The group theoretical description of the three-body problem

The group theoretical description of the three-particle problem provides successful techniques for the solution of different questions. We present here a review of this approach.Comment: 60 page

Proton-proton, pion-proton and pion-pion diffractive collisions at ultra-high energies

The LHC energies are those at which the asymptotic regime in hadron-hadron diffractive collisions ($pp,\pi p,\pi\pi$) might be switched on. Based on results of the Dakhno-Nikonov eikonal model which is a generalization of the Good-Walker eikonal approach for a continuous set of channels, we present a picture for transformation of the constituent quark mode to the black disk one. In the black disk mode ($\sqrt s \geq 10$ TeV) we have a growth of the logarithm squared type for total and elastic cross sections, $\sigma_{tot}\sim\ln^2s$ and $\sigma_{el}\sim\ln^2s$, and $(\tau={\bf q}_\perp^2\sigma_{tot})$-scaling for diffractive scattering and diffractive dissociation of hadrons. The diffractive dissociation cross section grows as $\sigma_{D}\sim\ln{s}$, $\sigma_{DD}\sim\ln{s}$, and their relative contribution tends to zero: $\sigma_{D}/\sigma_{tot}\to 0$, $\sigma_{DD}/\sigma_{tot}\to 0$. Asymptotic characteristics of diffractive and total cross sections are universal, and this results in the asymptotical equality of cross sections for all types of hadrons (the Gribov's universality). The energy scale for switching on the asymptotic mode is estimated for different processes.Comment: 14 pages. arXiv admin note: text overlap with arXiv:1310.283

Radiative decays of basic scalar, vector and tensor mesons and the determination of the P-wave q\bar q multiplet

We perform simultaneous calculations of the radiative decays of scalar mesons f_0(980)-> \gamma\gamma, a_0(980)-> \gamma\gamma, vector meson \phi(1020)-> \gamma f_0(980), \gamma a_0(980), \gamma \pi^0, \gamma \eta, \gamma \eta' and tensor mesons a_2(1320)-> \gamma\gamma, f_2(1270)-> \gamma\gamma, f_2(1525)-> \gamma\gamma assuming all these states to be dominantly the q\bar q ones. A good description of the considered radiative decays is reached by using almost the same radial wave functions for scalar and tensor mesons that supports the idea for the f_0(980), a_0(980) and a_2(1320), f_2(1270), f_2(1525) to belong to the same P -wave q\bar q multiplet.Comment: 28 pages, LaTeX, 9 PostScript figures, epsfig.st

Polarization degrees of freedom in near-threshold photoproduction of omega mesons in the pi^0 gamma decay channel

We study polarization variables in the photoproduction of omega-mesons with subsequent omega to gamma pi^0 decay. Single and double polarization observables are calculated as a function of different final-state angles. Reaction models include pomeron (natural parity) and pi^0 (unnatural parity) exchange in the t-channel. In addition, the contribution of s-channel resonances is considered. The sensitivity of the polarization observables to the reaction dynamics is discussed.Comment: 10 pages, 10 figures, explicit reference to sign of decay asymmetry adde