Selected Topics in Quark-Hadron Physics: From Scalar Nonets to Topological Glueballs

This contribution reviews recent progress in the low-lying scalar mesons and glueballs. We propose a new classification for the scalar nonet that includes $f_0(980)$ and $a_0(980)$ as the lowest states, while we identify $f_0(1500)$ as a primary glueball candidate. We demonstrate that the production yields of these states in heavy-ion collisions are mutually consistent across statistical, coalescence, and S-matrix frameworks. To investigate their internal structure, we move beyond standard phenomenology by describing glueballs as topological solitons. This approach yields an energy spectrum in excellent agreement with lattice QCD and experimental data, while interpreting $f_0(2470)$ as a tightly bound glueballonium to explain its anomalously long lifetime. This non-perturbative framework provides a predictive basis for the future experimental verification of exotic scalar states.