Abstract
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.
Highlights
The identification and interpretation of the low lying scalar mesons are questions of great current interest
In the effective chiral Lagrangian approach from which this paper is motivated, a light isoscalar σ (560) in addition to the known light isoscalar f0(980) are needed [1] to produce a ππ scattering amplitude which agrees with experiment
The pattern of masses, coupling constants and especially the isoscalar mixing angle was observed [3] to be much closer to the one expected from a four-quark picture rather than from the conventional two-quark picture for this scalar nonet
Summary
The identification and interpretation of the low lying scalar mesons are questions of great current interest. A light strange κ (900) state is needed [2] to understand the experimental πK amplitude These three particles were postulated [3] to form a nonet, taken together with the known isovector a0(980). If one adopts the above picture or, as a matter of fact, any other picture in which an unconventional non-qqnonet made of the σ (560), κ(900), a0(980) and f0(980) exists, there is an interesting puzzle concerning the conventional qqscalar nonet Such a nonet has an interpretation in the constituent quark model as a p-wave excitation and should share many characteristics of the other p-wave states (the tensor nonet and two axial vector nonets with different charge conjugation properties). To see the puzzling features let us focus attention on the experimental scalar candidates with non-trivial isospin quantum numbers in the greater than 1 GeV energy range These are the isovector a0(1450) and the strange isospinor K0∗(1430). The present scheme suggests a five-fold mixing between the σ(560), the f0(980), two heavier qqisoscalar scalars and a glueball
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