K-matrix analysis of the (IJ<Superscript>PC</Superscript> = 00<Superscript>+ +</Superscript>)-wave in the mass region below 1900 MeV

We present the results of the current analysis of the partial wave IJ ^PC = 00^{+ +} based on the available data for meson spectra ( ππ, KˉK,ηη,η,ππππ). In the framework of the K-matrix approach, the analytical amplitude has been reconstructed in the mass region 280 MeV < < 1900 MeV. The following scalar-isoscalar states are seen: comparatively narrow resonances f ₀(980), f ₀(1300), f ₀(1500), f ₀(1750) and the broad state f₀(1200-1600). The positions of the amplitude poles (masses and total widths of the resonances) are determined as well as pole residues (partial widths to meson channels ππ, KˉK,ηη,η,ππππ). The fitted amplitude gives us the positions of the K-matrix poles (bare states) and the values of bare-state couplings to meson channels thus allowing the quark-antiquark nonet classification of bare states. On the basis of the obtained partial widths to the channels ππ, KˉK,ηη,η, we estimate the quark/gluonium content of f ₀(980), f ₀(1300), f ₀(1500), f ₀(1750), f₀(1200-1600). For f ₀(980), f ₀(1300), f ₀(1500) and f ₀(1750), their partial widths testify the qˉq origin of these mesons though being unable to provide precise evaluation of the possible admixture of the gluonium component in these resonances. The ratios of the decay coupling constants for the f₀(1200-1600) support the idea about the gluonium nature of this broad state. Received: 14 May 2002 / Accepted: 20 August 2002 / Published online: 11 February 2003 RID="a" ID="a"e-mail: anisovic@thd.pnpi.spb.ru Communicated by A. Sch?fer     

Determination of hadronic partial widths for scalar-isoscalar resonances f0(980), f0(1300), f0(1500), f0(1750) and the broad state f0(1530 ?250+90 )

Recently [see V.V. Anisovich et al., Yad. Fiz. 63, 1489 (2000)], the K-matrix solutions for the wave IJ ^PC=00⁺⁺ were obtained in the mass region 450–1900 MeV, where four resonances f ₀(980), f ₀(1300), f ₀(1500), f ₀(1750) and the broad state f ₀(1530 ₋₂₅₀ ⁺⁹⁰ ) are located. Based on these solutions, partial widths are determined for scalar-isoscalar states decaying into the channels ππ, KK ηη, ηη′, ππππ and corresponding decay couplings. From Yadernaya Fizika, Vol. 65, No. 8, 2002, pp. 1583–1590. Original English Text Copyright ? 2002 by Anisovich, Nikonov, Sarantsev. This article was submitted by the authors in English.     

Mechanism of the production of the <Emphasis Type="Italic">a</Emphasis><Subscript>0</Subscript>(980) resonance in the γγ → π<Superscript>0</Superscript>η reaction

High-statistics Belle data on the γγ → π⁰η reaction have been analyzed in order to reveal the mechanism of two-photon production and the nature of the a ₀(980) resonance. The solution obtained for the γγ → π⁰η amplitude is in agreement with the predictions of the chiral theory for the πη-scattering length; with the strong coupling of the a ₀(980) resonance with the πη, K $ \bar K $ \bar K , and πη′ channels; and with the key role of the a ₀(980) → (K $ \bar K $ \bar K + π⁰η + π⁰η′) → γγ rescattering mechanisms in the a ₀(980) → γγ decay. This picture is much in favor of the q ² $ \bar q $ \bar q ² nature of a ₀(980) resonance and is consistent with the properties of its partners, σ₀(600) and f ₀(980) resonances, in particular, with those manifested in the γγ → ππ reactions. The important role of vector exchanges in the formation of the nonresonant background in the γγ → π⁰η reaction has been revealed. Preliminary information on the π⁰η → π⁰η reaction has been obtained.     

Observation of a tensor glueball in the reactions p\bar p \to \pi \pi ,\eta \eta ,\eta \eta '

Partial wave analysis of the reactions $p\bar p \to \pi \pi ,\eta \eta ,\eta \eta '$ in the region of invariant masses 1900–2400 MeV indicates the existence of four relatively narrow tensor-isoscalar resonances ? ₂(1920), ? ₂(2020), ? ₂(2240), ? ₂(2300), as well as the broad state ? ₂(2000). The determined decay couplings of the broad resonance ? ₂(2000) → π⁰π⁰, ηη, ηη′ satisfy the relations appropriate to those of a tensor glueball, while the couplings of other tensor states do not, thus verifying the glueball nature of ? ₂(2000).     

