Radiative decays of scalar mesons σ(600), f 0(980) and a 0(980) in the local Nambu-Jona-Lasinio model

The two-photon decay widths of scalar mesons σ(600), f ₀(980) and a ₀(980) as well a ₀ → ju(ω)γ and f ₀ → ju(ω)γ are calculated in the framework of the local Nambu-Jona-Lasinio model. The contributions of the quark loops (Hartree-Fock approximation) and the meson loops (next 1/N _c -approximation where N _c is the number of colors) are taken into account. The values of these contributions, as we show, are of the same order of magnitude. For the f ₀ decay the K-loop contribution plays the dominant role. The results for two-gamma decays are in satisfactory agreement with modern experimental data. The predictions for a ₀ → ju(ω)γ and f ₀ → ju(ω)γ widths are given.     

Partial widths for the decays η:(1295) →γγ and η:(1440) →γγ

We discuss γγ partial widths of pseudoscalar/isoscalar mesons η:(M) in the mass region M∼ 1000–1500 MeV. The transition amplitudes η:(1295) →γγ and η:(1440) →γγ are studied within an assumption that the decaying mesons are the members of the first radial excitation nonet 2¹ S ₀qˉq. The calculations show that partial widths being of the order of 0.1 keV are dominantly due to the nˉn meson component while the contribution of the sˉs component is small. Received: 24 September 1999     

Study of scalar meson f 0(980) from B→f 0(980)K * decays

We show how parton distributions unintegrated over the parton transverse momentum, k _t , may be generated, at NLO accuracy, from the known integrated (DGLAP-evolved) parton densities determined from global data analyses. A few numerical examples are given, which demonstrate that sufficient accuracy is obtained by keeping only the LO splitting functions together with the NLO integrated parton densities. However, it is important to keep the precise kinematics of the process, by taking the scale to be the virtuality rather than the transverse momentum, in order to be consistent with the calculation of the NLO splitting functions.     

Study of scalar meson a0(980) from B→a0(980)π decays

In this paper, we calculate the branching ratios and the direct CP-violating asymmetries for decays B0 →a00(980)π0, a0+(980)π-, a0-(980)π and B- →a00(980)π-, a0-(980)π0 by employing the perturbative QCD (pQCD) factorization approach at the leading order. We found that (a) the pQCD predictions for the branching ratios are around (0.4 - 2.8) × 10-6, consistent with currently available experimental upper limits; (b) the CP asymmetries of B0→ao(980)π0 and B-→a0-(980)π0 decays can be large, about (70-80)% for α = 100°.     

Study of f 0(980) and f 0(1500) from B s →f 0(980)π,f 0(1500)π decays

In this paper, we analyze the scalar mesons f ₀(980) and f ₀(1500) from the decays $\bar{B}^{0}_{s}\to f_{0}(980)\pi^{0},\allowbreak f_{0}(1500)\pi^{0}$ within Perturbative QCD approach. From the leading-order calculations, we find that (a) in the allowed mixing angle ranges, the branching ratio of $\bar{B}^{0}_{s}\to f_{0}(980)\pi^{0}$ is about (1.0～1.6)×10^?7, which is smaller than that of $\bar{B}^{0}_{s}\to f_{0}(980)K^{0}$ (the difference is a few times even one order); (b) the decay $\bar{B}^{0}_{s}\to f_{0}(1500)\pi^{0}$ is better to distinguish between the lowest lying state or the first excited state for f ₀(1500), because the branching ratios for two scenarios have about one-order difference in most of the mixing angle ranges; and (c) the direct CP asymmetries of $\bar{B}^{0}_{s}\to f_{0}(1500)\pi^{0}$ for two scenarios also exists great difference. In scenario II, the variation range of the value ${\mathcal{A}}^{\mathrm{dir}}_{CP}(\bar{B}^{0}_{s}\to f_{0}(1500)\pi^{0})$ according to the mixing angle in scenario II is very small, except for the values for mixing angles near 90° or 270°, while the variation range of ${\mathcal{A}}^{\mathrm{dir}}_{CP}(\bar{B}^{0}_{s}\to f_{0}(1500)\pi^{0})$ in scenario I is very large. Compared with the future data for the decay $\bar{B}^{0}_{s}\to f_{0}(1500)\pi^{0}$ , it is easy to determine the nature of the scalar meson f ₀(1500).     

f 0(980) and a 0(980) resonances near the thresholds of the γγ → K + K − and γγ → K 0 K̇ 0 reactions

High-statistical data on the γγ → K ⁺ K ^? and γγ → K ⁰ K? ⁰ reactions constitute the last missing link in investigations of light scalar mesons f ₀(980) and a ₀(980) in photon-photon collisions. It is expected that the manifestation of the four-quark structure of the f ₀(980) and a ₀(980) resonances in these reactions will be very peculiar. The possibilities of the observation of scalar contributions in the γγ → K ⁺ K ^? and γγ → K ⁰ K? ⁰ reactions near their thresholds at modern colliders have been estimated.     

