Light Scalar Mesons Research Articles

Experimental status of scalar and tensor mesons

The recent discoveries of a 0 (1450) and ƒ 0 (1370)/ƒ 0 (1500) in antiproton-proton annihilation at rest shed new light on the interpretation of light scalar mesons. The properties of ƒ 0 (1500) match the expectations of a scalar glueball mixed with nearby qq states. New decay modes of the ξ (2230) are reported in radiative J/Ψ decays, pointing also towards a (tensor) glueball nature of this state. Results from different experiments are discussed and compared.

A chiral effective lagrangian for nuclei

An effective hadronic lagrangian consistent with the symmetries of quantum chromodynamics and intended for applications to finite-density systems is constructed. The degrees of freedom are (valence) nucleons, pions and the low-lying non-Goldstone bosons, which account for the intermediate-range nucleon-nucleon interactions and conveniently describe the nonvanishing expectation values of nucleon bilinears. Chiral symmetry is realized nonlinearly, with a light scalar meson included as a chiral singlet to describe the mid-range nucleon-nucleon attraction. The low-energy electromagnetic structure of the nucleon is described within the theory using vector-meson dominance, so that external form factors are not needed. The effective lagrangian is expanded in powers of the fields and their derivatives, with the terms organized using Georgi's “naive dimensional analysis”. Results are presented for finite nuclei and nuclear matter at one-baryon-loop order, using the single-nucleon structure determined within the model. Parameters obtained from fits to nuclear properties show that naive dimensional analysis is a useful principle and that a truncation of the effective lagrangian at the first few powers of the fields and their derivatives is justified.

Charm nonleptonic decays and final state interactions

A global previous analysis of two-body nonleptonic decays of D mesons has been extended to the decays involving light scalar mesons. The allowance for final state interaction also in nonresonant channels provides a fit of much improved quality and with less symmetry breaking in the axial charges. We give predictions for about 50 decay branching ratios yet to be measured. We also discuss long distance contributions to the difference ΔΓ between the D S and D L widths.

Polaron variational methods in the particle representation of field theory. I. General formalism.

We apply nonperturbative variational techniques to a relativistic scalar field theory in which heavy bosons (``nucleons'') interact with light scalar mesons via a Yukawa coupling. Integrating out the meson field and neglecting the nucleon vacuum polarization one obtains an effective action in terms of the heavy particle coordinates which is nonlocal in the proper time. As in Feynman's polaron approach we approximate this action by a retarded quadratic action whose parameters are to be determined variationally on the pole of the two-point function. Several ans\"atze for the retardation function are studied and for the most general case we derive a system of coupled variational equations. An approximate analytic solution displays the instability of the system for coupling constants beyond a critical value.

Analysis of chiral mean-field models for nuclei

An analysis of nuclear properties based on a relativistic energy functional containing Dirac nucleons and classical scalar and vector meson fields is discussed. Density functional theory implies that this energy functional can include many-body effects that go beyond the simple Hartree approximation. Using basic ideas from effective field theory, a systematic truncation scheme is developed for the energy functional, which is based on an expansion in powers of the meson fields and their gradients. Chiral models are analyzed by considering specific lagrangians that realize the spontaneously broken chiral symmetry of QCD in different ways and by studying them at the Hartree level. Models that include a light scalar meson playing a dual role as the chiral partner of the pion and the mediator of the intermediate-range nucleon-nucleon interaction, and which include a "Mexican-hat" potential, fail to reproduce basic ground-state properties of nuclei. In contrast, chiral models with a nonlinear realization of the symmetry are shown to contain the full flexibility inherent in the general energy functional and can therefore successfully describe nuclei.

Finite nuclei in relativistic models with a light chiral scalar meson.

Relativistic chiral models with a light scalar meson appear to provide an economical marriage of successful relativistic mean-field theories and chiral symmetry. The scalar meson serves as both the chiral partner of the pion and the mediator of the intermediate-range nucleon-nucleon ([ital NN]) attraction. However, while some of these models can reproduce the empirical nuclear matter saturation point, they fail to reproduce observed properties of finite nuclei, such as spin-orbit splittings, shell structure, charge densities, and surface energetics. These deficiencies imply that this realization of chiral symmetry is incorrect. An alternative scenario, which features a heavy chiral scalar and dynamical generation of the [ital NN] attraction, is discussed.

Model solutions of regularized relativistic transport equations.

