Low-lying Mesons Research Articles

The Dalitz decay π0 → e + e – γ revisited

The amplitude of the Dalitz decay pi0 -> e+ e gamma is studied and its model-independent properties are discussed in detail. A calculation of radiative corrections is performed within the framework of two-flavour chiral perturbation theory, enlarged by virtual photons and leptons. The lowest meson dominance approximation, motivated by large N\_C considerations, is used for the description of the pi0 - gamma* - gamma* transition form factor and for the estimate of the NLO low energy constants involved in the analysis. The two photon reducible contributions is included and discussed. Previous calculations are extended to the whole kinematical range of the soft-photon approximation, thus allowing for the possibility to consider various experimental situations and observables.

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.

UA(1) Breaking Effects on the Light Scalar Meson Spectrum

Effects of the U_A(1) breaking interaction on the low-lying nonet scalar mesons are studied using the extended Nambu-Jona-Lasinio model. The strength of the U_A(1) breaking interaction is determined by the electromagnetic decays of the eta meson. We find that the U_A(1) breaking interaction gives rise to about 150 MeV mass difference between the sigma and a_0 mesons. We also find that the strangeness content in the \sigma meson is about 15%. The calculated mass of the I=1/2 state is about 200 MeV heavier than that of the I=1 state. The order of these masses is not likely to change within this model.

THE ρ0-ρ± ELECTROMAGNETIC MASS SPLITTING

A systematic method developed by us to evaluate the one-loop electromagnetic self-energies of the low-lying mesons is extended to the case of the ρ-meson. The theoretical prediction of ρ0-ρ± electromagnetic mass splitting is about 0.62 MeV, which is in agreement with the measurements.

Resonance estimates of $\mathcal{O}(p^6)$ low-energy constants and QCD short-distance constraints

Starting from the study of the low-energy and high-energy behaviours of the QCD three-point functions <VAP>, <VVP> and <AAP>, several O(p^6) low-energy constants of the chiral Lagrangian are evaluated within the framework of the lowest meson dominance (LMD) approximation to the large-N_C limit of QCD. In certain cases, values that differ substantially from estimates based on a resonance Lagrangian are obtained. It is pointed out that the differences arise through the fact that QCD short-distance constraints are in general not correctly taken into account in the approaches using resonance Lagrangians. We discuss the implications of our results for the O(p^6) counterterm contributions to the vector form factor of the pion and to the decay \pi -> e \nu_e \gamma, and for the pion-photon-photon transition form factor.

Is there diquark clustering in the nucleon?

It is shown that the instanton-induced interaction in $\mathrm{qq}$ pairs, iterated in the t channel, leads to a meson-exchange interaction between quarks. In this way one can achieve a simultaneous understanding of low-lying mesons, baryons, and the nuclear force. The discussion is general and does not necessarily rely on the instanton-induced interaction. Any nonperturbative gluonic interaction between quarks, which is a source of the dynamical chiral symmetry breaking and explains the $\ensuremath{\pi}\ensuremath{-}\ensuremath{\rho}$ mass splitting, will imply an effective meson exchange picture in the baryons. Because of the (anti)screening there is a large difference between the initial 't Hooft interaction and the effective meson-exchange interaction. It is demonstrated that the effective meson-exchange interaction, adjusted to the baryon spectrum, does not bind the scalar diquark and does not induce any significant quark-diquark clustering in the nucleon because of the nontrivial role played by the Pauli principle.

Decay of Pseudoscalars into Lepton Pairs and Large-NcQCD

The counterterm combination that describes the decay of pseudoscalar mesons into charged lepton pairs at lowest order in chiral perturbation theory is considered within the framework of QCD in the limit of a large number of colors ${N}_{c}$. When further restricted to the lowest meson dominance approximation to large- ${N}_{c}$ QCD, our results agree well with the available experimental data.

Effective quark model with chiralU(3)×U(3)symmetry for baryon octet and decuplet

We suggest an effective quark model for low-lying baryon octet and decuplet motivated by QCD with a linearly rising confinement potential incorporating the extended Nambu--Jona-Lasinio (ENJL) model with linear realization of chiral $U(3)\ifmmode\times\else\texttimes\fi{}U(3)$ symmetry. Baryons are considered as external heavy states coupled to local three-quark currents with fixed spinorial structure and to low-lying mesons through quark-meson interactions defined in the ENJL model. In the constituent quark loop representation we have calculated the coupling constants of the $\ensuremath{\pi}NN, \ensuremath{\pi}N\ensuremath{\Delta},$ and $\ensuremath{\gamma}N\ensuremath{\Delta}$ interactions and the ${\ensuremath{\sigma}}_{\ensuremath{\pi}N}$ term. The obtained results are in reasonable agreement with experimental data and other effective field theory approaches.

From η and ή to glueballs?

Abstract We discuss the effect of η-ή mixing and of axial current anomalies on various decay processes. We describe the 2γ decays of η and ή the radiative decays of low-lying vector mesons as well as the decays η → 3π, J/ψ → ηγ and J/ψ → ήγ and discuss briefly the enhancement of ή in Ds decays, suggesting an explanation in terms of gluon-mediated processes. The importance of the decays of the glueballs into ηή channels is stressed, in particular in connection with the candidates f o(1500) and f o(1590).

On the origin of the vector meson dominance

Abstract We consider a model, which has been suggested recently to describe low-lying vector mesons as collective excitations of q q pairs. That model is an explicit realization, in terms of a NJL-like effective lagrangian, of the old idea proposed by Caldi and Pagels to reconcile the quark model with PCAC. In this note we investigate the role of dormant Goldstone bosons in the electromagnetic current. We derive and discuss in detail the special features of this approach: the soft vector meson decoupling mechanism and the microscopic picture that unifies PCAC with vector meson dominance.

