Renata Jora

Global aspects of the scalar meson puzzle

A generalized linear sigma model for low-energy QCD is employed to study the quark structure of eight low-lying scalar isomultiplets as well as eight low-lying pseudoscalar isomultiplets. The model, building on earlier work, assumes the possible mixing of quark antiquark states with others made of two quarks and two antiquarks. No a priori assumption is made about the quark contents of the states, which emerge as predictions. An amusing and contrasting pattern for the quark structure is found; the lighter conventional pseudoscalars are, as expected, primarily of two-quark type whereas the lighter scalars have very large four-quark admixtures. The new feature of the present paper compared to earlier ones in this series involves the somewhat subtle and complicated effects of SU(3) flavor breaking. They do not alter the general pattern of two-quark vs four-quark mixing obtained in the SU(3)symmetric case but, of course, give a more detailed picture.

An approach to permutation symmetry for the electroweak theory

The form of the leptonic mixing matrix emerging from experiment has, in the last few years, generated a lot of interest in the so-called tribimaximal type. This form may be naturally associated with the possibility of a discrete permutation symmetry (S3) among the three generations. However, trying to implement this attractive symmetry has resulted in some problems and it seems to have fallen out of favor. We suggest an approach in which the S3 holds to first approximation, somewhat in the manner of the old SU(3) flavor symmetry of the three flavor quark model. It is shown that in the case of the neutrino sector, a presently large experimentally allowed region can be fairly well described in this first approximation. We briefly discuss the nature of the perturbations which are the analogs of the Gell-Mann Okubo perturbations but confine our attention for the most part to the S3 invariant model. We postulate that the S3 invariant mass spectrum consists of non zero masses for the (τ, b, t) and zero masses for the other charged fermions but approximately degenerate masses for the three neutrinos. The mixing matrices are assumed to be trivial for the charged fermions but of tribimaximal type for the neutrinos in the first approximation. It is shown that this can be implemented by allowing complex entries for the mass matrix and spontaneous breakdown of the S3 invariance of the Lagrangian.

Two chiral nonet model with massless quarks

We present a detailed study of a linear sigma model containing one chiral nonet transforming under

Chiral Nonet Mixing in pi pi Scattering

\mathrm{U}(1{)}_{\mathrm{A}}

Model for light scalars in QCD

as a quark-antiquark composite and another chiral nonet transforming as a diquark-antidiquark composite (or, equivalently from a symmetry point of view, as a two meson molecule). The model provides an intuitive explanation of a current puzzle in low energy QCD: Recent work has suggested the existence of a lighter than 1 GeV nonet of scalar mesons which behave like four quark composites. On the other hand, the validity of a spontaneously broken chiral symmetric description would suggest that these states be chiral partners of the light pseudoscalar mesons, which are two quark composites. The model solves the problem by starting with the two chiral nonets mentioned and allowing them to mix with each other. The input of physical masses in the SU(3) invariant limit for two scalar octets and an excited pion octet results in a mixing pattern wherein the light scalars have a large four quark content while the light pseudoscalars have a large two quark content. One light isosinglet scalar is exceptionally light. In addition, the pion pion scattering is also studied and the current algebra theorem is verified for massless pions which contain some four quark admixture.

Low energy scattering with a nontrivial pion

The underlying mixing of quark components of scalar mesons is probed in

NATURALNESS IN A SIMPLE TWO HIGGS DOUBLET MODEL

\pi K

Semi-leptonic

scattering within a generalized linear sigma model that contains two scalar meson nonets and two pseudoscalar meson nonets (a quark-antiquark and a four-quark). In the leading order of this model, all free parameters have been previously fixed using the mass spectra and several low-energy parameters known from experiment and consistent predictions have been made. As other predictions of the model, in the present work the isospins

D_s^+

I

(1968) decays as a scalar meson probe

= 1/2, 3/2 and