Within the standard three-neutrino framework, the absolute neutrino masses and their ordering (either normal, NO, or inverted, IO) are currently unknown. However, the combination of current data coming from oscillation experiments, neutrinoless double beta decay searches, and cosmological surveys, can provide interesting constraints for such unknowns in the sub-eV mass range, down to O(0.1) eV in some cases. We discuss current limits on absolute neutrino mass observables by performing a global data analysis, that includes the latest results from oscillation experiments, neutrinoless double beta decay bounds from the KamLAND-Zen experiment, and constraints from representative combinations of Planck measurements and other cosmological data sets. In general, NO appears to be somewhat favored with respect to IO at the level of ~2 sigma, mainly by neutrino oscillation data (especially atmospheric), corroborated by cosmological data in some cases. Detailed constraints are obtained via the chi^2 method, by expanding the parameter space either around separate minima in NO and IO, or around the absolute minimum in any ordering. Implications for upcoming oscillation and non-oscillation neutrino experiments, including beta-decay searches, are also discussed.
We revisit our previous work [Phys. Rev. D 95, 096014 (2017)] where neutrino oscillation and nonoscillation data were analyzed in the standard framework with three neutrino families, in order to constrain their absolute masses and to probe their ordering (either normal, NO, or inverted, IO). We include updated oscillation results to discuss best fits and allowed ranges for the two squared mass differences $δm^2$ and $Δm^2$, the three mixing angles $θ_{12}$, $θ_{23}$ and $θ_{13}$, as well as constraints on the CP-violating phase $δ$, plus significant indications in favor of NO vs IO at the leve…
Absolute neutrino masses provide a key to physics beyond the standard model. We discuss the impact of absolute neutrinos masses on physics beyond the standard model, the experimental possibilities to determine absolute neutrinos masses, and the intriguing connection with the Z-burst model for extreme-energy cosmic rays.
We discuss the possibility of using experiments timing the propagation of neutrino beams over large distances to help determine the absolute masses of the three neutrinos.
The phenomenology of absolute neutrino masses is reviewed, focusing on tritium beta decay, cosmological measurements and neutrinoless double-beta decay.
In the era of precision neutrino physics, we study the influence of matter NSI on the question of neutrino mass ordering and its resolution. At long baseline experiments, since matter effects play a crucial role in addressing this very important question, it is timely to investigate how sub-leading effects due to NSI may affect and drastically alter inferences pertaining to this question. We demonstrate that the sensitivity to mass ordering gets significantly impacted due to NSI effects for various long baseline experiments including the upcoming long baseline experiment, Deep Underground Neut…
We define the theoretical framework and deduce the conditions under which multi-messenger astronomy can provide useful information about neutrino masses and their ordering. The framework uses time differences between the arrival of neutrinos and the other light messenger, i.e. the graviton, emitted in astrophysical catastrophes. We also provide a preliminary feasibility study elucidating the experimental reach and challenges for planned neutrino detectors such as Hyper-Kamiokande as well as future several megaton detectors. This study shows that future experiments can be useful in testing inde…
The main aspects of the phenomenology of absolute neutrino masses are reviewed, focusing on the limits on neutrino masses obtained in tritium beta decay experiments, cosmological observations and neutrinoless double-beta decay experiments.
We quantify the extent to which future experiments will test the existence of neutrinoless double-beta decay mediated by light neutrinos with inverted-ordered masses. While it remains difficult to compare measurements performed with different isotopes, we find that future searches will fully test the inverted ordering scenario, as a global, multi-isotope endeavor. They will also test other possible mechanisms driving the decay, including a large uncharted region of the allowed parameter space assuming that neutrino masses follow the normal ordering.
