SCALAR MESONS: An Interesting Puzzle for QCD

Chiral Dynamics of Scalar Mesons: Radiative φ Decay and σ in the Medium through π^{0}π^{0} Nuclear Photoproduction
View Description Hide DescriptionIn order to assess the relevance of chiral dynamics in the scalar sector we address two recent problems: radiative decay of the φ, for which there are quite recent data from Frascati, and the modification of the σ properties in the nuclear medium seen through the π^{0}π^{0} photoproduction in nuclei.

The Present Status on σ and κ Meson Properties—Relation between scattering and production amplitudes
View Description Hide DescriptionThe recent experimental data of both ππ/Κπ scattering and production processes, suggesting the existence of scalar σ and κ mesons, are reviewed. In many ππ/Κπ production processes the direct effects of their productions are observed, while they are, because of chiral symmetry, hidden in scattering processes, and now σ(500∼600) and κ(800∼900) are considered to be confirmed experimentally. Relation between ππ/Κπ production amplitudes and scattering amplitudes are considered. The long believed prejudice of universal ππ/Κπ phase through scattering and production amplitudes is explained to be not correct. Common fit of the production processes with the scattering phase shift is not valid, and the production processes should be independently analyzed from the scattering phase shift.

A Bethe‐Salpeter Description of Light Mesons
View Description Hide DescriptionWe present a covariant approach to describe the low‐lying scalar, pseudoscalar, vector and axialvector mesons as quark‐antiquark bound states. This approach is based on an effective interaction modeling of the non‐perturbative structure of the gluon propagator that enters the quark Schwinger‐Dyson and meson Bethe‐Salpeter equations. We extract the meson masses and compute the pion and kaon decay constants. We obtain a quantitatively correct description for pions, kaons and vector mesons while the calculated spectra of scalar and axialvector mesons suggest that their structure is more complex than being quark‐antiquark bound states.

Recent progress on the light meson resonance description from unitarized Chiral Perturbation Theory and large N_{c}
View Description Hide DescriptionWe present a brief account of the developments in the description of light meson resonances using unitarized extensions of the Chiral Perturbation Theory series, both in energy and temperature. In particular, we describe how these methods have been recently shown to describe simultaneously the low energy and resonance regions of meson‐meson scattering. This approach could be of relevance to understand the light scalar mesons since it provides a formalism that respects chiral symmetry and unitarity and is able to generate resonant states without any a priori theoretical bias toward their existence, classification or spectroscopic nature. We will also review how this approach is also able to describe the thermal evolution of the ρ and σ mesons. In addition we review their extensions to higher orders, the most recent determination of the resonance pole properties, as well as their behavior in the large N_{c} limit, which could be of relevance to understand their spectroscopic nature.

Investigating scalar meson mixing in nucleon‐nucleon and deuteron‐deuteron collisions
View Description Hide DescriptionThe advantages to study charge‐symmetry breaking and especially the phenomenon of f _{0} ‐ a _{0} mixing in nucleon‐nucleon and deuteron‐deuteron induced reactions are discussed.

Effective Lagrangian Approach to Radiative Decays involving Light Scalar Mesons
View Description Hide DescriptionWe summarize some features of the vector meson dominance model which was recently proposed for studying radiative decays involving the scalar mesons. Using the experimental values of Γ(a _{0} → γγ), Γ(f _{0} → γγ) and Γ(φ → a _{0}γ) as inputs, we show that the model predicts a large hierarchy between Γ(a _{0} → ωγ) and Γ(a _{0} → ργ) as well as between Γ(f _{0} → ωγ) and Γ(f _{0} → ργ).

