No abstract

The differential realization of the recently proposed deformed Poincaré algebra is considered. The notion of covariant wave functions is introduced and their explicit form in the "minimal" (in Weinberg's sense) case is given. The deformed Dirac equation is constructed.

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. *

Mass formulae for light meson multiplets derived by means of exotic commutator technique are written for complex masses and considered as complex mass sum rules (CMSR). The real parts of the (CMSR) give the well known mass formulae for real masses (Gell-Mann-Okubo, Schwinger and Ideal Mixing ones) and the imaginary parts of CMSR give appropriate sum rules for the total hadronic widths -width sum rules (WSR). Most of the observed meson nonets satisfy the Schwinger mass formula (S nonets). The CMSR predict for S nonet that the points (m, Γ) form the rectilinear stitch (RS) on the complex mass plane. For low-mass nonets WSR are strongly violated due to "kinematical" suppression of the particle decays, but the violation decreases as the mass icreases and disappears above ∼ 1.5GeV . The slope ks of the RS is not predicted, but the data show that it is negative for all S nonets and its numerical values are concentrated in the vicinity of the value −0.5. If ks is known for a nonet, we can evaluate "kinematical" suppressions of its individual particles. The masses and the widths of the S nonet mesons submit to some rules of ordering which matter in understanding the properties of the nonet. We give the table of the S nonets indicating masses, widths, mass and width orderings. We show also mass-width diagrams for them. We suggest to recognize a few multiplets as degenerate octets. In Appendix we analyze the nonets of 1 + mesons.

The pseudoscalar mesons π(1300), K(1460), η(1295), η(1405) and η(1475) are assumed to form the meson decuplet which includes the glueball as the basis state supplementing the standard SU (3)F nonet of light qq states (q = u, d, s). The decuplet is investigated by using the algebraic approach based on the hypothesis of vanishing exotic commutators (VEC) of SU (3)F "charges" and their time derivatives. This leads to a system of master equations (ME) determining: (a) octet contents of the physical isoscalar mesons, (b) the mass formula relating all masses of the decuplet and (c) the mass ordering rule. The states of the physical isoscalar mesons η(1295), η(1405), η(1475) are expressed as superpositions of the "ideal" qq (N and S) states and the glueball G one. The "mixing matrix" realizing transformation from the unphysical states to the physical ones follows from the octet contents and is expressed totaly by the decuplet meson masses. Among four one-parameter families of the resulting mixing matrices (multitude of the solutions arising from bad quality of data on the π(1300) and K(1460) meson masses) there is a family attributing the glueball-dominated composition to the η(1405) meson. The pseudoscalar decuplet is similar in some respects to the scalar one: both are composed of the excited qq states and G; the mass ordering of their N, S, G -dominated isoscalars is the same. Contrary to the Lattice QCD and other predictions, the mass m G −+ of the pseudoscalar pure glueball state is smaller than the scalar m G