Collision rates for ϱ-, ω- and φ-mesons at nonzero temperature

The $\omega$ and $\phi$ mesons are exceptionally narrow in vacua being about 8 and 4 MeV. At finite temperature they will scatter with other hadrons in their approach to equilibrium and thereafter. These dynamics induce broadening to the already unstable vector mesons which is calculated in the framework of relativistic kinetic theory. A rather complete set of low-lying mesons provide reaction partners whose interactions are modeled using effective Lagrangians. Collision rates for $\rho$ and $\omega$ are found to be $\sim$ 100 MeV at $T$=200 MeV while the rate for $\phi$ is $\sim$ 25 MeV. Corresponding mean free paths are about 1 and 4 fm! Possible observable consequences are discussed.

The existence of low-lying mesons as a consequence of confinement

We use the Bethe-Salpeter equation for the investigation of the mass spectra of four nonets of low-lying mesons (pseudoscalar, scalar, vector and axial-vector) within QCD with a linearly rising potential. In leading order in the large- N expansion and in the chiral limit the mass spectra are found in agreement with those predicted by the extended Nambu-Jona-Lasinio model. We show that due to the confinement potential the nonets of vector and axial-vector mesons are stable under decays into quark-antiquark pairs.

Chiral lagrangian and low-lying meson resonances

The quartic derivative terms of the chiral Lagrangian for ππ scattering are reanalysed using the forward dispersion relation. It is shown that the π + π 0 and π 0 π 0 total cross sections above 1 GeV make contributions to the Skyrme and non-Skyrme terms, 10% and 30% respectively, of the low-energy contributions. For both the quartic terms, the high- contribution tends to cancel the finite width corrections, leaving a strength given by vector and scalar meson dominance, consistent with low-energy ππ data. In particular our analysis shows clearly that vector meson dominance, as often used in pion physics, can now be justified in a reliable manner.

The M1 radiative decay of low-lying mesons in the cloudy bag model with centre-of-mass correction

The radiative decays of a number of vector and pseudoscalar mesons (into pseudoscalar and vector mesons, respectively) have been studied within an SU(3) version of the cloudy bag model. Our results indicate that the inclusion of the centre-of-mass correction is very important in any comparison with data.

Low-energy hadronic interactions beyond the current algebra approach

Within chiral perturbation theory at the quark level (CHPT) q with linear realization of chiral U(3) × U(3) symmetry the new low-energy AP 3-interaction, produced by convergent box-constituent-quark-loop diagrams, is obtained, and its contributions to processes of low-energy interactions of low-lying mesons are investigated. The new interaction goes beyond the framework of the low-energy current algebra approach and effective chiral Lagrangians with linear realization of chiral symmetry, constructed at the hadronic level.

LOW-ENERGY CURRENT ALGEBRA APPROACH AT THE QUARK LEVEL

The low-energy theorem, derived by Terent'ev within the framework of current algebra, is proved at the quark level within the framework of the Extended Nambu–Jona-Lasinio model. The proposed method allows to evaluate a vacuum expectation value of any time-ordered product of QCD-hadronic currents in terms of constituent-quark loops and low-lying meson exchanges.

CHIRAL SYMMETRY BREAKING AND FORMULAS OF QUARK CONVERSION FOR LOW-ENERGY HADRONIC MATRIX ELEMENTS

By using the extended Nambu-Jona-Lasinio model for the low-energy approximation of QCD we derive the formulas, being due to spontaneous breaking of chiral symmetry and bosonization, and allowing to express matrix elements of any operator with current-quark fields in the definition in terms of matrix elements of this operator determined via constituent-quark fields interacting with low-lying meson states appearing as [Formula: see text]-collective excitations, which have the self-interactions too.

Gluon condensation and modelling of quark confinement in a QCD-motivated Nambu-Jona-Lasinio model

The possibility of modelling of a quark propagator without poles realizing quark confinement is considered on the basis of a nonperturbative gluon propagator including gluon condensation and a dynamical gluon mass. The property of spontaneous chiral-symmetry breaking is retained providing us with a reasonable pattern of low-lying meson properties.

QCD bound states at finite temperature and baryon density Mass spectrum

Quark-antiquark bound states are described with the help of the Bethe-Salpeter equation for a special Nambu-Jona-Lasinio model at finite temperature and baryon number density. The decomposition of the Bethe-Salpeter vertex functionsaccording to their Lorentzs tructures and the particle flavour content are used. As an application we determine the mass of low-lying mesons as a function of temperature and baryon number density.

LOW-LYING MESON SPECTROSCOPY AND CONFINEMENT

The paper is devoted to the construction of low-energy quark-scattering amplitudes. The amplitudes of dressed quarks qq→qq and [Formula: see text] are calculated in the framework of the dispersion N/D method with the help of the iteration bootstrap procedure including two types of point-like input interactions, namely the four-fermion interaction with quantum numbers of the gluon and four-fermion interaction induced by instantons (the exchanges of white states with JP=0±). The mass values of the lowest mesons (JP=0−, 1−, 0+) and their quark content are obtained. In the colour meson channel a bound state was found which corresponds to the constituent gluon with the mass MG=0.67 GeV . The qq-amplitudes in the colour state [Formula: see text] have the diquark levels with JP=0+ and the masses mud=0.72 GeV and mus=mds=0.86 GeV . The interaction of dressed quarks appeared to be an effectively short-range one. The calculated amplitudes satisfy the Okubo-Zweig-Iisuka rule. The creation of mesons (pion included) is mainly due to the gluon exchange. The mesons with heavy quarks (c and b) are considered also, using the calculated forces. We discuss the possibility of constructing the amplitudes which take into account the quark confinement.