Reconciling φ radiative decays with other data for a0(980), f0(980), ππ→KK and ππ→ηη

Data for φ→γ(ηπ⁰) are analysed using the KK loop model and compared with parameters of a₀(980) derived from Crystal Barrel data. The ηπ mass spectrum agrees closely and the absolute normalisation lies just within errors. However, BES parameters for f₀(980) predict a normalisation for φ→γ(π⁰π⁰) at least a factor 2 lower than is observed. This discrepancy may be eliminated by including constructive interference between f₀(980) and σ. The magnitude required for σ→KK is consistent with data on ππ→KK. A dispersion relation analysis by Büttiker, Descotes-Genon and Moussallam of ππ→KK leads to a similar conclusion. Data on ππ→ηη also require decays of σ to ηη. Four sets of ππ→KK data all require a small but definite f₀(1370) signal. PACS 13.25.Gv; 14.40.Gx; 13.40.Hq     

Search for the f1(1285) → π+π-π0 decay with the VES detector

The isospin-violating decay f ₁(1285) → π⁺π^-π⁰ has been studied at the VES facility. This study is based on the statistics acquired in π^- Be interactions at 27, 36.6 and 41 GeV/c in the diffractive reaction π^- N → (f ₁π^-)N . The f ₁(1285) → π⁺π^-π⁰ decay is observed. The preliminary ratio of decay probabilities BR(f ₁(1285) → π⁺π^-π⁰) to BR(f ₁(1285) → ηπ⁺π^-)^. BR(η → γγ) is ∼ 2% . Original article based on material presented at HADRON 2007.     

ππ scattering and the meson resonance spectrum

A ππ, ˉKK, and ρρ(ωω) fully coupled channel model is used to predict the lowest isospin S, P, D, F-wave phase shifts and inelasticities for elastic ππ scattering from threshold to 2.0 GeV. As input the S-matrix is required to exhibit poles corresponding to the meson resonance table of the Particle Data Group. As expected, the ππ inelasticity is very strongly related to the opening of the ˉK channel near 1 GeV, and the opening of ρρ(4π) and ωω(6π) channels in the 1.5 GeV region. The predictions of this model are compared to the various elastic ππ→ππ amplitudes, that were obtained from analyses of π⁻ p →π⁻π⁺n data. The role of the various resonances, in particular the glueball candidate f ₀(1500) and the f _J(1710) is investigated. Received: 19 November 1997     

A study in depth of f<Subscript>0</Subscript>(1370)

Claims have been made that f₀(1370) does not exist. The five primary sets of data requiring its existence are refitted with suitable Breit–Wigner amplitudes. Major dispersive effects due to the opening of the 4π threshold are included for the first time; the σ→4π amplitude plays a strong role. Crystal Barrel data on p̄p→3π⁰ at rest require f₀(1370) signals of at least 32 and 33 standard deviations (σ) in ¹S₀ and ³P₁ annihilation respectively. Furthermore, they agree within 5 MeV for mass and width. Data on p̄p→ηηπ⁰ agree and require at least a 19σ contribution. This alone is sufficient to demonstrate the existence of f₀(1370). BES II data for J/Ψ→φπ⁺π^- contain a visible f₀(1370) signal >8σ. In all cases, a resonant phase variation is required. Cern–Munich data for ππ elastic scattering are fitted well with the inclusion of some mixing between σ, f₀(1370) and f₀(1500). Values of Γ_2π for f₂(1565), ρ₃(1690), ρ₃(1990) and f₄(2040) are determined. PACS 13.25.Gv; 14.40.Gx; 13.40.Hq     

Quark-gluonium content of the scalar-isoscalar states f0(980), f0(1300), f0(1500), f0(1750), and f0(1420 ?70+150 ) from hadronic decays