γγ→π0 transition and asymptotics of γγ and γγ transitions of unflavored pseudoscalar mesons

For the spacelike momenta k of the virtual photon γ, the π⁰(p)γ(k)γ(k^′) transition form factor is considered in the coupled Schwinger–Dyson and Bethe-Salpeter approach in conjunction with the generalized impulse approximation using the dressed quark–photon–quark vertices of the Ball–Chiu and Curtis-Pennington type. These form factors are compared with the ones predicted by the vector meson dominance, operator product expansion, QCD sum rules, and the perturbative QCD for the large spacelike transferred momenta k. The most important qualitative feature of the asymptotic behavior, namely the 1/k² dependence, is in our approach obtained in the model-independent way. Again model-independently, our approach reproduces also the Adler–Bell–Jackiw anomaly result for the limit of both photons being real. For the case of one highly virtual photon, we find in the closed form the asymptotic expression which is then easily generalized both to the case of other unflavored pseudoscalar mesons P⁰=π⁰,η₈,η₀,η_c,η_b, and to the case of arbitrary virtuality of the other photon.     

Chiral symmetry amplitudes in the S-wave isoscalar and isovector channels and the σ, f0(980), a0(980) scalar mesons

We use a non-perturbative approach which combines coupled channel Lippmann-Schwinger equations with meson-meson potentials provided by the lowest order chiral Lagrangian. By means of one parameter, a cut off in the momentum of the loop integrals, which results of the order of 1 GeV, we obtain singularities in the S-wave amplitudes corresponding to the σ, f₀ and a₀ resonances. The ππ → ππ, phase shifts and inelasticities in the T = 0 scalar channel are well reproduced as well as the π⁰η and mass distributions in the T = 1 channel. Furthermore, the total and partial strong decay widths of the f₀ and a₀ resonances are properly reproduced. The results seem to indicate that chiral symmetry constraints at low energy and unitarity in coupled channels is the basic information contained in the meson-meson interaction below GeV.     

Radial excitations of scalar, η, and η′ mesons in a chiral quark model

First radial excitations of the scalar-meson nonet and of the pseudoscalar mesons η and η′ are described within a nonlocal chiral quark model of the Nambu-Jona-Lasinio type with ′t Hooft interaction. In this model, simple form factors are used, which allows us to describe first radial excitations of the mesons and to retain the gap equations describing spontaneous breakdown of chiral symmetry in the standard form. The external parameters of form factors are fixed by the masses of excited pseudoscalar mesons, and the same form factors are used to predict the masses of excited scalar mesons. The strong decays of excited scalar mesons and of η and η′ mesons are described in satisfactory agreement with experimental data.     

The radiative decay ϕ → γππ in a coupled-channel model and the structure of f0(980)

A coupled-channel model is used to study the nature of the scalar mesons produced in the decay ϕ → γππ. The K molecular picture of f₀(980) is found to be in a good agreement with the recent experimental data from SND and CMD-2. The structure of the light scalar mesons is elucidated by investigating the S-matrix poles and the q spectral density.     

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)     

Radiative decays and quark content of f 0(980) and φ(1020)

The quark structure of φ(1020) and f ₀(980) is studied on the basis of data on the radiative decays φ(1020) → γπ ⁰, γη, γη′, γ a ₀(980), γ f ₀(980) and f ₀(980) → γγ. The partial widths are calculated under the assumption that all the mesons under consideration are $\bar qq$ states: φ(1020) is a dominantly $s\bar s$ state ( $\eta ' = n\bar nsin\theta + s\bar scos\theta $ component contributes not more than 1%); η, η′, and π ⁰ are standard $q\bar q$ states, $\eta = n\bar ncos\theta - s\bar ssin\theta $ and $\eta ' = n\bar nsin\theta + s\bar scos\theta $ with θ?37°; and f ₀(980) is a e5 meson with the flavor wave function $n\bar ncos\varphi + s\bar ssin\varphi $ . The transition φ → γπ ⁰ specifies the admixture of the $n\bar n$ component in the φ meson: it is on the order of 0.5%. We argue that this order of $n\bar n$ value does not contradict data on the decay φ(1020) → γ a ₀(980). The partial widths calculated for the decays φ → γη, γη? are in reasonable agreement with experimental data. The measured branching-ratio value Br(φ→γf ₀(980))=(3.4±0.4 _?0.5 ^+1.5 ×10^?4) requires 25°≤|?|≤90°. For the decay f ₀(980) → γγ, the agreement with data, Γ(f ₀(980) → γγ)=0.28 _?0.13 ^+0.09 keV, is attained at either ?=85°±8° or ?=?46°±8°. A simultaneous analysis of the decays φ(1020) → γ f ₀(980) and f ₀(980) → γγ favors the solution with the negative mixing angle of ?=?48°±6°, setting f ₀(980) very close to the flavor octet (? _octet=±54.7°).     