The MiniBooNE and LSND experiments are compatible with each other when two sterile neutrinos are added to the three active ones. In this case there are eight possible mass orderings. In two of them both sterile neutrinos are heavier than the three active ones. In the next two scenarios both sterile neutrinos are lighter than the three active ones. The remaining four scenarios have one sterile neutrino heavier and another lighter than the three active ones. We analyze all scenarios with respect to their predictions for mass-related observables. These are the sum of neutrino masses as constraine…
We present a Bayesian analysis of the combination of current neutrino oscillation, neutrinoless double beta decay and CMB observations. Our major goal is to carefully investigate the possibility to single out one neutrino mass ordering, Normal Ordering or Inverted Ordering, with current data. Two possible parametrizations (three neutrino masses versus the lightest neutrino mass plus the two oscillation mass splittings) and priors (linear versus logarithmic) are examined. We find that the preference for NO is only driven by neutrino oscillation data. Moreover, the values of the Bayes factor ind…
The masses of the low-lying scalar mesons are investigated in the three-flavor Nambu Jona-Lasinio (NJL) model by treating the scalar mesons as composite objects of a quark and an antiquark. It is known that a simple $\bar qq$ picture fails to reproduce so-called inverse mass ordering for the scalar mesons. Recently a new mechanism to reproduce the observed mass spectrum of the scalar mesons was proposed in a linear sigma model by introducing flavor symmetry breaking induced by the U(1) axial anomaly. Motivated by this proposal, we examine whether this new mechanism works also in the NJL model.…
Various ways of determining the absolute neutrino masses are briefly reviewed and their sensitivities compared. The apparent tension between the announced but unconfirmed observation of the $0νββ$ decay and the neutrino mass upper limit based on observational cosmology is used as an example of what could happen eventually. The possibility of a ``nonstandard'' mechanism of the $0νββ$ decay is stressed and the ways of deciding which of the possible mechanisms is actually operational are described. The importance of the $0νββ$ nuclear matrix elements is discussed and their uncertainty estimated.
We point out that leptonic weak-basis invariants are an important tool for the study of the properties of lepton flavour models. In particular, we show that appropriately chosen invariants can give a clear indication of whether a particular lepton flavour model favours normal or inverted hierarchy for neutrino masses and what is the octant of $θ_{23}$. These invariants can be evaluated in any conveniently chosen weak-basis and can also be expressed in terms of neutrino masses, charged lepton masses, mixing angles and CP violation phases.
The atomic transition from an excited state $|{\rm e}\rangle$ to the ground state $|{\rm g}\rangle$ by emitting a neutrino pair and a photon, i.e., $|{\rm e}\rangle \to |{\rm g}\rangle + |γ\rangle + |ν^{}_i\rangle + |\barν^{}_j\rangle$ with $i, j = 1, 2, 3$, has been proposed by Yoshimura and his collaborators as an alternative way to determine the absolute scale $m^{}_0$ of neutrino masses. More recently, a statistical analysis of the fine structure of the photon spectrum from this atomic process has been performed [N. Song {\it et al.}, Phys.\ Rev.\ D {\bf 93}, 013020 (2016)] to quantitative…
In this followup to Phys. Rev. D 75, 053001 (2007) [arXiv:hep-ph/0608060] we report updated constraints on neutrino mass-mixing parameters, in light of recent neutrino oscillation data (KamLAND, SNO, and MINOS) and cosmological observations (WMAP 5-year and other data). We discuss their interplay with the final 0nu2beta decay results in 76-Ge claimed by part of the Heidelberg-Moscow Collaboration, using recent evaluations of the corresponding nuclear matrix elements, and their uncertainties. We also comment on the 0nu2beta limits in 130-Te recently set by Cuoricino, and on prospective limits o…
In the preprint arxiv:1703.03425 "strong evidence" for the normal neutrino mass ordering is claimed. The authors obtain Bayesian odds of 42:1 in favour of the normal ordering. Their conclusion is based on adopting a flat logarithmic prior for the three neutrino masses. Such an assumption favours a hierarchical spectrum for the masses, which is much easier to accommodate for the normal mass ordering, and hence their prior assumption makes the inverted ordering much less likely a priori. We argue that the claimed "evidence" for normal ordering is almost entirely driven by the adopted prior and n…
We derive the effective Lagrangian for the low-energy massive meson excitations of the color-flavor-locking (CFL) phase of QCD with 3 flavors of light quarks. We compute the decay constants, the maximum velocities, and the masses of the mesons at large baryon chemical potential mu. The decay constants are linear in mu. The meson maximum velocities are close to that of sound. The meson masses in the CFL phase are significantly smaller than in the normal QCD vacuum and depend only on bare quark masses. The order of the meson masses is, to some extent, reversed compared to that in the QCD vacuum.…
The neutrino oscillations probabilities depend on mass squared differences; in the case of 3-neutrino mixing, there are two independent differences, which have been measured experimentally. In order to calculate the absolute masses of neutrinos, we have conjectured a third relation, in the form of a sum of squared masses. The calculated masses look plausible and are in good agreement with the upper bounds coming from astrophysics.
