Towards resolution of the scalar meson nonet enigma: Gell-Mann-Okubo revisited

Abstract

The new SU(3) nonet mass formula 2M 2 (ss)+3M 2 (nn, I = 1) = 4M 2 (sn)+ M 2 (nn, I = 0) (n = u, d), obtained in our previous paper by using Regge phenomenology, is rederived for the pseudoscalar and scalar mesons in the Nambu-Jona-Lasinio model with instanton-induced interaction and applied to the problem of the correct qq assignment for the scalar meson nonet. The results strongly favor the masses of the scalar isoscalar mostly octet and mostly singlet states in the vicinity of 1.45 GeV and 1.1 GeV, respectively.

Towards resolution of the scalar meson nonet enigma

“…in agreement with naive expectations from the quark content of these states which is, in view of (10) [25],…”

“…which is the new Gell-Mann-Okubo mass formula for pseudoscalar mesons found in our previous publication [25] and which is satisfied to an accuracy of better than 1% by the measured pseudoscalar meson masses. We now turn to the derivation of the formula (7).…”

“…This term improves the accuracy of the Sakurai formula, which is not bad by itself, (∼2-3%) by a factor of 2 [25]. In this paper we present another derivation of the formula (7) for pseudoscalar and scalar mesons in the Nambu-Jona-Lasinio model with an instanton-induced interaction.…”

“…We consider the fact that the formula (7) can be derived in (at least) two completely independent ways, viz., from Regge phenomenology, as done in ref. [25], and in the NJL model, as done in the present paper, as sufficient to treat this formula as (almost) model-independent. 2 As discussed above, in the pseudoscalar meson case, this formula reduces to Eq.…”

“…[24]. In our previous paper [25], by using Regge phenomenology, we derived a new mass relation (I stands for isospin):…”