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

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

We continue the investigation of mesons in terms of the spectral integral equation initiated before [hep-ph/0510410, hep-ph/0511005] for the $b\bar b$ and $c\bar c$ systems: in this paper we consider the light-quark ($u, d,s$) mesons with masses $M\le 3$ GeV. The calculations have been performed for the mesons lying on linear trajectories in the $(n,M^2)$-planes, where $n$ is the radial quantum number. Our consideration relates to the $q\bar q$ states with one component in the flavor space, with the quark and antiquark masses equal to each other, such as $\pi(0^{-+})$, $\rho(1^{--})$, $\omega(1^{--})$, $\phi(1^{--})$, $a_0(0^{++})$, $a_1(1^{++})$, $a_2(2^{++})$, $b_1(1^{+-})$, $f_2(2^{++})$, $\pi_2(2^{-+})$, $\rho_3(3^{--})$, $\omega_3(3^{--})$, $\phi_3(3^{--})$, $\pi_4(4^{-+})$ at $n\le 6$. We obtained the wave functions and mass values of mesons lying on these trajectories. The corresponding trajectories are linear, in agreement with data. We have calculated the two-photon decays $\pi\to \gamma\gamma$, $a_0(980)\to \gamma\gamma$, $a_2(1320)\to \gamma\gamma$, $f_2(1285)\to \gamma\gamma$, $f_2(1525)\to \gamma\gamma$ and radiative transitions $\rho\to\gamma\pi$, $\omega\to\gamma\pi$, that agree qualitatively with the experiment. On this basis, we extract the singular part of the interaction amplitude, which corresponds to the so-called "confinement interaction". The description of the data requires the presence of the strong $t$-channel singularities for both scalar and vector exchanges.Comment: 48 pages, 24 figure

The rho -> gamma pi and omega -> gamma pi decays in quark-model approach and estimation of coupling for pion emission by quark

In the framework of the relativistic and gauge invariant spectral integral technique, we calculate radiative decays rho(770)-> gamma pi(140) and omega(780)-> gamma pi(140) supposing all mesons (pi, rho and omega) to be quark-antiquark states. The q anti-q wave functions found for mesons and photon lead to a reasonably good description of data ($\Gamma^{(exp)}_{\rho^{\pm} \to\gamma\pi^{\pm}}=68\pm 30$ keV, $\Gamma^{(exp)}_{\rho^{0}\to\gamma\pi^0}=77\pm 28$ keV, $\Gamma^{(exp)}_{\omega\to\gamma\pi^0}=776\pm 45$ keV) that makes it possible to estimate the coupling for the bremsstrahlung emission of pion by quarks $g_\pi\equiv g_\pi (u\to d \pi)$. We have found two values for the pion bremsstrahlung coupling: $|g_\pi|=16.7 \pm 0.3 ^{+0.1}_{-2.3}$ (Solution I) and $|g_\pi|=3.0 \pm 0.3 ^{+0.1}_{-2.1}$ (Solution II). Within SU(6)-symmetry for nucleons, Solution I gives us for pi NN coupling the value $16.4 \le g_{\pi NN}^2/(4\pi) \le 23.2$ that is in qualitative agreement with the pi N scattering data, $g_{\pi NN}^2/(4\pi)\simeq 14$. For excited states, we have estimated the partial widths in Solution I as follows: $\Gamma (\rho_{2S}^\pm\to \gamma\pi)\simeq 10 - 130$ keV, $\Gamma (\rho_{2S}^0\to \gamma\pi)\simeq 10 -130$ keV, $\Gamma (\omega_{2S}\to \gamma\pi)\simeq 60 - 1080$ keV. The large uncertainties emphasise the necessity to carry out measurements of the meson radiative processes in the region of large masses.Comment: 23 pages in IOP forma

Determination of quark-antiquark component of the photon wave function for u, d, s quarks

Based on the data for the transitions pi0, eta, eta' -> gamma gamma^*(Q^2) and reactions of the e^+ e^- -annihilations, e^+ e^- -> rho0, omega, phi and e^+ e^--> hadrons at 1<E_{e^+e^-}<3.7 GeV, we determine the light-quark components of the photon wave function gamma^*(Q^2) -> q anti-q (q= u, d, s) for the region 0< Q^2 <1 (GeV/c)^2.Comment: 17 pages, some typos correcte

D^+_s -> pi^+ pi^+ pi^- decay: the 1^3P_0 s anti-s component in scalar-isoscalar mesons

On the basis of data on the decay D^+_s -> pi^+ pi^+ pi^-, which goes dominantly via the transition D_s -> pi^+ s anti-s, we evaluate the 1^3P_0 s anti-s components in the scalar-isoscalar resonances f0(980), f0(1300), f0(1500) and broad state f0(1200-1600)$. The data point to a large s anti-s component in the f0(980): 40% < s anti-s < 70%. Nearly 30% of the 1^3P_0 s anti-s component flows to the mass region 1300-1500 MeV being shared by f0(1300), f0(1500) and broad state f0(1200-1600): the interference of these states results in a peak near 1400 MeV with the width around 200 MeV.Comment: 17 pages, 4 figures, epsfi

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

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

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

The two-pion spectra for the reaction \pi^- p -> \pi^0\pi^0 n at 38 GeV/c pion momentum and combined analysis of the GAMS, Crystal Barrel and BNL data

We perform the K-matrix analysis of meson partial waves with IJ^{PC} =00^{++}, 10^{++}, 02^{++}, 12^{++} basing on GAMS data on \pi^-p -> \pi^0\pi^0 n, \eta\eta n, \eta\eta' n together with BNL data on \pi^-p -> K\bar K n and Crystal Barrel data on p\bar p (at rest) -> \pi^0\pi^0\pi^0, \pi^0\eta\eta, \pi^0\pi^0\eta. The positions of the amplitude poles (physical resonances) are determined as well as the positions of the K-matrix poles (bare states) and the values of bare state couplings to two-meson channels. Nonet classification of the determined bare states is discussed.Comment: LaTex, 15 pages and 10 figure

Charmed quark component of the photon wave function

We determine the c-anti-c component of the photon wave function on the basis of (i) the data on the transitions e+ e- -> J/psi(3096), psi(3686), psi(4040), psi(4415), (ii) partial widths of the two-photon decays eta_{c0}(2979), chi_{c0}(3415), chi_{c2}(3556) -> gamma-gamma, and (iii) wave functions of the charmonium states obtained by solving the Bethe-Salpeter equation for the c-anti-c system. Using the obtained c-anti-c component of the photon wave function we calculate the gamma-gamma decay partial widths for radial excitation 2S state, eta_{c0}(3594) -> gamma-gamma, and 2P states chi_{c0}(3849), chi_{c2}(3950) -> gamma-gamma.Comment: 20 pages, 8 figure