Light‐Front Quark Model Analysis of Radiative Scalar Meson Decay
View Description Hide DescriptionWe construct a ^{3} P _{0} light‐front quark model wavefunction which is used to investigate various radiative scalar meson decays. Specifically, we look at decays involving f _{0}(1370), f _{0}(1500), and f _{0}(1710) which are assumed to be glueball—qq̄ mixtures, as well as a _{0}(980) and f _{0}(980) which are assumed to be qq̄. Although our results for the scalar mesons above 1 GeV are not inconsistent with the available experimental data, the results for the mesons below 1 GeV are inconsistent with the data. This further supports the idea that a _{0}(980) and f _{0}(980) are not conventional qq̄ states.

Threshold behavior of scattering poles
View Description Hide DescriptionThe results of a model for meson‐meson scattering are studied. The model is shown to be capable of on the one hand reproducing the scattering data, while on the other hand a quark‐antiquark confinement spectrum can be determined. It is concluded that adopting the model’s formulation of the transition matrix elements for data analysis , it may serve as a link between experiment and quenched lattice calculations.

Comparing linear sigma model K‐matrix studies of σ/f _{0} and the Higgs boson
View Description Hide DescriptionWe present a description of the low energy ππ scattering data using the Linear Sigma Model with K‐matrix unitarization. Then we carry out an analogous study of the strongly‐coupled minimal Higgs sector of the electroweak theory. We discuss the effect of the unitarization prescription on the WW or ZZ fusion processes and also suggest a related treatment for other Higgs production processes such as gluon fusion.

Role of Light Scalar Mesons in η, η′ → 3π
View Description Hide DescriptionWe study the role of a light scalar nonet in the interesting decay η → 3π. The framework is a Chiral effective Lagrangian of pseudo‐scalars, scalars and vectors. At leading order , the scalars increase the predicted width by about 14%. We note that although individual scalar contributions are not small, there are cancellations among the scalar diagrams. Including higher order symmetry breaking terms reduce the amount of cancellations among the scalar diagrams but the total predicted width remain the same. The vectors contribution is found to be very small. A preliminary discussion of the related decay η′ → 3π is given. We found that the leading order results of pseudo‐scalars alone are reasonable and close to the experimental data. Including the scalars or the vectors gives a huge enhancement indicating the importance of higher order corrections in this case.

Review of Vector Condensation at High Chemical Potential
View Description Hide DescriptionHere I review vectorial type condensation due to a non zero chemical potential associated to some of the global conserved charges of the theory. The phase structure is very rich since three distinct phases exists depending on the value assumed by one of the zero chemical potential vector self interaction terms. In a certain limit of the couplings and for large chemical potential the theory is not stable. This limit corresponds to a gauge type limit often employed to economically describe the ordinary vector mesons self interactions in QCD. Our analysis is relevant since it leads to a number of physical applications not limited to strongly interacting theories at non zero chemical potential.

Gaussian Sum‐Rule Analysis of Scalar Gluonium and Quark Mesons
View Description Hide DescriptionGaussian sum‐rules, which are related to a two‐parameter Gaussian‐weighted integral of a hadronic spectral function, are able to examine the possibility that more than one resonance makes a significant contribution to the spectral function. The Gaussian sum‐rules, including instanton effects, for scalar gluonic and non‐strange scalar quark currents clearly indicate a distribution of the resonance strength in their respective spectral functions. Furthermore, analysis of a two narrow resonance model leads to excellent agreement between theory and phenomenology in both channels. The scalar quark and gluonic sum‐rules are remarkably consistent in their prediction of masses of approximately 1 GeV and 1.4 GeV within this model. Such a similarity would be expected from hadronic states which are mixtures of gluonium and quark mesons.

Scalar glueball‐meson mixing
View Description Hide DescriptionA simple introduction to the topic of three‐state glueball‐meson is given explaining the different limits of the mixing schemes. The generalized Schwinger mass formula and the decay predictions for the different limits are explained. An analytical formula for the valence content is given. It is shown that the lattice QCD results for the decay of a scalar glueball to two pseudoscalar mesons can be explained by a picture where the glueball decays purely via mixing with scalar mesons, which then subsequently decay via the ^{3} P _{0} model. This picture predicts dominant a _{1}π and significant (ππ)_{ S }(ππ)_{ S } decay for the lattice scalar glueball.

