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Abstract
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.
Highlights
It is an ancient subject, the study of light scalar mesons has greatly intensified in the last generation
The results obtained [39] seem to provide support for the picture of light scalars having a predominant content of two quarks and two antiquarks while the heavier scalars appear to be made mainly from one quark and one antiquark, as one would expect from p wave states in the non relativistic quark model
While it appears a little unusual to think of say, the ordinary pion, as having some four quark content when treated in the effective Lagrangian framework, that is the standard picture in the parton model approach to QCD
Summary
It is an ancient subject, the study of light scalar mesons has greatly intensified in the last generation. The pattern, featuring an approximate degeneracy of one I=0 state and the I=1 state together with a flipping compared to the standard vector meson order, is very similar to the experimental one in Eq(1) These “tree level” predictions are expected to receive some non-trivial corrections as to be discussed later. The heavy pseudoscalar nonet members are predicted to be of predominantly “4-quark” type with a similar mass ordering as the light pseudoscalars; namely, π′(1215), K′(1195), η3(1225), η4(1784) In this multiplet, the distortion of the pattern from that of the standard vector multiplet seems to reflect the greater role of “instanton” effects over “4-quark” effects.
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