Abstract:
A searche for supernarrow dibaryons (SND) and exotic baryons with small masses is reviewed. As a result of the study of the reaction pd->p+pX_1, three narrow peaks at M_{pX_1}=1904, 1926, and 1942 MeV have been observed. The analysis of the angular distributions of the protons from the decay of the pX_1 states showed that the peaks found can be explained as a manifestation of the isovector SNDs, the decay of which into two nucleons is forbidden by the Pauli exclusion principle. The observation of the peaks in the missing mass M_{X_1} spectra at 966, 986, and 1003 MeV is an additional indication that the dibaryons found are the SNDs. The possible interpretation of these peaks in the M_{X_1} mass spectra and peaks observed in the reaction pp->pi^+pX at M_X=1004, 1044, and 1094 MeV as new exotic baryon states with small masses is discussed. The mass equation has been constructed which is used to calculate the masses and determine parities of the exotic baryons. The obtained values of the masses are in a good agreement with the experimental data. Two new exotic baryon states bellow the \pi production threshold have been predicted.

Abstract:
The mass formulae for the supernarrow dibaryons and the exotic baryons with small masses are consructed. With this aim their self energies are calculated in one loop approximation using the dispersion relations with two subtractions. The values of the masses obtained in this approach are in a good agreement with the experimental data. The mass formula for the baryons is also used to calculate the mass of the $\Delta(1232)$ resonance.

Abstract:
Using the fact that the contribution of the states with isospin I=0 in the difference of the amplitudes of the processes \gamma \gamma->\pi^+\pi^- and \gamma\gamma->\pi^0\pi^0 is very small, we have analyzed the dispersion sum rules for the difference between the dipole polarizabilities of the charged and neutral pions as a function of the \sigma-meson parameters. Then taken into account the current perturbation value of (\alpha-\beta)_\pi^0=-1.9, we have found (\alpha-\beta)_\pi^(+-)=9.4--8.2 for values of the \sigma-meson parameter within the region: M_s=400--550 MeV, \Gamma_s=400--600 MeV, \Gamma_{\s->\gamma\gamma}= 0--3 keV. It has been shown that the value of the decay width of the h_1(1170)- meson into \gamma\pi^0 can be found if the difference (\alpha-\beta)_\pi^(+-) is reliably determined from the experiment. Estimation of the optimal value of the decay width \sigma->\gamma\gamma has given \Gamma_{\s->\gamma\gamma}<0.7$keV.

Abstract:
The statement of the authors of the article Phys. Rev. C 77, 065211 (2008) that spurious singularities occur in the dispersion relation approach, where imaginary parts of the amplitudes of the process \gamma\gamma->\pi\pi are saturated by the contributions of meson resonances by using Breit-Wigner expressions, is analyzed. It is shown that there are no any additional singularities in this approach and the disagreement between the predictions of the dispersion relations and the chiral perturbation theory for (\alpha_1-\beta_1)_\pi^{\pm} remains.

Abstract:
A fit of the experimental data to the total cross section of the process $\gamma\gamma->\pi^+\pi^-$ in the energy region from threshold to 2500 MeV has been carried out using dispersion relations with subtractions for the invariant amplitudes, where the dipole and the quadrupole polarizabilities of the charged pion are free parameters. As a result, the sum and the difference of the electric and magnetic dipole and quadrupole polarizabilities of the charged pion have been found: $(alpha_1+\beta_1)=(0.18+0.11-0.02)10^(-4)fm^3$, $(alpha_1-\beta_1)=(13.0+3.6-1.9)10^(-4)fm^3$, $(alpha_2+\beta_2)=(0.133+- 0.015)10^(-4)fm^5$, $(alpha_2-\beta_2)=(25.0+0.8-0.3)10^(-4)fm^5$. These values agree with the dispersion sum rule predictions. The value found for the difference of the dipole polarizabilities is consistent with the results obtained from scattering of high energy $\pi^-$ mesons off the Coulomb field of heavy nuclei (Serpukhov (1983)) and from radiative $\pi^+$ photoproduction from the proton at MAMI (2005), while it is at variance with the calculations in the framework of chiral perturbation theory.

Abstract:
The Compton scattering on a charged pion is studied using the dispersion relations. Unknown mass, full width and decay width into \gamma \gamma of the sigma meson are found from a fit to the experimental data for the process \gamma+\gamma \to \pi^0+\pi^0. These parameters are used for the calculation of the cross section of the Compton scattering on the charged pion. The analysis of the obtained results shows that the data on the elastic \gamma\pion scattering in the energy region up to \sqrt{s}=1 GeV (together with the data on process \gamma\gamma \to \pi^0\pi^0) could be used both for a determination of the pion polarizability values with high precision and for research of the sigma meson.

Abstract:
The Compton scattering on a charged pion and the process \gamma\gamma \to \pi^0\pi^0 are studied using the dispersion relations. Unknown parameters of the S-wave \pi\pi interaction, represented as a board Breit-Wignar resonance, and a sum and a difference of the \pi^0 meson polarizabilities are found from a fit to the experimental data for the process \gamma+\gamma \to \pi^0+\pi^0. This fit gives \alpha+\beta=0.98\pm 0.03 and \alpha-\beta=-1.6\pm 2.2. The found parameters of the S-wave \pi\pi interaction are used for the calculation of the cross section of the Compton scattering on \pi^{\pm} meson. The analysis of the obtained results shows that the experimental data for the elastic \gamma\pi scattering in the energy region up to 1 GeV together with the data for the process \gamma+\gamma \to \pi^0+\pi^0 could be used both for a determination of the pion polarizability values with quite high accuracy and for study of the S-wave \pi\pi interaction.

Abstract:
Data on pion polarizabilities obtained in different experiments are reviewed. The values of the dipole and quadrupole polarizabilities of the pi^0 and pi^{+-} mesons found are compared with predictions of dispersion sum rules (DSRs) and two-loop calculations in the framework of chiral perturbation theory (ChPT). Possible reasons of a difference between the predictions of DSRs and ChPT are discussed.

Abstract:
A fit of the experimental data to the total cross section of the process \gamma\gamma->\pi^0\pi^0 in the energy region from 270 to 2250 MeV has been carried out using dispersion relations for the invariant amplitudes where the quadrupole polarizabilities are free parameters. As a result the sum and difference of the electric and magnetic quadrupole polarizabilities of the \pi^0 meson have been found for the first time: (\alpha2+\beta2)_\pi^0=(-0.181+-0.004)*10^{-4}fm^5, (\alpha2-\beta2)_pi^0=(39.70+-0.02)*10^{-4}fm^5. In addition, dispersion sum rules have been constructed for this sum and difference, respectively. The values of (\alpha2-\beta2)_\pi^0 and (\alpha2+\beta2)_\pi^0 extracted from the experimental data on the process \gamma\gamma->\pi^0\pi^0 are in good agreement with the result of calculations in the framework of these dispersion sum rules.

Abstract:
We study the reactions \gamma d --> \pi\gamma NN with the aim to search for six-quark states, the decay of which into two nucleons is forbidden by the Pauli exclusion principle. Such states predicted by a variety of QCD inspired models and recent evidence from Proton Linear Accelerator of INR (Moscow) strongly suggests the existence of such states with masses 1904, 1926, and 1942 MeV. We propose an experiment at MAMI-B which will provide a unique opportunity to observe such dibaryon states in mass region up to 2000 MeV and determine their masses and quantum numbers.