Fermion mass matrices, textures and beyond

Abstract

The issue of texture specific fermion mass matrices have been examined briefly from the `bottom-up' perspective. In case no conditions are imposed, the texture ansatze leads to a large number of viable possibilities. However, besides textures, if in case one incorporates the ideas of `natural mass matrices' and uses the facility of Weak Basis Transformations, then one is able to arrive at a minimal finite set of viable mass matrices in the case of quarks.Comment: 8 pages, 1 figur

Exploring the predictability of symmetric texture zeros in quark mass matrices

“…Attempts were also made [70] to integrate the concept of 'weak basis transformations' [32,35] and 'naturalness' [71] in quark mass matrices which were also consistent with hierarchical quark mass matrices. Some recent analyses predicted [51,[72][73][74][75][76] that texture four zero quark mass matrices in [52] were the only viable structures in the quark sector and that the elements in these matrices were only "weakly" hierarchical with M 22 >> m 2 [55] and not "strongly" hierarchical with M 22 ∼ m 2 . These analyses seemed to rule out the possibility of strongly hierarchical quark mass matrices in recent context.…”

Stable lepton mass matrices

“…We assume that physical quantities, in particular the hierarchical ones (the small ratio of charged fermion masses and the small ratio of the "solar" mass squared difference over the "atmospheric" one, |∆m 2 12 /∆m 2 23 |), are stable with respect to small (but finite) variations of the individual matrix entries. * Such an assumption is quite * See also [19][20][21][22] for alternative approaches to natural mass matrices.…”