(Based on the materials of the candidate dissertation.)

The BESIII Collaboration has collected unprecedentedly large and high-quality data sets on charmonia decays. The analysis of this data provides a unique opportunity to investigate the light hadron spectra. The study of these spectra and the identification of exotic states in particular, might be a key to understand QCD in the strong coupling regime. The following results will be presented:

1. The partial-wave analysis of \(J/\psi \to K^+K^-\pi^0\). In this work, the decay structure is determined and the parameters of intermediate states are measured with high precision; the relative contributions of resonances and the corresponding branching fractions are provided as well. The reported decay structure is notably different from the previous BESII results (the exotic state \(X(1575)\) is not observed) and the recent BABAR results. A dedicated method which considers the detector resolution and is applicable to the partial wave analysis has been suggested and separately published. Using this method, masses and widths of \(K^*(892)^\pm\) and \(K_2^*(1430)^\pm\) are measured with the world-best precision.

2. Scalar isoscalar mesons and the scalar glueball from radiative \(J/\psi\) decays. In this work, a coupled-channel analysis of the radiative \(J/\psi\) decays (S-wave) to \(\pi^0\pi^0\), \(K_SK_S\), \(\eta \eta\), and \(\omega \phi\) is performed. The fit is constrained by other data: proton-antiproton annihilation, elastic \(\pi^+\pi^-\) scattering, amplitudes squared of \(\pi\pi \to \pi\pi\), \(KK\), \(\eta\eta\), and \(\eta\eta'\) scattering. In the analysis, the spectrum of \(f_0\) mesons is determined and its interpretation is suggested. The found partial widths of the resonances provide evidence of the scalar glueball production. Its mass, width and production partial width are determined.