Light Scalar Mesons Research Articles

New Look at Scalar Mesons

Light scalar mesons are found to fit rather well a diquark-antidiquark description. The resulting nonet obeys mass formulas which respect, to a good extent, the Okubo-Zweig-Iizuka (OZI) rule. OZI allowed strong decays are reasonably reproduced by a single amplitude describing the switch of a qq pair, which transforms the state into two colorless pseudoscalar mesons. Predicted heavy states with one or more quarks replaced by charm or beauty are briefly described; they should give rise to narrow states with exotic quantum numbers.

QCD Sum Rules and Radial Excitations of Light Pseudoscalar and Scalar Mesons

The calculations of masses and decay constants of the radial excitations of light pseudoscalar and scalar mesons within the QCD sum rules method are briefly reviewed. The predictions are based on the 1/N c -supported model spectra, which consist of an infinite number of infinitely narrow resonances, and on the assumption that the ground states of light scalar mesons may be considered as \(\bar qq\)-bound states. The results of the studies are compared with the existing experimental data and with the predictions of other theoretical approaches.

Radiative decays of φ meson and nature of light scalar resonances

We show on gauge invariance grounds that a new threshold phenomenon has been discovered in the radiative decays φ → γa 0 → γπ 0 η and φ → γf 0 → γπ 0 π 0. This enables us to conclude that production of the light scalar mesons a 0(980) and f 0(980) in these decays is caused by the four-quark transitions, resulting in strong restrictions on the large-N c expansions of the decay amplitudes. The analysis shows that these constraints give new evidence in favor of the four-quark nature of a 0(980) and f 0(980) mesons.

Meson-meson interactions and resonances in the ’t Hooft model

We studied meson-meson interactions using the 't Hooft model, which represents QCD in 1+1 dimensions and assumes a large number of colors ($N_c$). The dominant interactions in this large $N_c$ limit are generated by quark exchange. Our results show that QCD in 1+1 dimensions allows the realization of a constituent-type quark model for the mesons, and generates a scalar ``$\sigma$''-like meson-meson resonance, whose effective coupling and mass are determined by the underlying QCD dynamics. These results suggest an interpretation of the lightest scalar mesons as $q\bar{q} q \bar{q}$ systems.

Sum rules for two-photon decay widths of meson resonances and quark-gluon configuration structure of low-lying scalar mesons

Abstract The earlier suggested and developed idea of quark-hadron duality, underlying “bremsstrahlung-weighted” sum rules for total or polarized photon interaction cross sections, is applied to the description of excitation of light scalar mesons in gamma-gamma interactions. The emphasis is put on the discussion of a role of the scalar diquark cluster degrees of freedom in the radiative formation of light scalar mesons.

SU(2) x SU(2) nonlocal quark model with confinement

The nonlocal version of the SU(2)xSU(2) symmetric four-quark interaction of the NJL type is considered. Each of the quark lines contains the form factors. These form factors remove the ultraviolet divergences in quark loops. The additional condition on quark mass function m(p) ensures the absence of the poles in the quark propagator(quark confinement). The constituent quark mass m(0) is expressed thought the cut-off parameter Lambda, m(0)=Lambda=340 MeV in the chiral limit. These parameters are fixed by the experimental value of the weak pion decay and allow us to describe the mass of the light scalar meson, strong decay rho -> pi pi and D/S ratio in the decay a_1 -> rho pi in satisfactory agreement with experimental data.

Pion and sigma meson properties in a relativistic quark model

A variety of strong and electroweak interaction properties of a pion and a light scalar $\ensuremath{\sigma}$ meson are computed in a relativistic quark model. Under the assumption that the resulting coupling of these mesons to the constituent quarks is identical, the $\ensuremath{\sigma}$ meson mass is determined as ${M}_{\ensuremath{\sigma}}=385.4\mathrm{MeV}.$ We discuss in detail the gauging of the nonlocal meson-quark interaction and calculate the electromagnetic form factor of the pion and the form factors of the ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ and $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}\ensuremath{\gamma}\ensuremath{\gamma}$ processes. We obtain explicit expressions for the relevant form factors and evaluate the leading and next-to-leading orders for large Euclidean photon virtualities. Turning to the decay properties of $\ensuremath{\sigma},$ we determine the width of the electromagnetic $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}\ensuremath{\gamma}\ensuremath{\gamma}$ transition and discuss the strong decay $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}\ensuremath{\pi}\ensuremath{\pi}.$ In a final step we compute the nonleptonic decays $\stackrel{\ensuremath{\rightarrow}}{D}\ensuremath{\sigma}\ensuremath{\pi}$ and $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\sigma}\ensuremath{\pi}$ relevant for the possible observation of the $\ensuremath{\sigma}$ meson. All our results are compared to available experimental data and to results of other theoretical studies.

