ar X iv : h ep - p h / 97 08 49 8 v 1 2 9 A ug 1 99 7 Gell - Mann – Okubo Mass Formula Revisited

We show that the application of Regge phenomenology to SU(4) meson multiplets leads to a new Gell-Mann–Okubo mass-mixing angle formula in the SU(3) sector, 3m 2 1 + cos 2 θ m 2 0 + sin 2 θ m 2 0 ′ + √ 2 sin 2θ m 2 0 − m 2 0 ′ = 4m 2 1/2 , where m 1 , m 1/2 , m 0 , m 0 ′ are the masses of the isovector, isodoublet, isoscalar mostly octet and isoscalar mostly singlet states, respectively, and θ is the nonet mixing angle. For an ideally mixed nonet, θ = arctan 1/ √ 2, this formula reduces to 2m 2 0 + 3m 2 1 = 4m 2 1/2 + m 2 0 ′ which holds with an accuracy of ∼ 1% for vector and tensor mesons. For pseudoscalar mesons, with the η-η ′ mixing angle − arctan 1/(2 √ 2) ≃ −19.5 o , in agreement with experiment, it leads to the relation 4m 2 K = 3m 2 π + m 2 η ′ which holds to an accuracy of better than 1% for the measured pseudoscalar meson masses. The original Gell-Mann–Okubo (GMO) mass formula [1] m 2 1 + 3m 2 8 = 4m 2 1/2 (1) relates the masses of the isovector (m 1), isodoublet (m 1/2) and isoscalar octet (m 8) states of a meson octet. It is usually cast into a form which relates m 1 and m 1/2 with the masses of the two physical isoscalar states, m 0 ′ and m 0 , which have n¯ n and s¯ s *