Where and what are the scalar mesons?

Abstract

A self-consistent analysis of the $J^{\mathrm{PC}}=0^{++}$ partial waves obtained from high-statistics $K\pi$, $K\overline{K}$, and $\pi \pi$ data has been performed to verify the existence and to determine the resonance parameters of the $I=\frac{1}{2}$ and $I=0\mathrm{}$ scalar mesons. A mass-dependent parametrization of the $K\pi$ partial wave yields one and only one strange scalar meson, the $\kappa \mathrm{}\left(1510\right)\mathrm{}$, with a width of several hundred MeV. Isoscalar ${\mathrm{O}}^{++}$ mesons found in simultaneous fits to $K\overline{K}$ and $\pi \pi$ data are the $\epsilon \mathrm{}\left(800\right)\mathrm{}$, $S^{*}\mathrm{}\left(1005\right)\mathrm{}$, and ${\epsilon }^{\prime }\mathrm{}\left(1540\right)\mathrm{}$ with widths of about 1000, 8, and 200 MeV, respectively. No simple interpretation of all these states and the $\delta \mathrm{}\left(980\right)\mathrm{}$ and possible ${\delta }^{\prime }\mathrm{}\left(1300\right)\mathrm{}$ as $q\overline{q}$ mesons, $q\overline{q}q\overline{q}$ bound states, or gluon-gluon bound states exists. Possible candidates for an SU(3) nonet of $q\overline{q}$ states are found to be (a) $\epsilon \mathrm{}\left(800\right)\mathrm{}$, ${\epsilon }^{\prime }\mathrm{}\left(1540\right)\mathrm{}$, $\sigma \mathrm{}\left(980\right)\mathrm{}$, and $\kappa \mathrm{}\left(1540\right)\mathrm{}$ or (b) $S^{*}\mathrm{}\left(1005\right)\mathrm{}$, ${\epsilon }^{\prime }\mathrm{}\left(1540\right)\mathrm{}$, ${\sigma }^{\prime }\mathrm{}\left(1300\right)\mathrm{}$, and $\kappa \mathrm{}\left(1540\right)\mathrm{}$. DOI: http://dx.doi.org/10.1103/PhysRevD.19.2678 © 1979 The American Physical Society