How can one understand the lightest scalars, especially the sigma

Abstract

We discuss how the a_0(980), f_0(980), K^*_0(1430) and particularly the broad sigma resonance can be understood within a coupled channel framework, which includes all light two-pseudoscalar thresholds together with constraints from Adler zeroes, flavour symmetric couplings, unitarity and physically acceptable analyticity. All (qbar q) scalars are, when unitarized, strongly distorted by hadronic mass shifts, and the nonstrange isoscalar state becomes a very broad resonance, with its pole at 470-i250 MeV. We believe this is the sigma meson required by models for spontaneous breaking of chiral symmetry. Recently this light resonance has clearly been observed in D-> sigma pi-> 3pi by the E791 experiment at Fermilab, and we discuss how this decay channel can be predicted in a Constituent Quark Meson Model (CQM), which incorporates heavy quark and chiral symmetries. We also discuss the less well known phenomenon that with a large coupling there can appear two physical resonance poles on the second sheet although only one bare quark-antiquark state is put in. The f_0(980) and f_0(1370) resonance poles can thus be two manifestations of the same (sbar s) quark state. Both of these states are seen clearly in D_s-> 3pi by the E791 experiment, where (sbar s) intermediate states are expected to be dominant.