We apply Bayesian methods to study the sensitivity to neutrino masses of a Galactic supernova neutrino signal. Our procedure makes use of the full statistics of events and is remarkably independent of astrophysical assumptions. Present detectors can reach a sensitivity down to $m_ν\sim 1$ eV. Future megaton detectors can yield up to a factor of two improvement; however, they will not be competitive with the next generation of tritium $β$-decay and neutrinoless double $β$-decay experiments.
We investigate constraints on neutrino mass ordering and degeneracy by considering the first cosmological result based on Planck measurements of the cosmic microwave background. It is shown that the result at 95% CL rejects a neutrino mass degeneracy larger than 85% (82.5%) for the normal (inverted) hierarchical case. We can also find some regions where the neutrino mass ordering will be able to be distinguished by combining a value of sum of the neutrino masses with an effective neutrino mass determined by neutrino-less double beta decay experiments.
Ultrahigh energy neutrinos (UHEν) scatter on relic neutrinos (Rν) producing Z bosons, which can decay hadronically producing protons (Z-burst). We compare the predicted proton spectrum with the observed ultrahigh energy cosmic ray (UHECR) spectrum and determine the mass of the heaviest Rνvia a maximum likelihood analysis. Our prediction depends on the origin of the power-like part of the UHECR spectrum: m_ν=2.75^{+1.28}_{-0.97} eV for Galactic halo and 0.26^{+0.20}_{-0.14} eV for extragalactic (EG) origin. The necessary UHEνflux should be detected in the near future.
The determination of absolute neutrino masses is crucial for the understanding of theories underlying the standard model, such as SUSY. We review the experimental prospects to determine absolute neutrino masses and the correlations among approaches, using the Delta m^2's inferred from neutrino oscillation experiments and assuming a three neutrino Universe.
Using data from atmospheric neutrino mixing, and a simple functional form for mixing angles, the absolute values of three neutrino masses are calculated: $m_3\cong 5.37\times 10^{-2} eV$, $m_2\cong 1.94\times 10^{-2} eV$, $m_1\cong 1.46\times 10^{-2} eV$. The quantities relevant for solar neutrino mixing are calculated: $(m_2^2-m_1^2) \cong 1.63\times 10^{-4} eV^2$, with non-maximal mixing $\tan^2θ_\sol \cong 0.56$. The analysis gives a suggestion of a dynamical origin for the empirical, large CP-violating phase associated with an intrinsically, very small mixing angle in the quark sector.
After a short review of the current status of three-neutrino mixing, the implications for the values of neutrino masses are discussed. The bounds on the absolute scale of neutrino masses from Tritium beta-decay and cosmological data are reviewed. Finally, we discuss the implications of three-neutrino mixing for neutrinoless double-beta decay.
We propose a simple method to quantify a possible exclusion of the inverted neutrino mass ordering from cosmological bounds on the sum of the neutrino masses. The method is based on Bayesian inference and allows for a calculation of the posterior odds of normal versus inverted ordering. We apply the method for a specific set of current data from Planck CMB data and large-scale structure surveys, providing an upper bound on the sum of neutrino masses of 0.14 eV at 95% CL. With this analysis we obtain posterior odds for normal versus inverted ordering of about 2:1. If cosmological data is combin…
It is found that the seesaw mechanism not only explain the smallness of neutrino masses but also account for the large mixing angles simultaneously, even if the unification of the neutrino Dirac mass matrix with that of up-type quark sector is realized. We show that provided the Majorana masses have hierarchical structure as is seen in the up-type quark sector and all mass matrices are real, we can reduce the information about the absolute values of neutrino masses through the data set of neutrino experiments. Especially for $θ_{13}=0$, we found that the neutrino masses are decided as $m_1:m_2…
Compelling evidences in favor of neutrino masses and mixing obtained in the last years in Super-Kamiokande, SNO, KamLAND and other neutrino experiments made the physics of massive and mixed neutrinos a frontier field of research in particle physics and astrophysics. There are many open problems in this new field. In this review we consider the problem of the absolute values of neutrino masses, which apparently is the most difficult one from the experimental point of view. We discuss the present limits and the future prospects of beta-decay neutrino mass measurements and neutrinoless double-bet…
