Texture zeros and weak basis transformations

Abstract

We investigate the physical meaning of some of the "texture zeros" which appear in most of the Ansätze on quark masses and mixings. It is shown that starting from arbitrary quark mass matrices and making a suitable weak basis transformation one can obtain some of these sets of zeros which therefore have no physical content. We then analyse the physical implications of a fourtexture zero Ansatz which is in agreement with all present experimental data.

Different kind of textures of Yukawa coupling matrices in the two Higgs doublet model type III

“…where J is the Jarlskog invariant given by J = ℑm (K us K cb K * ub K * cs ) [11,12]. This CP phase δ presents a discrepancy of about 30.54% with respect to the experimental value δ = 60.16…”

“…Furthermore, the Fukuyama-Nishiura ansatz is explored and a new type of ansatz which is controlling the FCNC processes in the top quark sector is proposed. It is worth to mention that phases are explicitly involved since the mass matrices are hermitic, and then they can be written always as M = PM P † , whereM is a real and symmetric matrix and P is a diagonal matrix which contains the phases [11]. For the three family case, a mass matrix ansatz proposed by Fritzsch has been widely discussed [1,10,14], it is…”

“…For example, quark mass matrix ansatze have been used in an analogous way in the leptonic sector, trying to get the lepton mixing matrix in order to explain the neutrino anomalies [9,14,15,16]. Also, new texture ansatze have been proposed motivated by more precise results on the elements of the quark mixing matrix [1,10,11,17]. Quark and lepton mass matrices have also been discussed in the context of the SO (10) Grand Unification theories [9].…”

Reply to “Comment on ‘Texture zeros and weak basis transformations in the quark sector of the standard model”’

“…Through WB transformations, Branco et al [1] show that is always possible to find, at most, three zeros in quark mass matrices with no physical meanings. But, this does not restrict the number of zeros can be found by applying the WB transformation to mass matrices, the case is that the model must be put into a physical context.…”

Lepton textures and neutrino oscillations

“…A particular texture structure is said to be texture n zero, if the sum of the number of diagonal zeros and half the number of the symmetrically placed off diagonal zeros is n. Interestingly in this approach, it becomes important to investigate when a set of texture zeros result only from the choice of a given basis and when these imply restrictions on fermion mass matrices. Recently 6,7 , it has been shown that some sets of texture zeros are physically insignificant since these can be obtained starting from arbitrary fermion mass matrices by making appropriate unitary transformations also called Weak Basis (WB) transformations. Such transformations allow one to obtain Hermitian fermion mass matrices involving a 'maximum' of three phenomenological texture zeros.…”