Existence of σ(600)/κ(900) and Possible Classification of Chiral Scalar Nonet

Recently, by reanalyzing the phase shift data of I = 0 ππ and of I = 1/2 Kπ scatterings, we showed the evidences for existence of light scalar mesons, σ(600) and κ(900), respectively, which had been sought but missing for a long time. The σ(600) and κ(900) together with the established resonances, a0(980) and f0(980), are shown to be consistently classified as the members of a single scalar σ-nonet, appearing in the SU(3) linear σ-model. Especially the mass value of the iso-singlet flavor-octet member satisfies, together with those of κ(900) and a0(980), the GellMann Okubo mass formula. The repulsive background phase shift δBG, which was essential to lead the σ/κ-existence in our phase shift analyses, is also shown to be quantitatively describable in the framework of linear σ model. Thus, the origin of δBG is reduced to the “compensating λφ 4-interaction,” necessary from the viewpoint of chiral symmetry. 1 ππ/Kπ phase shift analyses and existence of σ(600)/κ(900) We have recently made reanalyses of ππ andKπ phase shifts and found strong evidences for existence of I = 0 σ meson and I = 1/2 κ meson, respectively, which had been sought but missing for a long time. For detailed analyses, see ref. [1]. Through the analyses the masses and widths of σ and κ, and their pole positions are determined with the values (in MeV), mσ =585± 20(535 ∼ 675),Γσ = 385± 70, √ spole = 602± 26− i(196± 27), mκ =905 +65 −30,Γκ = 545 +235 −110, √ spole = 875± 75− i(335± 110). (1) Preprint submitted to Elsevier Preprint 1 February 2008 2 Gellmann-Okubo mass formula for scalar σ-nonet 1 Now we have scalars below 1 GeV, σ(600) and f0(980) with I = 0, κ(900) with I = 1/2 and a0(980) with I = 1. Among these scalar mesons, experimentally, f0(980) has a considerably small ππ-width regardless of its large phase volume, while having a rather large KK̄-width in spite of the fact that its mass is quite close to the KK̄-threshold. Assuming approximate validity of the OZI rule, this fact seems to suggest that f0(980) consists of almost pure ss̄-component. Here we simply assume that σ(600) and f0(980) are the ideal mixing[4] states of a single scalar nonet and that the squared-mass matrix takes a diagonal form in these ideal bases. The ideal-mixing states are related to the octet state σ8 and the singlet state σ1 through the orthogonal transformation: