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.     

First observation of η(1405) decays into f(0)(980)π0

The decays J/ψ → γ π+ π- π0 and J/ψ → γ π0 π0 π0 are analyzed using a sample of 225×10(6) J/ψ events collected with the BESIII detector. The decay of η(1405) → f(0)(980)π0 with a large isospin violation is observed for the first time. The width of the f(0)(980) observed in the dipion mass spectra is anomalously narrower than the world average. Decay rates for three-pion decays of the η' are also measured precisely.     

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.     

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°).     

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 scalar meson a_0(980) from B→a_0(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 →a00(980)π0 and B- →a0-(980)π0 decays can be large,about(70-80)% for α=100-.     

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.     

B→f0(980)(π,η') decays in the PQCD approach

Based on the assumption of a two-quark structure of the scalar meson f0(980), we calculate the branching ratios and CP-violating asymmetries for the four B→f0(980)π and B→f0(980)η(') decays by employing the perturbative QCD (Pqcd) factorization approach. The leading order Pqcd predictions for branching ratios are, Br(B-→f0(980)π-)～2.5×10-6, Br(B0→f0(980)πo)～2.6×10-7, Br(B0→f0(980)η)～ 2.5×10-7 and Br(B0→f0(980)η')～6.7×10-7, which are consistent with both the QCD factorization predictions and the experimental upper limits.     

$$f_0(500)$$, $$f_0(980)$$f0(980), and $$a_0(980)$$a0(980) production in the $$\chi _{c1} \rightarrow \eta \pi ^+\pi ^-$$χc1→ηπ+π- reaction

We study the \(\chi _{c1} \rightarrow \eta \pi ^+ \pi ^-\) decay, paying attention to the production of \(f_0(500)\), \(f_0(980)\), and \(a_0(980)\) from the final state interaction of pairs of mesons that can lead to these three mesons in the final state, which is implemented using the chiral unitary approach. Very clean and strong signals are obtained for the \(a_0(980)\) excitation in the \(\eta \pi \) invariant mass distribution and for the \(f_0(500)\) in the \(\pi ^+ \pi ^-\) mass distribution. A smaller, but also clear signal for the \(f_0(980)\) excitation is obtained. The results are contrasted with experimental data and the agreement found is good, providing yet one more test in support of the picture where these resonances are dynamically generated from the meson–meson interaction.     

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.     

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.     

How exotic is thea 0 (980)?

The mass and hadronic width of the scalar isovector mesona ₀(980) are estimated in QCD for two possible quark assignments: (a \(\bar qq\) and (b) \(\bar qq\bar qq\) . The two-photon width of thea ₀(980) is also discussed.     

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)     

标量介子f0(980)光生过程γp→pf0(980)的研究

轻标量介子性质研究是当今中高能核物理研究中的热点问题之一,特别是质量低于1 GeV的标量介子f₀（980）的内部结构一直存在争议,至今未达成共识。基于前人的研究结果,运用有效拉氏量方法,对f₀（980）粒子的光生过程γp→pf₀（980）进行了更深入的理论研究。探讨了两种传播子形式下得矢量介子ρ和ω交换的贡献,第一种是选择雷吉传播子,第二种是选择普通费曼传播子。第二种形式的微分散射截面理论结果与现有实验数据符合比第一种形式的结果好。基于此,计算了两种形式的总截面,两种形式给出的理论结果相差很大。另外,给出了γp→pf₀（980）→pπ+π-过程的π+π-不变质量分布的理论预言,发现π+π-不变质量分布对于f₀（980）于K-K的耦合常数（g_f0KK）有很强的依赖关系,不同的g_f0KK给出明显不同的π+π-不变质量分布。将来相关实验数据可以验证这些理论预言,并对矢量介子传播子形式和耦合常数g_f0KK做出限制,加深人们对f₀（980）粒子的认识。We study the scalar meson f0(980) in the γp→pf0(980) reaction within an effective Lagrangian approach. Based on previous studies, we calculate the differential cross sections of this reaction. We take two types of the propagators of vector mesons ρ and ω, one is the Regge form, the other one is the normal Feynman propagator. It is found that our theoretical results for the differential cross sections with the Feynman propagator are in agreement with the current experimental data. For the total cross sections, the results with the two types of propagator are much different. On the other hand, we predict the π+π- invariant mass distribution of the γp→pf0(980)→pπ+π- reaction. We find that the π+π- invariant mass distribution depends sensitively on the value of the coupling constant gf0KK. We hope that the future experiments can test our model calculation and give further constraints on the value of gf0KK and also the nature of f0(980).     

Triangle singularity enhancing isospin violation in B~0_s→ J/ψπ~0f_0(980)

We perform calculations for theB~0_s→J/ψπ~0f_0(980) andB~0_s→J/ψπ~0a_0(980) reactions, showing that the first is isospin-suppressed while the second is isospin-allowed. The reaction proceeds via a triangle mechanism, with B~0_s→J/ψK* Kˉ+c.c., followed by the decay K*→Kπ and a further fusion of K Kˉ into the f0(980) or a0(980). We show that the mechanism develops a singularity around the π~0f_0(980) or πa_0(980) invariant mass of 1420 Me V, where the π~0f_0 and π~0a_0 decay modes are magnified and also the ratio of π~0f_0 to π~0a_0 production. Using experimental information for theB~0_s→J/ψK* Kˉ+c.c. decay, we are able to obtain absolute values for the reactions studied which fall into the experimentally accessible range. The reactions proposed and the observables evaluated, when contrasted with actual experiments, should be very valuable to obtain information on the nature of the low lying scalar mesons.