Two chiral nonet model with massless quarks

Abstract

We present a detailed study of a linear sigma model containing one chiral nonet transforming under U(1)$_A$ as a quark-antiquark composite and another chiral nonet transforming as a diquark-anti diquark 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.Comment: 22 pages, 8 figure

π0−η−η′mixing in a generalized multiquark interaction scheme

“…It is our understanding that this results partly from the fact that already at mesonic tree level there are signatures of quark-antiquark as well as of admixtures of 2 quark-2 antiquark states present, from the underlying multiquark Lagrangian, which contribute in the long distance asymptotics to the internal structure of the mesons as well as to the mesonic interaction terms. In many other approaches the more complex quark structures enter only through the explicit inclusion of meson loops, tetraquark configurations, and so on [66][67][68][69][70][71][72][73][74][75][76][77][78]. Table II shows the current and constituent quark masses in the isospin limit and the model parameters which do not break explicitly the chiral symmetry, the 4-quark coupling G, the 6-quark 't Hooft determinant coupling κ, and two 8-quark couplings g 1 , g 2 , of which g 1 is OZI-violating.…”

Are three flavors special?

“…In the present approach either is allowable. In fact it was shown in the first of [30] that the molecular form can be transformed using Fierz identities to a linear combination of the "diquark-antidiquark" forms. We thus assume that some unspecified linear combination of M (2) , M (3) and M (4) , denoted by M ′ , represents the qqqq chiral nonet which mixes with M .…”

“…A more detailed picture with a particular choice of interaction terms was given in the first of [23]. In a series of papers, the model was explored for an arbitrary choice of interactions [32], a choice of interactions based on including terms containing less than a fixed number of underlying quark or antiquark fields [33] and the zero quark mass limit [34]. In addition the modeling of the axial anomaly was discussed [30] as well as the details of pion pion scattering [35].…”

“…In a series of papers, the model was explored for an arbitrary choice of interactions [32], a choice of interactions based on including terms containing less than a fixed number of underlying quark or antiquark fields [33] and the zero quark mass limit [34]. In addition the modeling of the axial anomaly was discussed [30] as well as the details of pion pion scattering [35]. In the most recent of these papers [36], the possible identification with all observed states was studied in further detail; after mixing there are two physical scalar nonets and two physical pseudoscalar nonets.…”

Electromagnetic trace anomaly in a generalized linear sigma model

“…In a series of papers [27][28][29][30][31][32] we proposed and studied in detail a generalized linear sigma model with two chiral nonets, one with a two quark substructure and the other one with a four-quark content. In this framework the physical scalar states were found to have a significant admixture of two-and four-quark components, with those below 1 GeV generally containing a larger four-quark component compared to those above 1 GeV.…”