Eur. Phys. J. C (2006) 46: 759-770
https://doi.org/10.1140/epjc/s2006-02516-8

Theoretical Physics

The multiplets of finite-width 0⁺⁺ mesons and encounters with exotics

Department of Theoretical Physics II, University of Lodz, Pomorska 149/153, 90-236, Lodz, Poland

^* e-mail: m.majewski@merlin.fic.uni.lodz.pl

Received: 7 October 2005
Revised: 22 December 2005
Published online: 30 March 2006

Abstract

The complex-mass (finite-width) 0⁺⁺ nonet and decuplet are investigated by means of the exotic commutator method. The hypothesis of the vanishing of the exotic commutators leads to the system of master equations (ME). Solvability conditions of these equations define relations between the complex masses of the nonet and decuplet mesons which, in turn, determine relations between the real masses (mass formulae), as well as between the masses and widths of the mesons. Mass formulae are independent of the particle widths. The masses of the nonet and decuplet particles obey simple ordering rules. The nonet mixing angle and the mixing matrix of the isoscalar states of the decuplet are completely determined by solution of ME; they are real and do not depend on the widths. All known scalar mesons with the mass smaller than 2000 MeV (excluding σ(600)) and one with the mass belong to two multiplets: the nonet (a₀(980),K₀(1430),f₀(980),f₀(1710)) and the decuplet (a₀(1450),K₀(1950),f₀(1370),f₀(1500),f₀(2200)/f₀(2330)). It is shown that the famed anomalies of the f₀(980) and a₀(980) widths arise from an extra “kinematical” mechanism, suppressing decay, which is not conditioned by the flavor coupling constant. Therefore, they do not justify rejecting the qq̄ structure of them. A unitary singlet state (glueball) is included into the higher lying multiplet (decuplet) and is divided among the f₀(1370) and f₀(1500) mesons. The glueball contents of these particles are totally determined by the masses of decuplet particles. Mass ordering rules indicate that the meson σ(600) does not mix with the nonet particles.