The glueball among the light scalar mesons

In our phenomenological analysis of the spectroscopy of light scalar mesons we do not find compelling evidence for the existence of the low mass κ(900) or σ(600) states nor for ƒ 0 (1370) as single resonance. If the ƒ 0 (980) and and ƒ 0 (1500) are taken as members of the q q nonet there remains a broad object formed by ƒ 0 (400 – 1200) and ƒ 0 (1370) which is a glueball candidate gb(1000).

Vector-meson-dominance model for radiative decays involving light scalar mesons

We present a vector dominance model to describe radiative decays involving the light scalar mesons. Assuming that the light scalar mesons form a nonet this model gives relations among various decay amplitudes of the form S → γγ, V → Sγ and S → Vγ, where S and V denote scalar and vector mesons. By comparing with experimental radiative decay rates, including those recently measured for φ → PP′ γ, we obtain a fairly large number of predictions. We discuss briefly ongoing extensions of the present work in an attempt to describe the radiative φ decay measurements in detail.

KLOE results on φ radiative decays

We report the results on the radiatve decays θ → η′γ, θ → π 0 π 0 γ and θ → ηπ 0 γ obtained with the KLOE detector at the DAΦNE θ-factory, using a sample of ∼ 16 pb −1. The value of the branching ratio for the θ → η′γ decay is related to the s s and gluon content of the η′. A fit to the two-pseudoscalar invariant mass for the π 0 π 0 γ and ηπ 0 γ final states gives the contribution of the direct terms θ → f 0 γ, σ → σγ and θ → a 0 γ, allowing us to investigate the nature of these light scalar mesons.

Effects of light scalar mesons inη→3πdecay

We study the role of a possible nonet of light scalar mesons in the still interesting � ! 3� decay process, with the primary motivation of learning more about the scalars themselves. The framework is a conventional non-linear chiral Lagrangian of pseudoscalars and vectors, extended to include the scalars. The parameters involving the scalars were previously obtained to fit the s-wave �� and �K scatterings in the region up to about 1 GeV as well as the strong decay � ' ! ���. At first, one might expect a large enhancement from diagrams including a light �(560). However there is an amusing cancellation mechanism which prevents this from occurring. In the simplest model there is an enhancement of about 13 per cent in the � ! 3� decay rate due to the scalars. In a more complicated model which includes derivative type symmetry breakers, the cancellation is modified and the scalars contribute about 30 percent of the total decay rate (although the total is not significantly changed). The vectors do not contribute much. Our model produces a reasonable estimate for the related a0(980) f0(980) mixing strength, which has been a topic of current debate. Promising directions for future work along the present line are suggested.

Mixing among light scalar mesons and L = 1 qq̄ scalar mesons

Following the re-establishment of the σ(500) and the κ(900), the light scalar mesons a0(980) and f0(980) together with the σ(500) and the κ(900) are considered as the chiral scalar partner of pseudoscalar nonet in SU(3) chiral symmetry, and the high mass scalar mesons a0(1450), K*0(1430), f0(1370) and f0(1710) turned out to be considered as the L = 1 qq̄ scalar mesons. We assume that the high mass of the L = 1 qq̄ scalar mesons is caused by the mixing with the light scalar mesons. For the structure of the light scalar mesons, we adopted the qqq̄q̄ model in order to explain the ‘scalar meson puzzle’. The inter-mixing between the light scalar nonet and the high mass L = 1 qq̄ nonet and the intra-mixing among each nonet are analysed by including the glueball into the high mass scalar nonet.

Vector-meson-dominance model for radiative decays involving light scalar mesons.

We study a vector-dominance model which predicts quite a large number of currently interesting decay amplitudes of the types S-->gammagamma, V-->Sgamma, and S-->Vgamma, where S and V denote scalar and vector mesons, in terms of three parameters. As an application, the model makes it easy to study in detail a recent proposal to boost the ratio Gamma(phi-->f(0)gamma)/Gamma(phi-->a(0)(0)gamma) by including the isospin violating a(0)(0)-f(0) mixing. However, we find that this effect is actually small in our model.

