Smallness of gluon coupling to constituent quarks in baryons and validity of nonrelativistic quark model

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Abstract
A study of the parametrization of baryon masses and other quantities leads to a ratio ≅ ⅕ for two-gluon-exchange versus one-gluon-exchange terms between two constituent quarks in a baryon. This fact (plus the factor 3 reduction from each additional order in flavor breaking) explains the success, to a part per thousand, of a new baryon mass formula [Phys. Rev. Lett. 68, 139 (1992)]. It also explains why the results of SU(3) that neglect second-order flavor breaking (such as the Gell-Mann-Okubo baryon mass formula) work much better than expected. Finally the general parametrization, plus the above reduction factors, clarify why the "naive" nonrelativistic quark model (NRQM) is quantitatively fairly good. The reasons are twofold: (a) The structure of the general parametrization (an exact consequence of any QCD-like relativistic field theory) is similar to that of the NRQM; (b) the smallness of the gluon coupling and the reduction factor due to flavor imply that the additive (one-body) terms in the parametrization prevail on the two-body terms and the latter on the three-body ones, the typical feature of the "naive" NRQM.