Scalar mesons above and below 1 GeV

We show that two nonets and a glueball provide a consistent description of data on scalar mesons below 1.7 GeV. Above 1 GeV the states form a conventional qq̄ nonet mixed with the glueball of lattice QCD. Below 1 GeV the states also form a nonet, as implied by the attractive forces of QCD, but of more complicated nature. Near the center they are (qq)3̄(q̄q̄)3 in S-wave, with some qq̄ in P-wave, but further out they rearrange as (qq̄)1(qq̄)1 and finally as meson-meson states. A simple effective chiral model for such a system with two scalar nonets can be made involving two coupled linear sigma models. One of these could be looked upon as the Higgs sector of nonpertubative QCD. e-mail: [email protected] e-mail: [email protected] 1 The Enigmatic Scalar Mesons In the heavy flavour sector there are clearly established scalar mesons cc̄ and bb̄. They behave as canonical P0 states which partner P1,2 siblings. Their production (e.g in radiative transitions from 2S1 states) and decays (into 1S1 or light hadrons) are all in accord with this. There is nothing to suggest that there is anything “exotic” about such scalar mesons. For light flavours too there are clearly identified P1,2 nonets which call for analogous P0 siblings. However, while all other J PC combinations appear to be realised as expected, (apart from well known and understood anomalies in the 0−+ pseudoscalars), the light scalars empirically stand out as singular. The interpretation of the nature of the lightest scalar mesons has been controversial for over thirty years. There is still no general agreement on where are the qq̄ states, whether there is necessarily a glueball among the light scalars, and whether some of the too numerous scalars are multiquark, KK̄ or other meson-meson bound states. These are fundamental questions of great importance in particle physics. The mesons with vacuum quantum numbers are known to be crucial for a full understanding of the symmetry breaking mechanisms in QCD, and presumably also for confinement. In this paper we propose a resolution of the enigma of the scalar mesons. Theory and data are now converging that QCD forces are at work but with different dynamics dominating below and above 1 GeV mass. The experimental proliferation of light scalar mesons is consistent with two nonets, one in the 1 GeV region (a meson-meson nonet) and another one near 1.5 GeV (a qq̄ nonet), with evidence for glueball degrees of freedom. At the constituent level these arise naturally from the attractive interquark forces of QCD. Below 1 GeV these give a strong attraction between pairs of quarks and antiquarks in S-wave leading to a nonet which is “inverted” relative to the ideal nonets of the simple qq̄ model. Conversely, above 1 GeV the states seeded by P0 qq̄ are present. The scalar glueball, predicted by lattice QCD in the quenched approximation, causes mixing among these states. The phenomenon of multiplet doubling now requires a new effective model