Modified Breit–Wigner formula for mesonic resonances describing OZI decays of confined $q\bar{q}$ states and the light scalar mesons

A general expression resembling the Breit–Wigner formula is derived for the description of resonances which appear in meson–meson scattering. Our starting point is a unitarised meson model, but reduced to a simpler form and freed from the specific assumption about the confining force. The parameters of the resulting “resonance-spectrum expansion” are directly related to the confinement spectrum and the mechanism of $^3P_0$ valence-quark-pair creation for OZI-allowed hadronic decay, and not to the central positions and widths of resonances. This method also provides us with a straightforward explanation for the origin of the light scalar mesons without requiring extra degrees of freedom.

Unitarized pseudoscalar meson scattering amplitudes from three flavor linear sigma models

The three flavor linear sigma model is studied as a {open_quotes}toy model{close_quotes} for understanding the role of possible light scalar mesons in the {pi}{pi}, {pi}K and {pi}{eta} scattering channels. The approach involves computing the tree level partial wave amplitude for each channel and unitarizing by a simple K-matrix prescription which does not introduce any new parameters. If the renormalizable version of the model is used there is only one free parameter. While this highly constrained version has the right general structure to explain {pi}{pi} scattering, it is {open_quotes}not quite{close_quotes} right. A reasonable fit can be made if the renormalizability (for the effective Lagrangian) is relaxed while chiral symmetry is maintained. The occurrence of a Ramsauer-Townsend mechanism for the f{sub 0}(980) region naturally emerges. The effect of unitarization is very important and leads to {open_quotes}physical{close_quotes} masses for the scalar nonet all less than about 1 GeV. The a{sub 0}(1450) and K{sub 0}{sup *}(1430) appear to be {open_quotes}outsiders{close_quotes} in this picture and to require additional fields. Comparison is made with a scattering treatment using a more general nonlinear sigma model approach. In addition some speculative remarks and a highly simplified larger toy model are devoted to the question of the quark substructuremore » of the light scalar mesons.« less

Experiments at the VEPP-2M e+e− collider in Novosibirsk

The present status of experiments at VEPP-2M e + e − collider, operating in Novosibirsk in the energy range 2 E 0 from 0.4 to 1.4 GeV with two detectors SND and CMD-2, is given. The total integrated luminosity, collected by the both detectors is close to 70 pb −1. New radiative decays of light vector mesons ρ, ω, φ into ππγ and ηπ 0γ were measured, indicating on a possible exotic structure of light scalar mesons a 0(980), f 0(980). The decay φ → η′γ was measured with branching ratio, consistent with no large gluonium content in η′. The accuracy of many rare decays of light vector mesons was improved significantly. A broad peak was observed at the cross section of the e + e − → π +π −π 0 reaction with the visible mass M vis = 1220 ± 20 MeV and cross section in the maximum σ 0 ⋍ 5 nb. The peak can be interpreted as a ω-like resonance ω(1200).

Mixing of thef0anda0scalar mesons in threshold photoproduction

We examine the photoproduction of the light scalar mesons $f_0$-$a_0 (980)$ with emphasis on isospin-violating $f_0$ and $a_0$ mixing due to the mass difference between neutral and charged kaons. General forms for the invariant amplitude for scalar meson photoproduction are derived, which yield expressions for the invariant mass distribution of the final meson pairs. A final state interaction form factor is obtained which incorporates $f_0$ and $a_0$ mesons, $K\bar K$ threshold effects, and $f_0-a_0$ mixing. This form factor is applied to predict the effective mass distribution of the $\pi\pi$ and $K\bar K$ pairs in the vicinity of the $K\bar K$ threshold. An estimate of the role of isospin mixing near threshold is provided. The potential role of polarized photons and protons is also discussed.

Insight into the scalar mesons from a lattice calculation

Abstract We study the possibility that the light scalar mesons are q 2 q 2 states rather than q q . We perform a lattice QCD calculation of pseudoscalar meson scattering amplitudes, ignoring quark loops and quark annihilation, and find indications that for sufficiently heavy quarks there is a stable four-quark bound state with J PC =0 ++ and non-exotic flavor quantum numbers.

Detection of pseudoscalar and scalar mesons at DAfNE with KLOE

The KLOE experiment at the DAfNE f-factory has just started collecting data. One of the first analysis items is the study of the f radiative decays, which allows us to investigate the nature of light pseudoscalar and scalar mesons. An integrated luminosity of 100 pb −1 is expected for next KLOE run, resulting in 3 × 10 8 f collected. A detailed simulation and full event reconstruction of both signal and background events indicates a sensitivity reach of 1 ÷ 2% on the branching ratios. Some preliminary studies on real data are also presented, showing a good agreement with MonteCarlo distributions.

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\(\bar K\) 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\(\bar q\) spectral density.