With the KATRIN experiment, the determination of the absolute neutrino mass scale down to cosmologically favored values has come into reach. We show that this measurement provides the missing link between the Standard Model and the dark sector in scotogenic models, where the suppression of the neutrino masses is economically explained by their only indirect coupling to the Higgs field. We determine the linear relation between the electron neutrino mass and the scalar coupling $λ_5$ associated with the dark neutral scalar mass splitting to be $λ_5=3.1\times10^{-9}\ m_{ν_e}/$eV. This relation th…
We perform a global Bayesian analysis of currently available neutrino data, putting data from oscillation experiments, neutrinoless double beta decay ($0νββ$), and precision cosmology on an equal footing. We evaluate the discovery potential of future $0νββ$ experiments and the Bayes factor of the two possible neutrino mass ordering schemes for different prior choices. We show that the indication for normal ordering is still very mild and does not strongly depend on realistic prior assumptions or different combinations of cosmological data sets. We find a wide range for $0νββ$ discovery potenti…
A high-statistics measurement of the neutrinos from a galactic core-collapse supernova is extremely important for understanding the explosion mechanism, and studying the intrinsic properties of neutrinos themselves. In this paper, we explore the possibility to constrain the absolute scale of neutrino masses $m^{}_ν$ via the detection of galactic supernova neutrinos at the Jiangmen Underground Neutrino Observatory (JUNO) with a 20 kiloton liquid-scintillator detector. In assumption of a nearly-degenerate neutrino mass spectrum and a normal mass ordering, the upper bound on the absolute neutrino…
We investigate what could be learned about the absolute scale of neutrino masses from comparisons among the patterns within quark and lepton mass hierarchies. First, we observe that the existing information on neutrino masses fits quite well to the unexplained, but apparently present regularities in the quark and charged lepton sectors. Second, we discuss several possible mass patterns, pointing out that this quite generally leads towards hierarchical neutrino mass patterns especially disfavoring the vacuum solution.
We present new constraints on the neutrino Majorana masses from the current data of neutrinoless double beta decay and neutrino flavour mixing. With the latest results of $0νββ$ progresses from various isotopes, including the recent calculations of the nuclear matrix elements, we find that the strongest constraint of the effective Majorana neutrino mass is from the $^{136}\rm{Xe}$ data of the EXO-200 and KamLAND-Zen collaborations. Further more, by combining the $0νββ$ experimental data with the neutrino mixing parameters from new analyses, we get the mass upper limits of neutrino mass eigenst…
A model for neutrino masses and mixing is devised appointing the see-saw mechanism. The proffered model is fabricated with a combination of Type -I and Type-II see-saw contributions of which the latter dominates. The scalars and the leptons in the model are assigned $A4$ charges conducive to obtain the mass matrices viable for the scheme. The Type -II see-saw mass matrix accommodates atmospheric mass splitting and maximal mixing in the atmospheric sector ($θ_{23}=π/4$). It is characterized by vanishing solar mass splitting and $θ_{13}$ whereas the third neutrino mixing angle is free to acquire…
The ordering of the neutrino masses is a crucial input for a deep understanding of flavor physics, and its determination may provide the key to establish the relationship among the lepton masses and mixings and their analogous properties in the quark sector. The extraction of the neutrino mass ordering is a data-driven field expected to evolve very rapidly in the next decade. In this review, we both analyze the present status and describe the physics of subsequent prospects. Firstly, the different current available tools to measure the neutrino mass ordering are described. Namely, reactor, lon…
We propose a Pati-Salam extension of the standard model incorporating a flavor symmetry based on the $Δ\left( 27\right)$ group. The theory realizes a realistic Froggatt-Nielsen picture of quark mixing and a predictive pattern of neutrino oscillations. We find that, for normal neutrino mass ordering, the atmospheric angle must lie in the higher octant, CP must be violated in oscillations, and there is a lower bound for the $0νββ$ decay rate. For the case of inverted mass ordering, we find that the lower atmospheric octant is preferred, and that CP can be conserved in oscillations. Neutrino mass…
Determining the absolute masses of neutrinos is of fundamental importance in particle physics, nuclear physics, and astrophysics. We conjecture that intrinsic mass relations exist between leptons and quarks. Using these relations and neutrino oscillation data, we show that the inverted neutrino mass hierarchy is strongly disfavored and estimate the absolute neutrino masses to be m_{1}=0.21^{+1.70}_{-0.21} \times 10^{-4} {eV}, m_{2}=(8.7 \pm 0.1) \times 10^{-3} {eV}, and m_{3}=(4.9 \pm 0.1) \times 10^{-2} {eV}.
