On nature of the scalar-isoscalar mesons in the uniformizing-variable method based on analyticity and unitarity

The experimental data on the processes $\pi\pi\to\pi\pi,K\bar{K},\eta\eta,\eta\eta^\prime$ in the $I^GJ^{PC}=0^+0^{++}$ channel have been jointly analyzed to study the status and nature of the $f_0$. 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.Comment: 18 pages, 5 figures, 9 table

The lightest scalar glueball

Recently performed investigations of meson spectra allow us to determine the resonance structure for the waves $IJ^{PC}=00^{++}$, $10^{++}$, $02^{++}$, $12^{++}$ = $IJ^P= 1/2 0^+$ in the mass region up to 1900 MeV, thus establishing the meson multiplets $1^3P_0q\bar q$ and $2^3P_0q\bar q$. Experimental data demonstrate that there are five scalar/isoscalar states in this mass region. Four of them are $q\bar q$ states, that is, members of the $1^3P_0q\bar q$ and $2^3P_0q\bar q$ nonets, while the fifth state is an extra one not accomodated by $q \bar q$ systematics; it has the properties of the lightest scalar glueball. Analysis of the $00^{++}$-wave performed within the framework of the dispersion relation technique allows us to reconstruct the mixing of a pure gluonium with neighbouring scalar $q \bar q$ states belonging to $1^3P_0q\bar q$ and $2^3P_0q\bar q$ nonets: three scalar mesons share the gluonium state between each other -- those are two comparatively narrow resonances $f_0(1300)$ and $f_0(1500)$ and a broad resonance $f_0(1530^{+90}_{-250})$. The broad state is a descendant of the gluonium, keeping about 40-50% of its component.Comment: 48 pages, LaTeX, 25 PostScript figures, epsfig.sty. Submitted to Russian Journal Uspekhi Fiz. Nauk (Phys-Uspekhi

Study of the ηπo\eta\pi^o system in the mass range up to 1200 MeV

The reaction $\pi^-p \to \eta\pi^o n$ has been studied with GAMS-2000 spectrometer in the secondary 38 GeV/c $\pi^-$-beam of the IHEP U-70 accelerator. Partial wave analysis of the reaction has been performed in the $\eta\pi^o$ mass range up to 1200 MeV. The $a_0(980)$-meson is seen as a sharp peak in S-wave. The $t$-dependence of $a_0(980)$ production cross section has been studied. Dominant production of the $a_0(980)$ at a small transfer momentum $t$ confirms the hypothesis of Achasov and Shestakov about significant contribution of the $\rho_2$ exchange ($I^GJ^{PC}=1^+2^{--}$) in the mechanism of $a_0(980)$ meson production in $t$-channel of the reaction.Comment: 4 pages, 3 figures, talk given at HADRON'9

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

Process pi p -> pi pi N at high energies and moderate momenta transferred to the nucleon and the determination of parameters of the f_0(980) and f_0(1300)

We present the results of simultaneous analysis of the S-wave pi pi-spectra in the reactions pi^- p -> (pi^0 pi^0)_S n at p_{lab}=38 GeV/c (GAMS) and pi^- p -> (pi^+ pi^-)_S n at p_{lab}=18 GeV/c (E852 Collaboration) at moderate momenta transferred to the nucleon, |t| < 1.5 (GeV/c)^2. The t-distributions are described by the reggeized pi- and a_1-exchanges provided by the leading and daughter trajectories, while the M_{pi pi}-spectra are determined by a set of scalar-isoscalar resonances. With M_{pi pi}-distributions averaged over t-intervals, we have found several solutions given by different t-channel exchange mechanisms at |t| ~ (0.5-1.5) (GeV/c)^2, with resonance parameters close to each other. We conclude that despite a poor knowledge of the structure of the t-exchange, the characteristics of resonances such as masses and widths can be reliably determined using the processes under discussion. As to pole positions, we have found (1031 +/- 10) - i(35 +/- 6) MeV for f_0(980) and (1315 +/- 20) - i(150 +/- 30) MeV for f_0(1300).Comment: 17 pages, RevTeX, 10 EPS figures, misprints correcte

Search for the scalar a0a_0 and f0f_0 mesons in the reactions e+e−→γπ0π0(η)e^+e^-\to\gamma\pi^0\pi^0(\eta)

It is shown that the reactions $e^+e^-\to\gamma\pi^0\pi^0(\eta)$ give a good chance for observing scalar $a_0$ and $f_0$ mesons. In the photon energy region less then 100 MeV the vector meson contributions $e^+e^-\to V^0\to\pi^0 V'^0\to\gamma\pi^0\pi^0(\eta)$ are negligible in comparison with the scalar mesons $e^+e^-\to\phi\to\gamma f_0(a_0)\to\gamma\pi^0\pi^0(\eta)$ for $BR(\phi\to\gamma f_0(a_0)\to\gamma\pi^0\pi^0(\eta))$ greater than $5\cdot10^{-6}(10^{-5})$. Using two-channel treatment of the $\pi\pi$ scattering the predictions for $BR(\phi\to\gamma (f_0+\sigma)\to\gamma\pi\pi)$ are derived. The four quark model, the model of $K\bar K$ molecule and the$s\bar s$ model of scalar $f_0$ and $a_0$ mesons are discussed.Comment: 31 pages, 10 ps files of figures, minor numerical changes, Appendix corrected, to be published in Phys.Rev.

A Study of the \eta \pi^{0} Spectrum and Search for a J^{PC} = 1^{-+} Exotic Meson

A partial wave analysis (PWA) of the of the $\eta \pi ^0$ system (where $\eta \to \gamma \gamma$) produced in the charge exchange reaction $\pi ^-p\to \eta \pi ^0n$ at an incident momentum of 18 GeV$/c$ is presented as a function of ${\eta \pi ^0}$ invariant mass, $m_{\eta\pi^0}$, and momentum transfer squared, $t_{\pi^{-}\to\eta\pi}$, from the incident $\pi^-$ to the outgoing ${\eta\pi ^0}$ system. $S$, $P$ and $D$ waves were included in the PWA. The $a_0(980)$ and $a_2(1320)$ states are clearly observed in the overall ${\eta\pi ^0}$ effective mass distribution as well as in the amplitudes associated with $S$ wave and $D$ waves respectively after partial wave decomposition. The observed distributions in moments (averages of spherical harmonics) were compared to the results from the PWA and the two are consistent. The distribution in $t_{\pi^{-}\to\eta\pi}$ for individual $D$ waves associated with natural and unnatural parity exchange in the $t$-channel are consistent with Regge phenomenology. Of particular interest in this study is the $P$ wave since this leads to an exotic $J^{PC}=1^{-+}$ for the $\eta \pi$ system. A $P$ wave is present in the data, however attempts to describe the mass dependence of the amplitude and phase motion with respect to the $D$ wave as a Breit-Wigner resonance are problematic. This has implications regarding the existence of a reported exotic $J^{PC} = 1^{-+}$ meson decaying into $\eta \pi^0$ with a mass near 1.4 GeV$/c^2$.Comment: 19 pages, 29 figures, to appear in Phys. Rev.