Hierarchies of the 4 Texture Zero Quark Mass Matrices and their equal spacing rule

Abstract

We show that the parameters of the quark mass matrices M_u and M_d of a 4 texture zero model, exhibit an interesting hierarchical regularity we have called equal spacing rule, and that this regularity leads us to a further observation that the quark mass matrices (M_u, M_d) appear to exist in a plurality of states, each state labelled by two numbers (N,k). We give interpretation to these observations.