Systematics of q anti-q states in the (n,M^2) and (J,M^2) planes

In the mass region up to M < 2400 MeV we systematise mesons on the plots (n,M^2) and (J,M^2), thus setting their classification in terms of n^{2S+1}L_J q anti-q states. The trajectories on the (n,M^2)-plots are drawn for the following (IJ^{PC})-states: a_0(10^{++}), a_1(11^{++}), a_2(12^{++}), a_3(13^{++}), a_4(14^{++}), pi(10^{-+}), pi_2(12^{-+}), eta(00^{-+}), eta_2(02^{-+})$, rho(11^{--}), f_0(00^{++}), f_2(02^{++}). All trajectories are linear, with nearly the same slopes. At the (J,M^2)-plot we set out meson states for leading and daughter trajectories: for pi, rho, a_1, a_2 and P'.Comment: 6 pages, LaTeX, 16 EPS figures, epsfig.st

Partial decay widths of baryons in the spin-momentum operator expansion method

The cross sections for photo- and pion-induced production of baryon resonances and their partial decay widths to the two--body and multi--body final states are calculated in the framework of the operator expansion method. The approach is fully relativistic invariant, and it allows us to perform combined analyses of different reactions imposing directly the analyticity and unitarity constraints. All formulae are given explicitly in the form used by the Crystal Barrel collaboration in the partial wave analysis.Comment: 15 pages, 6 figure

Quark-gluonium content of the scalar-isoscalar states f_0(980), f_0(1300), f_0(1500), f_0(1750), f_0(1420 ^{+150}_{- 70}) from hadronic decays

On the basis of the decay couplings f_0 -> \pi\pi, K\bar K, \eta\eta, \eta\eta', which had been found before, in the study of analytical (IJ^{PC}=00^{++})-amplitude in the mass range 450-1900 MeV, we analyse the quark-gluonium content of resonances f_0(980), f_0(1300), f_0(1500), f_0(1750) and the broad state f_0(1420 ^{+ 150}_{-70}). The K-matrix technique used in the analysis makes it possible to evaluate the quark-gluonium content both for the states with switched-off decay channels (bare states, f^{bare}_0) and the real resonances. We observe significant change of the quark-gluonium composition in the evolution from bare states to real resonances, that is due to the mixing of states in the transitions f_0(m_1)-> real mesons-> f_0(m_2) responsible for the decay processes as well. For the f_0(980), the analysis confirmed the dominance of q\bar q component thus proving the n\bar n/s\bar s composition found in the study of the radiative decays. For the mesons f_0(1300), f_0(1500) and f_0(1750), the hadronic decays do not allow one to determine uniquely the n\bar n, s\bar s and gluonium components providing relative pecentage only. The analysis shows that the broad state f_0(1420 ^{+ 150}_{-70}) can mix with the flavour singlet q\bar q component only, that is consistent with gluonium origin of the broad resonance.Comment: 20 pages, LaTeX, 10 PostScript figures, epsfig.st

Radiative decays of quarkonium states, momentum operator expansion and nilpotent operators

We present the method of calculation of radiative decays of composite quark-antiquark systems with different J^{PC}: (Q\bar Q)_{in} -> gamma (Q\bar Q)_{out}. The method is relativistic invariant, it is based on the double dispersion relation integrals over the masses of composite mesons, it can be used for the high spin particles and provides us with the gauge invariant transition amplitudes. We apply this method to the case when the photon is emitted by a constituent in the intermediate state (additive quark model). We perform the momentum operator expansion of the spin amplitudes for the decay processes. The problem of nilpotent spin operators is discussed.Comment: 21 pages, 1 figur

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

Three-body dispersion-relation N/D equations for the coupled decay channels ppbar (J^{PC}=0^{-+}) --> pi^0 pi^0 pi^0, eta pi^0 pi^0, eta eta pi^0, K Kbar pi^0

