Year: 1999
Type: article
Abstract: We investigate the ``family'' relationship of a possible scalar nonet composed of the ${a}_{0}(980),$ the ${f}_{0}(980)$ and the $\ensuremath{\sigma}$ and $\ensuremath{\kappa}$ type states found in recent treatments of $\ensuremath{\pi}\ensuremath{\pi}$ and $\ensuremath{\pi}K$ scattering. We work in the effective Lagrangian framework, starting from terms which yield ``ideal mixing'' according to Okubo's original formulation. It is noted that there is another solution corresponding to dual ideal mixing which agrees with Jaffe's picture of scalars as $\mathrm{qq}\overline{q}\overline{q}$ states rather than $q\overline{q}$ states. At the Lagrangian level there is no difference in the formulation of the two cases (other than the numerical values of the coefficients). In order to agree with experiment, additional mass and coupling terms which break ideal mixing are included. The resulting model turns out to be closer to dual ideal mixing than to conventional ideal mixing; the scalar mixing angle is roughly $\ensuremath{-}17\ifmmode^\circ\else\textdegree\fi{}$ in a convention where dual ideal mixing is $0\ifmmode^\circ\else\textdegree\fi{}.$
Institutions: Syracuse University, Yale University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: U.S. Department of Energy
OpenAlex ID: W1966058162