We present numerical solutions of recently proposed relativistic transport equations for fluctuating hadronic fields with simplified model Lagrangians containing a spin-1/2 nucleon and a light scalar or pseudoscalar meson. We introduce and implement a method for regularizing tadpoles and vector loops which is consistent with the previously proposed regularization of the scalar loops. The resulting solutions in vacuum are well behaved, exhibiting the expected differences between the scalar and pseudoscalar cases without apparent pathologies.

Mid-range nucleon-nucleon interaction in the linear sigma model

The mid-range attraction between two nucleons is described by correlated two-pion exchange in the linear σ model. In contrast to previous work, chiral symmetry is incorporated dynamically, rather than by enforcing chiral constraints by hand. The input chiral σ mass is a free parameter, but the range and strength of the nucleon-nucleon (NN) attraction are insensitive to its value, which can be taken to be very large. A large σ mass reduces the strength of the nonlinear σ-meson interactions. The resulting strong NN attraction and small many-nucleon forces qualitatively reproduce the scalar dynamics in the Walecka model. To describe correlated two-pion exchange, the s-wave ππ phase shift is computed by summing the tree-level amplitude using the lowest-order Padé approximant. Unitarity and dispersion relations then determine the s-wave N N → ππ amplitude in the pseudophysical and physical regions. This amplitude contains important ππ rescattering effects and respects chiral symmetry. Unitarity and dispersion relations are then used again to calculate the spectral function for the scalar-isoscalar part of the NN interaction. The result can be approximated by a light scalar meson with a broadly distributed mass, which is consistent with the earlier results of Durso, Jackson and Verwest; moreover, the computed mass distribution is insensitive to the input σ mass, as long as it is large ( ⪆1 GeV ). Finally, nuclear matter properties are calculated in a Hartree approximation with the model scalar-isoscalar interaction and an elementary ω meson.

Compatibility of chiral and non-chiral models in quantum hadrodynamics

Non-chiral models of quantum hadrodynamics with a light (500–600 MeV) scalar meson successfully describe bulk nuclear properties. In contrast, chirally symmetric models are necessary to correctly describe pion dynamics. If the chiral scalar meson is taken to be light, however, the resulting strong non-linearities preclude a viable description of nuclear matter saturation. A resolution of this dilemma is discussed based on the linear σ model with a heavy chiral scalar and correlated two-pion exchange in the scalar-isoscalar channel.

Mechanism of chiral symmetry breakdown in quantum chromodynamics

Abstract A specific dynamical mechanism is proposed of chiral symmetry breakdown in QCD according to which a light pseudoscalar bound state is formed out of every color-neutral quark-antiquark combination of light quarks for which the associated axial current q γ μ γ 5 q is conserved exactly in the limit of vanishing quark masses. The pseudoscalar meson mass is of order m Λ s where Λ s is the QCD mass scale and m the quark mass assumed much smaller than Λs. No light scalar or vector meson is formed by this mechanism.

Erratum: Neutral weak currents and a light scalar meson

Erratum: Neutral weak currents and a light scalar meson

Neutral weak currents and a light scalar meson

It has been noted that present discrepancies between the QED theoretical predictions and the experimental values of certain muonic x-ray transitions can be explained if a very light scalar meson exists with a product of coupling constants to muons and to nucleons of greater than about 2 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}7}$. If such a meson couples to the muon neutrino, elastic scattering can occur with $\frac{\ensuremath{\sigma}({\ensuremath{\nu}}_{\ensuremath{\mu}}({\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}})+N\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\mu}}({\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}})+N)}{\ensuremath{\sigma}({\ensuremath{\nu}}_{\ensuremath{\mu}}+n\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}+p)}\ensuremath{\gtrsim}17%$ for neutrinos of about 1 GeV laboratory energy.

Separation Method forO18Using One-Boson-Exchange Potentials

Realistic, generalized, and regularized velocity-dependent one-boson-exchange-potential models of the nucleon-nucleon interaction are applied to calculate the low-lying energy levels of the nucleus ${\mathrm{O}}^{18}$ in the harmonic-oscillator shell model. The singlet even states are treated by the Moszkowski-Scott separation method technique. The energy levels so obtained are comparable to those obtained from the phenomenological Hamada-Johnston hard-core potential. We do not attempt to calculate core-polarization effects explicitly, but rather we attempt to simulate them by varying the coupling constant of the light scalar meson.