This paper presents the results of calculations of spectroscopic parameters of three-particle quantum systems, in particular the exotic helium atom (He-3(2+), e, (H-3) over bar). These calculations were made within the framework of a nonrelativistic quantum-mechanical model for the problem of three bodies interacting according to the Coulomb's law.

The basic shape of di-pion mass spectra in the two-pion transitions of both charmonia and bottomonia states is explained by a unified mechanism based on contributions of the ππ, KK̅, and ηη coupled channels including their interference. The role of the individual f0 resonances in shaping the di-pion mass distributions in the charmonia and bottomonia decays is considered.

It is shown that the basic shape of dipion mass distributions in the twopion transitions of both charmonia and bottomonia states are explained by an unified mechanism based on the contribution of the ππ, KK̄ and ηη coupled channels including their interference.

The effect of isoscalar S-wave multi-channel pion-pion scattering (ππ → ππ, KK̄, ηη) is considered in the analysis of data on decays – ϒ(2S) → ϒ(1S)ππ, ϒ(3S) → ϒ(1S)ππ and ϒ(3S) → ϒ(2S)ππ.

The effect of isoscalar S-wave multi-channel pion-pion scattering ($\pi\pi\to\pi\pi,K\bar{K},\eta\eta$) is considered in the analysis of data on decays of the $\Upsilon$-meson family -- $\Upsilon(2S)\to\Upsilon(1S)\pi\pi$, $\Upsilon(3S)\to\Upsilon(1S)\pi\pi$ and $\Upsilon(3S)\to\Upsilon(2S)\pi\pi$. The analysis, which aims at studying the scalar mesons, is performed jointly considering the multi-channel pion-pion scattering, which is described in our model-independent approach based on analyticity and unitarity and using an uniformizing variable method, and the charmonium decay processes $J/\psi\to\phi(\pi\pi, K\bar{K})$, $\psi(2S)\to J/\psi(\pi\pi)$. Results of the analysis confirm all our earlier conclusions on the scalar mesons. It is also shown that in the final states of the $\Upsilon$-meson family decays (except for the $\pi\pi$ scattering) the contribution of the coupled processes, e.g., $K\bar{K}\to\pi\pi$, is important even if these processes are energetically forbidden. This is in accordance with our previous conclusions on the wide resonances: If a wide resonance cannot decay into a channel which opens above its mass but the resonance is strongly connected with this channel (e.g. the $f_0(500)$ and the $K\bar}$ channel), one should consider this resonance as a multi-channel state with allowing for the indicated channel taking into account the Riemann-surface sheets related to the threshold branch-point of this channel and performing the combined analysis of the considered and coupled channels.

The f0 mesons are studied in a combined analysis of data on isoscalar S-wave processes ππ→ππ,KK¯,ηη and on decays J/ψ→ϕ(ππ,KK¯),ψ(2S)→J/ψ(ππ) and ϒ(2S)→ϒ(1S)ππ from the Argus, Crystal Ball, CLEO, CUSB, DM2, Mark II, Mark III, and BES III Collaborations. The method of analysis is based on analyticity and unitarity and uses an uniformization procedure. Some spectroscopic implications from results of the analysis are discussed.

The coupled processes -- the pion-pion scattering and pi pi --> K antiK in the I^GJ^{PC}=0^+0^{++} channel -- are analyzed (both separately and combined) in a model-independent approach based on analyticity and unitarity and using a uniformization procedure. It is shown: 1) a structure of the Riemann surface of the S-matrix for considered coupled processes must be allowed for calculating both amplitudes and resonance parameters, such as the mass and width; 2) the combined analysis of coupled processes is needed as the analysis of only pi-pi channel does not give correct values of resonance parameters even if the Riemann surface structure is included.

Peculiarities of obtaining parameters for broad multichannel resonances from data are discussed analyzing the experimental data on processes ππ → ππ , , in the scalar channel in a model-independent approach based on analyticity and unitarity and using an uniformization procedure. It is shown that one can obtain a good description of the ππ scattering data from the threshold up to 1.89 GeV with values of resonance parameters cited in the PDG tables as preferred. However, in this case the representation of the ππ background is not satisfactory and the data on the coupled process ππ → are not well described, above 1.15 GeV even qualitatively. The combined analysis of the considered coupled processes is needed, which is also carried out satisfactorily. Then both above-indicated deficiencies related to the one-channel analysis are removed. The most important change concerns parameters of the f 0 (600) which are now in some accordance with the prediction by Weinberg on the basis of mended symmetry. The obtained ππ - scattering length agrees well with the values extracted from the data on K e 4 decay and DIRAC experiment and also with results from ChPT.

