How we discovered the nonet of light scalar mesons

As has been confirmed meanwhile by lattice-QCD calculations (see e.g. Ref. [1]), the confinement spectrum of non-exotic quark-antiquark systems has its ground state for scalar mesons well above 1 GeV in the Resonance Spectrum Expansion (RSE). For instance, in the S-wave Kπ RSE amplitude, a broad resonance was predicted slightly above 1.4 GeV [2], which is confirmed by experiment as the K 0 (1430). However, a complete nonet of light scalar mesons was predicted [3] as well, when a model strongly related to the RSE and initially developed to describe the cc and bb resonance spectra [4] was applied in the light-quark sector. Thus, it was found that the light scalar-meson nonet constitutes part of the ordinary meson spectrum, albeit represented by “extraordinary” [5] poles [2]. Similar resonances and bound states appear in the charmed sector [6], and are predicted in the B-meson spectrum [7, 8]. A recent work [9] confirmed the presence of light scalar-meson poles in the RSE amplitude for S-wave and P -wave ππ and Kπ contributions to three-body decay processes measured by the BES, E791 and FOCUS collaborations. Scattering poles It is generally accepted that resonances in scattering are represented by poles in the “second” Riemann sheet of the complex energy plane [10]. Let us assume here that in a process of elastic and non-exotic meson-meson scattering one obtains scattering poles at E = P0 , P1 , P2 , . . . . (1) Centro de F́ısica Teórica, Departamento de F́ısica, Universidade de Coimbra, P-3004516 Coimbra, Portugal. Centro de F́ısica das Interacções Fundamentais, Instituto Superior Técnico, Universidade Técnica de Lisboa, Edif́ıcio Ciência, P-1049-001 Lisboa, Portugal. The RSE was designed for the description of the complete resonance structure in meson-meson scattering, for both the heavyand light-quark sectors.