On the basis of the decay couplings f ₀ → ππ, K , ηη, ηη′ found earlier in the study of analytical (IJ ^PC =00⁺⁺) amplitude in the mass range 450–1900 MeV, we analyze the quark-gluonium content of the resonances f ₀(980), f ₀(1300), f ₀(1500), and f ₀(1750) and the broad state f ₀(1420 ₋₇₀ ⁺¹⁵⁰ ). 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 ₀ ^bare ) and for the real resonances. We observe a significant change in the quark-gluonium composition in the evolution from bare states to real resonances, which 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 f ₀(980), the analysis confirmed the dominance of q component, thus proving the n /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 , s , and gluonium components, providing relative percentage only. The analysis shows that the broad state f ₀(1420 ₋₇₀ ⁺¹⁵⁰ ) can mix with the flavor singlet q component only, which is consistent with gluonium origin of the broad resonance. From Yadernaya Fizika, Vol. 66, No. 4, 2003, pp. 772–785. Original English Text Copyright ? 2003 by Anisovich, Nikonov, Sarantsev. This article was submitted by the authors in English.     

On lower scalar quark-antiquark nonets

Two-and three-channel analyses of experimental data on the coupled processes ππ → ππ, k, ηη in the channel with I ^G J ^PC = 0⁺0⁺⁺ are carried out and discussed. In a model-independent approach, confirmation of the σ-meson below 1GeV and definite indications of the QCD nature of other f₀ resonances are obtained. An assignment of the scalar mesons below 1.9 GeV to lower nonets is proposed.     

Decays of σ, κ, a0(980) and f0(980)

Ratios of coupling constants for these decays are compared with qq̄ predictions and Jaffe’s q²q̄² model. In both models, the predicted ratio g²(κ→Kπ)/g²(σ→ππ) is much too small. Also, for qq̄, the predicted ratio g²(κ→Kη’)/g²(κ→Kπ) is much larger than observed. Both models fail for g²(f₀→KK)/g²(a₀→KK). This ratio requires that f₀ has a dominant KK component. It arises naturally because the f₀ pole lies very close to the KK threshold, giving its wave function a long KK tail. PACS 13.25.Gv, 14.40.Gx, 13.40.Hq     

The model-independent analysis indications for spectroscopy of scalar mesons. Proof for the K0* (900)

In a model-independent approach the data on ππ → ππ, K $ \bar K $ \bar K , ηη, ηη′ in the I ^G J ^PC = 0⁺0⁺⁺ channel and on the Kπ scattering in the $ I\left( {J^P } \right) = \frac{1} {2}\left( {0^ + } \right) $ I\left( {J^P } \right) = \frac{1} {2}\left( {0^ + } \right) channel are analyzed jointly for studying the status and QCD nature of the f ₀- and the K*₀-mesons. It is shown that in the 1500-MeV region, there are two states, wide (interpreted as a glueball) and narrow (q $ \bar q $ \bar q ). In the Kπ-scattering data analysis, the proof for the K*₀(900) is given.     

Comments on preliminary data on the reactions e + e −→φ→γ f 0(980)→γπ0π0

Preliminary data on the reactions e ⁺ e ⁻→φ→γ f ₀(980)→γπ⁰π⁰ together with data on ππ scattering and the reactions J/ψ→φπ⁺π⁻ and K ⁻ p→π ⁺π⁻(Λ,Σ) are analyzed. The analysis shows that the mass of the f ₀(980) meson is = 950 MeV, and BR(φ→γf ₀→γπ⁰π⁰)≃ 1× 10⁻⁴, indicating that the f ₀(980) resonance is of a four-quark nature. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 7, 445–449 (10 April 1998)     

On the high-statistics investigation of the <Emphasis Type="Italic">a</Emphasis><Subscript>0</Subscript>(980) resonance in the γγ → π<Superscript>0</Superscript>η reaction

High-statistics data on the γγ → π⁰η reaction will make it possible to conclude whether the K ⁺ K ⁻-loop rescattering mechanism, γγ → K ⁺ K ⁻ → a ₀(980) → π⁰η, is the main mechanism of the production of a ₀(980) isovector resonance. This mechanism provides a reasonable value of 20–30 nb at the maximum for the manifestation of a ₀(980) in the γγ → π⁰η cross section. It also gives rise to a noticeable narrowing of the a ₀(980) peak to its effective (observed) width ≈20–30 MeV in the γγ → π⁰η channel. The decay width averaged over the resonance mass distribution is 〈Γ_{α 0} → K ⁺ K ⁻ → γγ〉_πη ≈ 0.13 keV. The experimental confirmation of this scenario would be important evidence in favor of the q ² $ \bar q $ \bar q ² nature of light scalar mesons.     