The evidence for non-vanishing neutrino masses from solar and atmospheric neutrinos provides the first solid hint towards physics beyond the standard model. A full reconstruction of the neutrino spectrum may well provide a key to the theoretical structures underlying the standard model such as supersymmetry, grand unification or extra space dimensions. In this article we discuss the impact of absolute neutrinos masses on physics beyond the standard model. We review the information obtained from neutrino oscillation data and discuss the prospects of the crucial determination of the absolute neu…
In the light of recent neutrino oscillation and non-oscillation data, we revisit the phenomenological constraints applicable to three observables sensitive to absolute neutrino masses: The effective neutrino mass in single beta decay (m_beta); the effective Majorana neutrino mass in neutrinoless double beta decay (m_2beta); and the sum of neutrino masses in cosmology (Sigma). In particular, we include the constraints coming from the first Main Injector Neutrino Oscillation Search (MINOS) data and from the Wilkinson Microwave Anisotropy Probe (WMAP) three-year (3y) data, as well as other releva…
The effects of CP-phases on the three absolute quasi-degenerate Majorana neutrino (QDN) masses are stud-ied with neutrino mass matrices obeying μ - τ symmetry for normal as well as inverted hierarchical mass patterns. We have made further investigations on 1) the prediction of solar mixing angle which lies below tri-bimaximal mixing value in consistent with neutrino oscillation observational data, 2) the prediction on absolute neutrino mass parameter (mee) in 0νββ decay, and 3) cosmological bound on the sum of the three absolute neutrino masses. The numerical analysis is carried out through th…
Whether the neutrino mass ordering is normal or inverted remains an experimentally open issue in neutrino physics. The knowledge of neutrino mass ordering has great importance for neutrinoless double-beta ($ 0νββ$) decay experiments, which can establish the nature of massive neutrinos, i.e., whether they are Dirac or Majorana fermions. Recently, the KamLAND-Zen 800 measurement has reached for the first time the parameter space of the inverted ordering with a vanishing lightest neutrino mass. By assuming the inverted ordering, we attempt to derive the physical information of the neutrino nature…
Whether the neutrino mass spectrum is normal (m_1 < m_2 < m_3) or abnormal (m_3 < m_1 < m_2) remains an open question, but we show that the latter possibility looks quite unnatural when it is related to the lepton flavor mixing matrix U in a way similar to the reasonable correlation between the quark mass spectrum and the quark flavor mixing matrix. Taking into account the freedom in choosing the basis of weak interactions, we make a novel prediction for |U_{tau 1}|/|U_{tau 2}| in terms of the three neutrino masses in the large tau mass limit. This result is testable, and it implies that the n…
We present an $A4$-based model where neutrino masses arise from a combination of see-saw mechanisms. The model is motivated by several small mixing and mass parameters indicated by the data. These are $θ_{13}$, the solar mass splitting, and the small deviation of $θ_{23}$ from maximal mixing (= $π/4$). We take the above as indications that at some level the small quantities are well-approximated by zero. In particular the mixing angles, to a zero order, should be either 0 or $π/4$. Accordingly, in this model the Type-II see-saw dominates and generates the larger atmospheric mass splitting and …
In this thesis, I describe a number of recent important developments in neutrino cosmology on three fronts. Firstly, focusing on Large-Scale Structure (LSS) data, I will show that current cosmological probes contain a wealth of information on the sum of the neutrino masses. I report on the analysis leading to the currently best upper limit on the sum of the neutrino masses of $0.12\,{\rm eV}$. I show how cosmological data exhibits a weak preference for the normal neutrino mass ordering because of parameter space volume effects, and propose a simple method to quantify this preference. Secondly,…
In the context of three-flavor neutrino mixing, we present a thorough study of the phenomenological constraints applicable to three observables sensitive to absolute neutrino masses: The effective neutrino mass in Tritium beta decay (m_beta); the effective Majorana neutrino mass in neutrinoless double beta decay (m_2beta); and the sum of neutrino masses in cosmology (Sigma). We discuss the correlations among these variables which arise from the combination of all the available neutrino oscillation data, in both normal and inverse neutrino mass hierarchy. We set upper limits on m_beta by combin…