Internal Structure of the Scalar Mesons and the Scalar Glueball Mass
View Description Hide DescriptionThis talk is based on the work of ref. [1]. Within a non‐linear chiral Lagrangian framework, the mass spectrum of I = 0 scalar mesons below 2 GeV [σ(550), f _{0}(980), f _{0}(1370), f _{0}(1500) and f _{0}(1710)] is studied, and some speculations on the internal structure of these states is presented. The scalar glueball mass is estimated in the range 1.47–1.64 GeV.

The Lightest Scalar Nonet and Its Mixing Angle
View Description Hide DescriptionWe show that the κ, a _{0}(980), σ and the f _{0}(980) resonances constitute the lightest scalar nonet in three different ways. First, by establishing the continuous movement of the poles from the physical to a SU(3) limit. Second, by performing an analysis of the couplings of the scalar mesons to pairs of pseudoscalars and third, by analysing the couplings of the scalars with two pseudoscalars SU(3) scattering eigenstates. Every of the last two methods agree that the mixing angle between the singlet and the octet I = 0 states is θ = 19° ± 5 degrees, so that the σ is mainly the singlet and the f _{0}(980) the isosinglet octet state.

SU (3) Mass Splittings for q̄q Mesons and qqq Baryons
View Description Hide DescriptionBy comparing SU (3)‐breaking scales of linear mass formulae, it is shown that the lowest vector, axial‐vector, and scalar mesons all have a q̄q configuration, while the ground‐state octet and decuplet baryons are qqq. Also, the quark‐level linear σ model is employed to predict similar q̄q and qqq states. Finally, the approximate mass degeneracy of the scalar a _{0}(980) and f _{0}(980) mesons is demonstrated to be accidental.

The heavy‐quark hybrid meson spectrum in lattice QCD
View Description Hide DescriptionRecent findings on the spectrum of heavy‐quark mesons from computer simulations of quarks and gluons in lattice QCD are summarized, with particular attention to quark‐antiquark states bound by an excited gluon field. The validity of a Born‐Oppenheimer treatment for such systems is discussed. Recent results on glueball masses, the light‐quark 1^{−+} hybrid meson mass, and the static three‐quark potential are summarized.

Scalar Mesons as q̄ ^{2} q ^{2}? Insight from the Lattice
View Description Hide DescriptionI describe some insight obtained from a lattice calculation on the possibility that the light scalar mesons are q̄ ^{2} q ^{2} states rather than q̄q. First I review some general features of q̄ ^{2} q ^{2} states in QCD inspired quark models. Then I describe a lattice QCD calculation of pseudoscalar meson scattering amplitudes, ignoring quark loops and quark annihilation, which finds indications that for sufficiently heavy quarks there is a stable four‐quark bound state with J^{PC} = 0^{++} and non‐exotic flavor quantum numbers.

Simulating the scalar glueball on the lattice
View Description Hide DescriptionTechniques for efficient computation of the scalar glueball mass on the lattice are described. Directions and physics goals of proposed future calculations will be outlined.

Dalitz Analyses of D‐meson Decays at CLEO
View Description Hide DescriptionUsing e^{+}e^{−} collision statistics accumulated by CLEO II.V, III detector configurations at CESR we perform Dalitz plot analyses of D‐meson decays into three pseudoscalars. On this Workshop we present recently published and preliminary results of ongoing analyses of the decays, , D ^{0} → π^{+}π^{−}π^{0}, . The goal of this study is to find out the leading intermediate states for each decay and to present their relative contribution in terms of complex amplitudes and relevant fit fractions. For first observed decays we measure the branching ratios. For the decays with high rate we perform a search for CP violation in terms of integrated rate, fit fractions and complex amplitude parameters.