The quark mass gap and quark mass hierarchy is obtained by introducing a BCS interaction among ur-quarks. A 3×3 quark mass matrix with equal matrix elements, i.e., with all ur-flavors interacting with the same strength, has eigenvalues 0, 0 and 3; both the quark charge −1/3 and charge +2/3 systems with one heavy quark and two almost massless quarks resemble these eigenvalues. The physical mass splittings between the two lightest quarks come from higher-order corrections to the mass matrix which are obtained by fitting the Kobayashi-Maskawa matrix VKM.
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Kaus et al. (1988) studied this question.