Understanding the scalar meson$q\bar q$ nonet

Abstract

It is shown that one can fit the available data on thea _o(980),f _o(1300) andK ^*_o (1430) mesons as a distorted 0⁺⁺ $q\bar q$ nonet using very few (5–6) parameters and an improved version of the unitarized quark model. This includes all light two-pseudoscalar thresholds, constraints from Adler zeroes, flavour symmetric couplings, unitarity and physically acceptable analyticity. The parameters include a bare$u\bar u$ or$d\bar d$ mass, an over-all coupling constant, a cutoff and a strange quark mass of 100 MeV, which is in accord with expectations from the quark model. It is found that in particular for thea ₀(980) andf ₀(980) the$K\bar K$ component, in the wave function is large, i.e., for a large fraction of the time the$q\bar q$ state is transformed into a virtual$K\bar K$ pair. This$K\bar K$ component, together with a similar component of η′π for thea ₀(980), and ηη, ηη′ and η′η′ components for thef ₀(980), causes the substantial shift to a lower mass than what is naively expected from the$q\bar q$ component alone. Mass, width and mixing parameters, including sheet and pole positions, of the four resonances are given, with a detailed pedagogical discussion of their meaning.