SU 3 subsectors ofSU 4 and mass sum rules for charmed hadrons

New mass relation for meson 25-plet

“…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 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, b b, sn, cn, cs, bn, bs, bc mesons, respectively 3 The linear mass relations…”

“…Then, in the same way Eq. ( 26) follows from the standard Gell-Mann-Okubo formula, the following relation may be derived from (38) [7]: η ℓ + η ℓ c = 2D ℓ , which for ℓ = 2 disagrees with experiment, and for ℓ = 1, although perhaps justified for vector mesons, fails for other multiplets, as discussed in the beginning of the paper. Thus, the failure of group theory to produce correct mass relations for heavy quarkonia is solely due to the large bare masses of the c-and b-quarks as compared to those of u-, d-and s-quarks.…”

Silicon Dioxide Thin Films Prepared by Thermal Decomposition of Silicon Tetraacetate

“…The whole difference of the above formula from the standard Gell-Mann-Okubo one [1] is the presence of Z in place of Y in the standard formula. Then, in the same way as equation (26) follows from the standard Gell-Mann-Okubo formula, the following relation may be derived from (38) [7]:…”

“…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 [12] to accommodate the higher symmetry breaking effects [13], and (e) applying alternative methods, such as the linear mass spectrum for meson multiplets + [14,15]. In the following * , 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 .…”