Mechanism for a next-to-lowest lying scalar meson nonet

Recent work suggests the existence of a nonconventional lowest-lying scalar nonet containing the $a_0\mathrm{}\left(980\right).$ Then the $a_0\mathrm{}\left(1450\right)\mathrm{}$ and also the $K_0^{*}\mathrm{}\left(1430\right)\mathrm{}$ are likely candidates to belong to a conventional p-wave $q\overline{q}$ 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 $q\overline{q}$ nonet to mix with a lighter four-quark $\mathrm{qq}\overline{q}\overline{q}$ 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 $\mathrm{qq}\overline{q}\overline{q}$ multiplet.