e + e − annihilation to π 0 π 0 γ and π 0 η γ as a source of information on scalar and vector mesons

We present a general framework for the model-independent decomposition of the fully differential cross section of the reactions e ⁺ e ^?→γ ^?→π ⁰ π ⁰ γ and e ⁺ e ^?→γ ^?→π ⁰ η γ, which can provide important information on the properties of scalar mesons: f ₀(600), f ₀(980) and a ₀(980). For the model-dependent ingredients in the differential cross section, an approach is developed, which relies on Resonance Chiral Theory with vector and scalar mesons. Numerical results are compared to data. The framework is convenient for development of a Monte Carlo generator and can also be applied to the reaction e ⁺ e ^?→γ ^?→π ⁺ π ^? γ.     

Light scalar mesons in experimental data on the decay ϕ → π 0 π 0 γ and ππ scattering

Results of a simultaneous analysis of data from the KLOE detector (Italy) on the decay ? → π ⁰ π ⁰ γ and data on ππ scattering and on the reaction ππ → K $ \bar K Results of a simultaneous analysis of data from the KLOE detector (Italy) on the decay ϕ → π ⁰ π ⁰ γ and data on ππ scattering and on the reaction ππ → K are presented. These data are described with allowance for the chiral shielding of the σ(600) meson. The results favor the four-quark nature of the σ(600) and f ₀(980) mesons. Original Russian Text ? N.N. Achasov, A.V. Kiselev, 2007, published in Yadernaya Fizika, 2007, Vol. 70, No. 11, pp. 2005–2021.     

2γ decays of scalar mesons (σ(600), f0(980), and a0(980)) in the Nambu-Jona-Lasinio model

The two-photon decay widths of scalar mesons σ(600), f ₀(980), and a ₀(980) are calculated in the framework of the local Nambu-Jona-Lasinio model. The contributions of the quark loops (Hartree-Fock approximation) and the meson loops (next 1/N _c approximation, where N _c is the number of colors) are taken into account. These contributions, as we show, are the values of the same order of magnitude. For the f ₀ decay the K-loop contribution turns out to play the dominant role. The results are in satisfactory agreement with modern experimental data.     

On the possibility of observing a 0 0 (980)-ƒ 0(980) mixing in the reaction π − p → ηπ 0 n on a polarized target

It is shown that the spin asymmetry in the reaction π ^? p → a ₀ ⁰ (980)n → (ηπ ⁰)S _n is highly sensitive to the mixing of the a ₀ ⁰ (980) and ? ₀(980) resonances. At low momentum transfers (namely, in any of the intervals 0 ≤ ?t ≤ 0.025, …, 0.1 GeV²), the asymmetry normalized in such a way that it takes values between ?1 and 1must undergo a jump close inmagnitude to unity in the region of the ηπ ⁰ invariant masses between 0.965 and 1.01 GeV. A large jump of the asymmetry is due exclusively to a ₀ ⁰ (980)?? ₀(980) mixing. A very high resolution in the ηπ ⁰ invariant mass is not required for observing the jump of the asymmetry. The energy dependence of the polarization effect is expected to be rather weak; therefore, the polarization effect in question can be studied at any high energy—for example, in the range between 8 and 100 GeV.     

Search for e + e − → f 0(600)γ, f 0(980)γ, f 0(1350)γ, and f 2(1270)γ processes in the energy range from 1.05 to 1.38 GeV

In the energy range from 1.05 to 1.38 GeV, the upper limits for the cross sections of e ⁺ e ^? → f ₀(600)γ, f ₀(980)γ, f ₀(1350)γ, and f ₂(1270)γ → π⁰π⁰γ processes have been established. Measurements are performed in accordance with the statistics gathered in experiment with a spherical neutral detector (SND) on the VEPP-2M e ⁺ e ^? collider. The resultant upper limits vary from 6 to 42 pb depending on the energy and the model.