Mechanism for a next-to-lowest lying scalar meson nonet

Recent work suggests the existence of a non-conventional lowest-lying scalar nonet containing the a0(980). Then the a0(1450) and also the K0*(1430) are likely candidates to belong to a conventional p-wave $q \bar q$ nonet. However a comparison of their properties with those expected on this basis reveals a number of puzzling features. It is pointed out that these puzzles can be resolved in a natural and robust way by assuming a ``bare'' conventional p-wave scalar $q \bar q$ nonet to mix with a lighter four quark $qq \bar q \bar q$ scalar nonet to form new ``physical'' states. The essential mechanism is driven by the fact that the isospinor is lighter than the isovector in the unmixed $qq \bar q \bar q$ multiplet.Comment: 22 pages, 6 figure

Equation of state for the 2+1 dimensional Gross-Neveu model at order 1/N

We calculate the equation of state of the Gross-Neveu model in 2+1 dimensions at order 1/N, where N is the number of fermion species. We make use of a general formula valid for four-fermion theories, previously applied to the model in 1+1 dimensions. We consider both the discrete and continuous symmetry versions of the model. We show that the pion-like excitations give the dominant contribution at low temperatures. The range of validity for such pion dominance is analyzed. The complete analysis from low to high temperatures also shows that in the critical region the role of composite states is relevant, even for quite large N, and that the free-component behaviour at high T starts at about twice the mean field critical temperature.Comment: 19 pages, RevTeX, 10 figures.p

Chiral symmetry breaking in hot matter

This series of three lectures covers (a) a basic introduction to symmetry breaking in general and chiral symmetry breaking in QCD, (b) an overview of the present status of lattice data and the knowlegde that we have at finite temperature from chiral perturbation theory. (c) Results obtained from the Nambu--Jona-Lasinio model describing static mesonic properties are discussed as well as the bulk thermodynamic quantities. Divergences that are observed in the elastic quark-antiquark scattering cross-section, reminiscent of the phenomenon of critical opalescence in light scattering, is also discussed. (d) Finally, we deal with the realm of systems out of equilibrium, and examine the effects of a medium dependent condensate in a system of interacting quarks.Comment: 62 LaTex pages, incorporating 23 figures. Lectures given at the eleventh Chris-Engelbrecht Summer School in Theoretical Physics, 4-13 February, 1998, to be published by Springer Verla

Hadronization in the SU(3) Nambu-Jona-Lasinio Model

The hadronization process for quarks combining into two mesons, q\bar q\to MM' at temperature T is described within the SU(3) Nambu- Jona-Lasinio model with finite current quark masses. Invariant matrix elements, cross-sections and transition rates are calculated to leading order in a 1/N_c expansion. Four independent classes, u\bar d, u\bar s, u\bar u and s\bar s\to hadrons are analysed, and the yield is found to be dominated by pion production. Threshold behaviour is determined by the exothermic or endothermic nature of the processes constituting the hadronization class. A strong suppression of transition rates is found at the pionic Mott temperature T_{M\pi}=212 MeV, at which the pion becomes a resonant state. The mean time for hadronization is calculated to be 2-4 fm/c near the Mott temperature. The calculation of strangeness changing processes indicates that hadronization accounts for a 1% increase in the absolute value of the kaon to pion ratio at T=150 MeV.Comment: 43 Pages REVTeX, 25 Figures as separate fil

Putative Light Scalar Nonet

We investigate the "family" relationship of a possible scalar nonet composed of the a_0(980), the f_0(980) and the \sigma and \kappa type states found in recent treatments of \pi\pi and \pi K scattering. We work in the effective Lagrangian framework, starting from terms which yield "ideal mixing" according to Okubo's original formulation. It is noted that there is another solution corresponding to dual ideal mixing which agrees with Jaffe's picture of scalars as qq\bar q \bar q states rather than as q\bar q states. At the Lagrangian level there is no difference in the formulation of the two cases (other than the numerical values of the coefficients). In order to agree with experiment, additional mass and coupling terms which break ideal mixing are included. The resulting model turns out to be closer to dual ideal mixing than to conventional ideal mixing; the scalar mixing angle is roughly -17 degrees in a convention where dual ideal mixing is 0 degrees.Comment: 24 pages, 3 figure

eta' to eta pi pi Decay as a Probe of a Possible Lowest-Lying Scalar Nonet

We study the eta' to eta pi pi decay within an effective chiral Lagrangian approach in which the lowest lying scalar meson candidates sigma(560) and kappa(900) together with the f0(980) and a0(980) are combined into a possible nonet. We show that there exists a unique choice of the free parameters of this model which, in addition to fitting the pi pi and pi K scattering amplitudes, well describes the experimental measurements for the partial decay width of eta' to eta pi pi and the energy dependence of this decay. As a by-product, we estimate the a0(980) width to be 70 MeV, in agreement with a new experimental analysis.Comment: 25 pages, 11 figure