Radiative decays with light scalar mesons and singlet–octet mixing in ChPT

We study different types of radiative decays involving f₀(980) and a₀(980) mesons within a unified ChPT-based approach at one-loop level. Light scalar resonances, which are seen in the ππ, πη and KK̄ channels of the φ(1020) radiative decays and in the J/ψ decays are responsible for key questions of low-energy dynamics in the strong interaction sector, and the decays φ(1020)→γa₀(980), φ(1020)→γf₀(980), a₀(980)→γγ and f₀(980)→γγ are of interest for current experimental programs in Jülich, Frascati and Novosibirsk. From the theoretical point of view it is important to verify whether light scalar mesons are members of some flavor octet or nonet. We find a value for the mixing angle dictated by consistency with experiment and the coupling structures of the ChPT Lagrangian. The decay widths f₀(980)/a₀(980)→γρ(770)/ω(782), which have not been experimentally studied yet, are predicted. We also obtain several relations between the widths, which hold independently of the coupling constants and which represent a fingerprint of the model. PACS 11.30.Hv; 12.39.Fe; 13.30.Eg; 14.40.-n     

Di-pion emission in heavy quarkonia decays

The dipion spectrum for the ϒ(nS) → ϒ(n′S) transition with n < 4 has the form dw/dq ∼ (phase space) |η − x|², with x = q ² − 4m _π² / (ΔM)² − 4m _π² < q ² ≡ M _ππ², and ΔM = M(nS) − M(n′S). The parameter η is calculated and the spectrum is shown to reproduce the experimental data for all three types of decays: 3 → 1, 2 → 1, and 3 → 2 with η ≈ 0.5, 0, and −3, respectively. The text was submitted by the author in English.     

Photoproduction of η -mesons off protons

Photoproduction of η -mesons was studied with the Crystal-Barrel detector at ELSA for photon energies in the range from 0.75 to 3GeV. Total and differential cross-sections are presented. The η mesons are detected in two decay modes, in η → 2γ and in η → 3π⁰ → 6γ . The cross-sections vary slowly as functions of energy and η production angle suggesting that only few resonances make significant contributions to the cross-section. For photon energies above 1.5GeV, the differential cross-sections show a strong forward peak due to meson exchanges in the t channel. A comparison of the η -photoproduction cross-sections with SAID and MAID as well as with a partial-wave analysis performed on our data in combination with other data sets shows good agreement. The Bonn-Gatchina partial-wave analysis suggests that the largest contribution to η photoproduction for energies below 3GeV proceeds via three resonances, the well-known N(1535)S ₁₁ , via N(1720)P ₁₃ , and a newly suggested N(2070)D ₁₅ .     

Study of the reaction γp → pπ0η

The reaction γp → pπ⁰η has been studied with the CBELSA detector at the tagged photon beam of the Bonn electron stretcher facility. The reaction shows contributions from Δ⁺(1232)η , N(1535)⁺π⁰ and pa ₀(980) as intermediate states. A partial-wave analysis suggests that the reaction proceeds via formation of six Δ -resonances, Δ(1600)P ₃₃ , Δ(1920)P ₃₃ , Δ(1700)D ₃₃ , Δ(1940)D ₃₃ , Δ(1905)F ₃₅ , Δ(2360)D ₃₃ , and two nucleon resonances N(1880)P ₁₁ and N(2200)P ₁₃ , for which pole positions and decay branching ratios are given.     

What can we learn from the decay of NX(1625) in the molecule picture?

Considering two assumptions on the molecular state, i.e. the S-wave Λ̄–K^- and S-wave Σ̄⁰–K^- molecular states, we study the possible decays of N̄_X(1625) that include N̄_X(1625)→K^-Λ̄,π⁰p̄,ηp̄,π^-n̄. Our results indicate that (1) if N̄_X(1625) is the Λ̄–K^- molecular state, K^-Λ̄ is the main decay mode of N̄_X(1625), and the branching ratios of the rest decay modes are tiny; (2) if N̄_X(1625) is the Σ̄⁰–K^- molecular state, the branching ratio of N̄_X(1625)→K^-Λ̄ is one or two orders smaller than that of N̄_X(1625)→π⁰p̄,ηp̄,π^-n̄. Thus the search for N̄_X(1625)→π⁰p̄,ηp̄,π^-n̄ will be helpful to shed light on the nature of N̄_X(1625). PACS 13.30.Eg, 13.75.Jz