The flavor-blind principle: A symmetrical approach to the Gatto-Sartori-Tonin relation

Abstract

We perform a systematic study of the generic Gatto-Sartori-Tonin relation, tan 2 θ ij = m i /m j . This study of fermion mixing phenomena leads us to the necessary conditions that are needed in order to obtain it without any approximation. We begin by considering two Dirac fermion families. By means of the hierarchy in the masses, it is found that a sufficient and necessary condition is to have a normal matrix with m 11 = 0. This matrix can be decomposed into two different linearly independent contributions. The origin for such two independent contributions can be naturally explained by what we shall call the flavor-blind principle. This principle states that Yukawa couplings shall be either flavor-blind or decomposed into several sets obeying distinct permutation symmetries. In general, it is shown that the symmetry properties of the introduced set of Yukawa matrices follow for n fermion families the unique sequential breakingThe particular case of three fermion families explains why the four mass ratios parametrization that we recently proposed can be used even in the case of no hierarchical masses.

The mass ratios parametrization

“…where we used the corresponding sum rule in Eq. (59). Curiously enough, the same value may be reached through the ratio mµ mτ = 0.059.…”

“…5 For an example where such kind of matrix structures can be produced see Ref. [59]. 6 A somewhat similar approach can be found in Ref.…”

“…From our mixing sum rules in Eq. (59) we know that it is safe to neglect the electron mass. Therefore, not having evidence for the ocurrence for this decay would not necessarily mean, within the MRP, that neutrinos are not Majorana.…”

Fermion masses as mixing parameters in the SM

“…In fact, this assumption needs a more careful treatment and its details can be found in [10]. It is straightforward to show that |m 23 | = √ m 2 m 3 and |m 33 | = m 3 − m 2 .…”

A principle for the Yukawa couplings

“…But that is all we know about them, i.e., that we do not know them. Here we try to briefly summarize the essence of a recently proposed principle called the Flavor-Blind Principle [1] that gives an origin to the Yukawa couplings in agreement to the emerged structures appearing under the phenomenological application of hierarchical fermion masses [2].…”