Investigating texture six zero lepton mass matrices

Abstract

Texture six zero Fritzsch like as well as non Fritzsch like hermitian lepton mass matrices (144 combinations in all) have been investigated for both Majorana and Dirac neutrinos for their compatibility with the current neutrino oscillation data, keeping in mind the hierarchy of neutrino masses. All the combinations considered here for Majorana neutrino masses are ruled out by the existing data in the case of inverted hierarchy and degenerate scenario. For Majorana neutrinos with normal hierarchy, only 16 combinations can accommodate the experimental data. Assuming neutrinos to be Dirac particles, normal hierarchy, inverted hierarchy as well as degenerate neutrinos are ruled out for all combinations of texture 6 zero hermitian mass matrices. §1. IntroductionThe large value of θ 13 determined by the reactor neutrino experiments 1) has not only thrown open the door for search of CP violation in the lepton sector, but has also provided impetus to formulate the theories for understanding the origin of neutrino masses and their mixing. Apart from the recent θ 13 measurement, there also has been considerable progress in the measurement of neutrino mass square differences and mixing angles θ 12 and θ 23 in the last few years. However, not much information is available about the leptonic CP violation phase δ l from the neutrino oscillation data. Also, the absolute neutrino mass scale is still unknown. Further, the presently available neutrino oscillation data does not throw any light on the neutrino mass hierarchy, which may be normal/inverted hierarchy and may even be degenerate. Furthermore, the situation becomes complicated when one realizes that neutrino masses are much smaller than charged fermion masses as well as it is yet not clear whether neutrinos are Dirac or Majorana particles.In the absence of a convincing fermion flavor theory, several approaches have been considered to understand fermion mass generation problem, e.g., texture zeros, 2) seesaw mechanism, 3) radiative mechanisms, 4) flavor symmetries, 5) extra dimensions, 6) etc.. In this context, texture specific mass matrices have received a good deal of attention in the literature, in particular, Fritzsch-like texture specific mass matrices seem to be very helpful in understanding the pattern of quark mixings and CP violation. 7)-9) Taking clues from the success of these matrices in the context of quarks, several attempts have been made to consider texture specific lepton mass matrices 10)-14) for explaining the pattern of neutrino masses and mixings. In the absence of a sufficient amount of data regarding neutrino masses and mixings, it would require a very careful scrutiny of all possible textures to find viable structures, which are compatible with data and theoretical ideas, so that these are kept in mind while formulating mass matrices at the grand unified theory (GUT) scale.In the quark sector, both Fritzsch like as well as non Fritzsch like texture six zero mass matrices have been completely ruled out. 9) In leptonic sector, most of the analyses hav...

Generic lepton mass matrices and neutrino oscillations

“…which are in good agreement with recent analyses by several authors [7,10,16,22]. These neutrino masses are stable to the radiative corrections introduced by the renormalization group equations [23] when the lepton mass matrices are energy rescaled.…”

“…Among these, the "texture zero" ansatz initiated by Weinberg and Fritzsch [6] has been quite successful in explaining the fermion masses and flavor mixing patterns. As a result, several texture zero possibilities of lepton mass matrices have been investigated in the literature [7].…”

“…Among the several possibilities of texture specific lepton mass matrices, the Hermitian Fritzsch-type lepton mass matrices involving six [7,10] texture zeros have been exhaustively studied due to a lesser number of parameters involved in these matrices. Such matrices were recently revisited by Fukugita et al (FSTY) [10].…”

A complete survey of texture zeros in the lepton mass matrices

“…If neutrinos are Dirac particles, then one has more freedom for texture zeros in the corresponding mass matrix M D [27] because M D is an arbitrary complex 3 × 3 matrix, in contrast to M L which has to be symmetric. As for cases with M ℓ non-diagonal, studies are usually confined to instances where both the charged-lepton and the neutrino mass matrix have a Fritzsch-like texture [28,29] or extensions of it-see [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44] and references therein. In general, one can define "parallel textures" as those where M ℓ and M L or M D have the same texture [45,46].…”