Systematics of Quark-Antiquark States: Where are the Lightest Glueballs?

Abstract

The analysis of the experimental data of Crystal Barrel Collaboration on the pp annihilation in flight with the production of mesons in the final state resulted in a discovery of a large number of mesons over the region 1900-2400 MeV, thus allowing us to systematize quark-antiquark states in the (n, M 2 ) and (J, M 2 ) planes, where n and J are radial quantum number and spin of the meson with the mass M . The data point to meson trajectories in these planes being approximately linear, with a universal slope. Basing on these data and results of the recent K-matrix analysis a nonet classification is performed. In the scalar-isoscalar sector, the broad resonance state f0(1200−1600) is superfluous for the qq classification, i.e. it is an exotic state. The ratios of coupling constants for the transitions f0 → ππ, KK, ηη, ηη point to the gluonium nature of the broad state f0(1200 − 1600). The problem of the location of the lightest pseudoscalar glueball is also discussed.The search for exotic mesons should be based on the classification of qq-states. Exotic mesons are those which are superfluous for the qq systematics. The quark-antiquark systematics means: (i) classification of qq states as states located on the (n, M 2 ) and (J, M 2 ) trajectories, and (ii) determination of the quark-gluonium content of states from the analysis of the decay coupling constants, namely, hadronic and radiative decay couplings as well as weak ones.For the hadronic decay coupling constants, the most reliable information comes from the K-matrix analysis. In addition, the K-matrix analysis allows us to study bare states (the states before the onset of the decay processes).1.Systematics of the qq-states on the (n, M 2 ) and (J, M 2 ) planes. The analysis of experimental data on the pp annihilation in flight with the production of mesons in the final state resulted in a discovery of the large number of mesons over the region 1900-2400 MeV [1]. This allowed us to systematize quark-antiquark states on the (n, M 2 ) and (J, M 2 ) planes. The data point to almost the linear meson trajectories on these planes, with a universal slope [2].In Fig. 1, one can see the (n, M 2 ) trajectories for the (I = 1) states, which are drown for the a 1 -and a 3 -mesons (Fig. 1a), π-, π 2 -and π 4 -mesons (Fig. 1b), b 1 -and b 3 -mesons (Fig. 1c). All these trajectories reveal linear behaviour, such aswith µ 2 1.2 GeV 2 ; M 0 is the mass of the ground (basic) state, n = 1. The pion, being beyond the trajectory, is an exception, that is not a surprise, for the pion is a special particle in certain respect. In the classification, all these mesons should be treated as qq-states. Using the spectroscopy notations for qq-states, 2S+1 L J where S is the quark spin and L is their orbital momentum, we assign the trajectories to mesons as follows: a 1 (1230) trajectory: n 3 P 1 qq-states, a 3 (2030) trajectory: n 3 F 3 qq-states; π(140) trajectory: n 1 S 0 qq-states, π 2 (1670) trajectory: n 1 D 2 qq-states, π 4 (2250) trajectory: n 1 G 4 qq-states; b 1 (1235) trajectory: ...

Holographic glueball structure

“…The corresponding ground state glueball mass predictions are then m (D) S = 1.80 GeV and m (N) S = 1.34 GeV (where m S ≡ m 1 ). The latter is significantly smaller than most quenched lattice results but close to the f (1270) and to results of K-matrix analyses of scalar resonance data [68], mixing schemes with only one 0 ++ multiplet below 1.8 GeV [69], a topological knot model [70] and the QCD sum rule prediction m S = 1.25 ± 0.2 GeV [32]. One might speculate that fixing z −1 m in the flavored meson sector takes some light-quark effects into account and hence corresponds to a lower, unquenched value of the scalar glueball mass (at least under Neumann IR boundary conditions).…”

QCD Glueball Sum Rules and Vacuum Topology

“…(The mass stays well beyond 1 GeV, however, in contrast to obsolete predictions based on purely perturbative coefficients.) This value is somewhat smaller than the quenched lattice results 15 (which will probably be reduced by light-quark effects) and consistent with the broad glueball state found in a comprehensive K-matrix analysis 16 . The systematics among our different Borel moments likewise indicates a rather large width of the scalar glueball, Γ S 0.3 GeV.…”

Hadron collisions at ultrahigh energies: Black disk or resonant disk modes?

“…The growth of the radius of the black disk is slow; the small value of R 0 is caused by the large mass of glueballs [29,30] and the effective mass of gluons [31,32]. The black disk mode results in σ tot ≃ 2πðR 0 ξÞ 2 ;…”