built? Furthermore, why the pairs $u\overline{u}$ and $d\overline{d}$ are repeated in both mesons?

Answer 1

They are not degenerate in the technical sense: the η has three times the mass of the π. They are different blends with differing symmetries, of similar quark-antiquark pairs. But not quite, as you see from the quantum-mechanical wavefunctions of these valence quarks--the 2nd and third rows of this list.

These wavefunctions, $\mathrm{\tfrac{u\bar{u} - d\bar{d}}{\sqrt{2}}}$, (π), and $\mathrm{\tfrac{u\bar{u} + d\bar{d} - 2s\bar{s}}{\sqrt{6}}}$, (η), are superposition of two-fermion states, but they are only evocative of their symmetry structure; in addition, there are zillions, indefinite numbers, of "sea" quark-antiquark pairs, and gluons, comprising the actual mesons, implied but omitted.

There are technical explanations of the mass difference, but they might not make sense to you. You might think of them as different constructions your may arrange out of a small number of the same lego blocks.