New mass relation for meson 25-plet

Abstract

By assuming the existence of (quasi)-linear Regge trajectories for 25-plet mesons in the low energy region, we derive a new, 14th power, meson mass relation. This relation may be reduced to a quadratic Gell-Mann-Okubo type formula by fitting the values of the Regge slopes of these (quasi)-linear trajectories. Such a formula holds with an accuracy of ∼ 2% for vector mesons, and * also suggests that the quantum number I(J P ) = 1 2 (2 + ) should be assigned to the both B J (5732) and B sJ (5850) mesons discovered recently. We also discuss reasons for the failure of group theory to produce correct mass relations for heavy quarkonia.The generalization of the standard SU(3) Gell-Mann-Okubo mass formula [1] to higher symmetry groups, e.g., SU(4) and SU (5), became a natural subject of investigation after the discovery of the fourth and fifth quark flavors in the mid-70's [2]. Attempts have been made in the literature to derive such a formula, either quadratic or linear in mass, by a) using group theoretical methods [3,4,5,6,7], b) generalizing the perturbative treatment of U(3) × U(3) chiral symmetry breaking and the corresponding Gell-Mann-Oakes-Renner relation [8] to U(4)×U(4) [9, 10], c) assuming the asymptotic realization of SU(4) symmetry in the algebra [A α , A β ] = if αβγ V γ (where V α , A β are vector and axial-vector charges, respectively) [11], d) extending the Weinberg spectral function sum rules [13] to accommodate the higher symmetry breaking effects [12], and e) applying alternative methods, such as the linear mass spectrum for meson multiplets 1 [14,15]. In the following stand for the masses of the nn (n ≡ u or d), ss, cc, bb, sn, cn, cs, bn, bs, bc mesons, respectively 3 The linear mass relations

Gaussian sum-rules and prediction of resonance properties

“…The phenomenological results for thenn quark scalar mesons (see Table 1) provide valuable information for interpretation of the scalar mesons. In particular, the Gaussian sum-rule analysis is in excellent agreement with the identification of the a 0 (1450) as the lightest quark scalar meson with a significantnn content, supporting the conclusions of [27,28], and suggests that a light (≪ 1 GeV) I = 0 scalar meson does not have a significant nn component. The I = 1 excited state in Table 1 suggests identification of the X(1775) [10] as a scalar state containingnn.…”

On the Regge slopes intramultiplet relation

“…(7)) is inconsistent with the heavy quark limit. This confirms the conclusion, drawn before on the basis of meson spectroscopy [7,8,9,10], that it is Eq. (5) that is realized in the real world.…”

“…[1], the slopes and intercepts of the Regge trajectories are the fundamental constants of hadron dynamics, perhaps generally more important than the mass of any particular state. Thus, not only the derivation of mass relations [7,8,9,10] but also the determination of the parameters a(0) and α ′ of heavy quarkonia is of great importance, since they afford opportunities for better understanding of the dynamics of the strong interactions in the processes of production of charmed and beauty hadrons at high energies, and estimations of their production rates.…”

“…In a series of our previous publications [7,8,9,10] we chose Eq. (5), since it is much more consistent with (3) than is Eq.…”

Identification of the glueballs and the scalar meson nonet of lowest mass

“…The alternative choice II would treat f 0 (980) as purely nonstrange state which is not attractive phenomenologically as will be discussed below. The pure ss state f 0 > with mass as in (35) could then be associated with the J = 0 component of f J (1710) (see, Sect. 6) but not much is known about the flavor properties of this state.…”