Gell-Mann-Okubo mass formula forSU (4) meson hexadecuplet

Abstract

Using a linear mass spectrum of an SU (4) meson hexadecuplet, we derive the Gell-Mann-Okubo mass formula for the charmed mesons, in good agreement with experiment. Possible generalization of this method to a higher symmetry group is briefly discussed.

Mass spectrum of a meson nonet is linear

“…The method of the derivation of the Gell-Mann-Okubo mass relations described above may be easily generalized to the case of four or more flavors. In our recent paper [35], by applying this method to an SU(4) hexadecuplet, we have derived the corresponding Gell-Mann-Okubo mass formula and found it to be in good agreement with the experimentally established masses of the charmed mesons.…”

New mass relations for heavy quarkonia

“…As shown in ref. [13], this relation holds with an accuracy of up to ∼ 5% for all well established meson hexadecuplets. It is well known that the hadrons composed of light (u, d, s) quarks populate linear Regge trajectories; i.e., the square of the mass of a state with orbital momentum ℓ is proportional to ℓ : M 2 (ℓ) = ℓ/α ′ + const, where the slope α ′ depends weakly on the flavor content of the states lying on the corresponding trajectory,…”

“…Key words: flavor symmetry, quark model, charmed mesons, Gell-Mann-Okubo, Regge phenomenology PACS: 11.30.Hv,11.55.Jy,12.40.Nn,12.40.Yx,14.40.Lb 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], b) generalizing the perturbative treatment of U(3) × U(3) chiral symmetry breaking and the corresponding Gell-Mann-Oakes-Renner relation [6] to U(4) × U(4) [7,8], 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) [9], d) extending the Weinberg spectral function sum rules [11] to accommodate the higher symmetry breaking effects [10], and e) applying alternative methods, such as the linear mass spectrum for meson multiplets 1 [12,13]. In the following 2 , η, η s , η c , η b , K, D, D s , B, B s , B c stand for the masses of the nn (n ≡ u or d), ss, cc, bb, sn, cn, cs, bn, bs, bc mesons, respectively 3 .…”

“…One may also find from Eqs. (12), (13) with equal slopes, and the standard SU (3) Gell-Mann-Okubo relation,…”

New mass relation for meson 25-plet

“…In ref. [15] by the application of the linear spectrum to SU(4) meson 16-plet, the following relation was obtained,…”