Cascade Global Symmetry and Quark Mass Hierarchy

Cascade global symmetry and multi-vacuum expectation values are combined to produce an initial texture of the quark mass matrices. Required corrections to the initial texture zeros (ITZ) are all at the order of 10 −3 m t or less. The possibility of radiative corrections as the source of the complete mass matrices is briefly discussed. The discovery of the top quark makes the fermion spectrum in the standard model complete. We are now puzzled by the pattern of the mass spectrum in the standard model (SM) (Fig.1), as we were thirty years ago by the spectrum of hadrons. However, history does not repeat itself without some varieties. Obviously, the masses of quarks and leptons are regulated by mass ratios (hierarchy), instead of mass differences in the case of hadrons. Dr. Tanaka has just reviewed some previous works in resolving this puzzle. I here would like to present an alternative approach which relates this puzzle to the structure of the Higgs sector, a sector yet completely in the dark. So far, no electroweak scalar (Higgs) has ever been found. However, the best limits are only set for the minimal standard model Higgs boson. For a more complicated spectrum of scalar particles (why are there not many scalars, while there are so many fermions ?), only one mass eigenstate, which is in the direction of the physical vacuum, has dimension three couplings with the weak gauge bosons; all the other Higgs particles, if they exist, are orthogonal to this single state and possess only dimension four couplings with gauge bosons, and therefore are more difficult to discover. The main feature of this approach is to use a natural global symmetry of the standard gauge-fermion interaction sector to protect the small matrix elements in the mass matrices of the quarks. The basic ideas behind this approach[1,2] are the following: 1. Approximate global symmetry which is non-abelian in order to be more restrictive. 2. Multi-Higgs doublets with different vacuum expectation values (VEVs) contribute to dif