During several years the data on different channels ppbar (J^{PC}=0^{-+}) --> 3 mesons presented by Crystal Barrel Collaboration were successfully analyzed by extracting the leading amplitude singularities - pole singularities - with the aim to obtain information about two-meson resonances. But these analyses do not take into account three-body final state interactions (FSI) in an explicitly correct way. This paper is devoted to the consideration of this problem.Comment: 16 pages, no figure

Systematization of tensor mesons and the determination of the 2++2^{++} glueball

It is shown that new data on the $(J^{PC}=2^{++})$-resonances in the mass range $M\sim1700-2400$MeV support the linearity of the $(n,M^2)$-trajectories, where $n$ is the radial quantum number of quark--antiquark state. In this way all vacancies for the isoscalar tensor $q\bar q$-mesons in the range up to 2450 MeV are filled in. This allows one to fix the broad $f_2$-state with $M=2000\pm30$MeV and $\Gamma=530\pm40$MeV as the lowest tensor glueball. PACS numbers: 14.40.-n, 12.38.-t, 12.39.-MkComment: 10 pages, 1 figur

Colour effective particles and confinement

Here I present a brief review of papers where the idea is pushed forward that colour confinement is realized by singular interaction at large distances between colour effective particles (constituent quarks, diquarks, massive effective gluons).Comment: Talk at Workshop ''Hadron Structure and QCD'' Gatchina, Russia, July 5 - July 9, 201

Partial widths for the decays eta(1295) -> gamma gamma and eta(1440) -> gamma gamma

We discuss gamma gamma partial widths of pseudoscalar/isoscalar mesons eta(M) in the mass region M = 1000-1500 MeV. The transition amplitudes eta(1295) -> gamma gamma and eta(1440) -> gamma gamma are studied within an assumption that the decaying mesons are the members of the first radial excitation nonet 2^1S_0 q\bar q. The calculations show that partial widths being of the order of 0.1 keV are dominantly due to the n\bar n meson component while the contribution of the s\bar s component is small.Comment: 3 pages, LaTeX, 4 EPS figures, epsfig.st

Quark--antiquark states and their radiative transitions in terms of the spectral integral equation. {\Huge II.} Charmonia

In the precedent paper of the authors (hep-ph/0510410), the $b\bar b$ states were treated in the framework of the spectral integral equation, together with simultaneous calculations of radiative decays of the considered bottomonia. In the present paper, such a study is carried out for the charmonium $(c\bar c)$ states. We reconstruct the interaction in the $c\bar c$-sector on the basis of data for the charmonium levels with $J^{PC}=0^{-+}$, $1^{--}$, $0^{++}$, $1^{++}$, $2^{++}$, $1^{+-}$ and radiative transitions $\psi(2S)\to\gamma\chi_{c0}(1P)$, $\gamma\chi_{c1}(1P)$, $\gamma\chi_{c2}(1P)$, $\gamma\eta_{c}(1S)$ and $\chi_{c0}(1P)$, $\chi_{c1}(1P)$, $\chi_{c2}(1P)\to\gamma J/\psi$. The $c\bar c$ levels and their wave functions are calculated for the radial excitations with $n\le 6$. Also, we determine the $c\bar c$ component of the photon wave function using the $e^+e^-$ annihilation data: $e^+e^- \to J/\psi(3097)$, $\psi(3686)$, $\psi(3770)$, $\psi(4040)$, $\psi(4160)$, $\psi(4415)$ and perform the calculations of the partial widths of the two-photon decays for the $n=1$ states: $\eta_{c0}(1S)$, $\chi_{c0}(1P)$, $\chi_{c2}(1P)\to\gamma\gamma$, and $n=2$ states: $\eta_{c0}(2S)\to\gamma\gamma$, $\chi_{c0}(2P)$, $\chi_{c2}(2P)\to \gamma\gamma$. We discuss the status of the recently observed $c\bar c$ states X(3872) and Y(3941): according to our results, the X(3872) can be either $\chi_{c1}(2P)$ or $\eta_{c2}(1D)$, while Y(3941) is $\chi_{c2}(2P)$.Comment: 24 pages, 9 figure