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

Abstract

Complex-mass (finite-width) 0 ++ nonet and decuplet are investigated by means of exotic commutator method. The hypothesis of 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 2000M eV (excluding σ(600)) and one with the mass 2200 ÷ 2400M eV 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 qq 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. *

Where is the pseudoscalar glueball?

“…For the decuplet we have following system of the ME [34,33] which determines masses and mixings of the decuplet states [30]: where x 1 , x 2 , x 3 are the masses squared of the isoscalar mesons η 1 , η 2 , η 3 . The coefficients l 1 , l 2 , l 3 , are real, as all isoscalar mesons are neutral particles.…”

“…In this case the mass formula and ordering rule do not arise. The restrictions on the masses are not so strict and follow from the conditions (30).…”

“…If the masses of ten mesons with proper quantum numbers are known and satisfy (30), but do not satisfy the MF, the decuplet is of the kind S. If one of the masses is unknown then we can determine it from the MF and the decuplet becomes of the kind I, provided the masses satisfy (30). However, the states constituting these two distinct decuplets may be not very different.…”

“…The ME ( 9) are considered as a system of linear equations with respect to unknown coefficients l 2 i . The solution is given by three kinds of relations [34,30]: a) the octet contents (OC) of the isoscalar states…”

“…Also the width of the η 1 cannot be the base for conclusion about its q q structure. An attempt to call in question this structure resembles confusion which arose after denying the q q structure of the f 0 (980) meson motivated by its small width [30].…”