Parameters of ρ-like resonances are obtained in the multichannel analysis of the ππ-scattering data below 1.9 GeV and a possible classification of the resonance states is discussed. In the 3-channel analysis, we confirmed the existence of the ρ(1250) meson and showed that the simultaneous existence of the ρ(1450) and ρ(1250) mesons does not contradict the data. The analysis indicates an importance of presence of some effective channel with the threshold at 1512 MeV, which might be interpreted as the ρσ channel.

In a multi-channel S-matrix approach, data on �� ! ��,KK,�� in the I G J PC = 0 + 2 ++ sector and �� scattering in the 1 + 3 −− sector are analyzed to study the f2- and �3-mesons, respectively. Spectroscopic implications and possible classification of the f2-states in terms of the SU(3) multiplets are also discussed.

The f(0) mesons and pi pi-scattering length a(0)(0) are studyed in a model-independent analysis of data on the isoscalar S-wave processes pi pi -> pi pi, K (K) over bar including the very precise NA48/2-Collaboration pi pi-data and taking the alternative pi pi-scattering data by B. Hyams et al.(1973) and by R. Kaminski et al.(2002).

The status and parameters of the scalar, vector, and tensor mesonic resonances are obtained in the multichannel analysis of processes pi pi -> pi pi, K (K) over bar, eta eta, and eta eta' and compared with other results. For example, we obtained the f(0)(600) meson with mass 774 +/- 15 MeV and width 988 +/- 36 MeV (the pole position on sheet II is 596 - i494 MeV) and the first rho-like meson with mass 1275 +/- 32 MeV and total width 304 +/- 24 MeV, which differ significantly from the mean value 1459 +/- 11 MeV cited in the Particle Data Group tables. Spectroscopic implications from results of these analyses and possible classification of the resonance states in terms of the SU(3) multiplets are also discussed.

In the analysis a status and parameters of the scalar, vector, and tensor mesonic resonances are obtained and compared with other results. Possible classification of the resonance states in terms of the SU(3) multiplets is discussed.

In the analysis a status and parameters of the scalar, vector, and tensor mesonic resonances are obtained and compared with other results. Possible classification of the resonance states in terms of the SU (3) multiplets is discussed.

In the analysis a status and parameters of the scalar, vector, and tensor mesonic resonances are obtained and compared with other results. Possible classification of the resonance states in terms of the SU(3) multiplets is discussed.

In approach, based on analyticity and unitarity, experimental data on the isoscalar S- and D-waves of processes ππ → ππ, [Formula: see text], ηη, ηη′ have been analyzed for studying the status and QCD nature of the f0- and f2-mesons below 2.3 GeV. Assignment of scalar and tensor mesons to lower nonets is proposed.

Analysis of the isoscalar S- and D-waves of processes ππ → ππ, K, η is carried out aimed at studying the status and QCD nature of scalar and tensor mesons below 2 GeV and 2.3 Gev, respectively. Assignment of these mesons to lower scalar and tensor nonets is proposed.

Two-and three-channel analyses of experimental data on the coupled processes ππ → ππ, k, ηη in the channel with I G J PC = 0 + 0 ++ are carried out and discussed. In a model-independent approach, confirmation of the σ-meson below 1GeV and definite indications of the QCD nature of other f 0 resonances are obtained. An assignment of the scalar mesons below 1.9 GeV to lower nonets is proposed.

Analysis of the isoscalar S- and D-waves of processes pi pi -> pi pi, K (K) over bar, eta eta is carried out aimed at studying the QCD nature of scalar and tensor mesons below 2 GeV. An assignment of the scalar mesons below to lower nonets is proposed.

Methods are set forth for determining the hadron electromagnetic structure in the sub-N (N) over bar -threshold timelike region of the virtual-photon "mass" and for investigating the nucleon weak structure in the spacelike region from experimental data on the process pi N -> e(+)e(-)N at low energies. These methods are formulated using the unified description of photoproduction, electroproduction, and inverse electroproduction of pions in the first resonance region in the framework of the dispersion-relation model and on the basis of the model-independent properties of inverse electroproduction. Applications of these methods are also shown.