We have built a renormalizable $U(1)_X$ model with a $Σ(18)\times Z_4$ symmetry, whose spontaneous breaking yields the observed SM fermion masses and fermionic mixing parameters. The tiny masses of the light active neutrinos are produced by the type I seesaw mechanism mediated by very heavy right handed Majorana neutrinos. To the best of our knowledge, this model is the first implementation of the $Σ(18)$ flavor symmetry in a renormalizable $U(1)_X$ model. Our model allows a successful fit for the SM fermion masses, fermionic mixing angles and CP phases for both quark and lepton sectors. The o…
There is still a problem in neutrino physics related to the configuration of neutrino masses: Are neutrinos arranged by masses following the Standard Model as three generations of fundamental particles, Gen III>Gen II>Gen I, thus forming a structural-normal hierarchy, or deviate from that principle? The biggest obstacle that is still present is the sign of the absolute value of the difference of the square of neutrino masses. It was avoided by applying the theory of neutrino oscillation probability for each structure of the neutrino mass hierarchy. With such a theoretical approach the equation…
Recently, several reactor oscillation experiments have successively measured a nonzero value for the neutrino mixing angle ${θ_{13}}$, which is greater than 5 standard deviations. Within framework of the $μ$ from $ν$ Supersymmetric Standard Model ($μν$SSM), three tiny neutrino masses are generated at the tree level through TeV scale seesaw mechanism. In this work, we analyze the neutrino masses and mixing in the $μν$SSM with a "top down" method, assuming neutrino mass spectrum with normal ordering (NO) or inverted ordering (IO).
We show that successful strong thermal leptogenesis, where the final asymmetry is independent of the initial conditions and in particular a large pre-existing asymmetry is efficiently washed-out, favours values of the lightest neutrino mass $m_1 \gtrsim 10\,{\rm meV}$ for normal ordering (NO) and $m_1 \gtrsim 3\,{\rm meV}$ for inverted ordering (IO) for models with orthogonal matrix entries respecting $|Ω_{ij}^2| \lesssim 2$. . We show analytically why lower values of $m_1$ require a high level of fine tuning in the seesaw formula and/or in the flavoured decay parameters (in the electronic for…
One of the few remaining unknowns in the standard three-flavor neutrino oscillation paradigm is the ordering of neutrino masses. In this work we propose a novel method for determining neutrino mass ordering using the time information on early supernova neutrino events. In a core-collapse supernova, neutrinos are produced earlier than antineutrinos and, depending on the mass ordering which affects the adiabatic flavor evolution, may cause earlier observable signals in $ν_e$ detection channels than in others. Hence, the time differences are sensitive to the mass ordering. We find that using the …
The extraction of the neutrino mass ordering is one of the major challenges in particle physics and cosmology, not only for its implications for a fundamental theory of mass generation in nature, but also for its decisive role in the scale of future neutrinoless double beta decay experimental searches. It has been recently claimed that current oscillation, beta decay and cosmological limits on the different observables describing the neutrino mass parameter space provide robust decisive Bayesian evidence in favor of the normal ordering of the neutrino mass spectrum [arXiv:2203.14247]. We furth…
Most of what is known about neutrino masses and mixings results from studies of oscillation phenomena. We focus on those neutrino properties that are not amenable to such studies: $Σ$, the sum of the absolute values of the neutrino masses; $m_β$, the effective mass of the electron neutrino; and $m_{ββ} $, the parameter governing neutrinoless double beta decay. Each of these is the subject of ongoing experimental or observational studies. Here we deduce constraints on these observables resulting from any one of six {\it ad hoc\} hypotheses that involve the three complex mass parameters $m_i$: (…
Texture zeroes in neutrino mass matrix $M_ν$ may give us hints about the symmetries involved in neutrino mass generation. We examine the viability of such texture zeroes in a model independent way through a bottom-up approach. Using constraints from the neutrino oscillation data, we develop an analytic framework that can identify these symmetries and quantify deviations from them. We analyze the textures of $M_ν$ as well as those of $M_M$, the mass matrix of heavy Majorana neutrinos in the context of Type-I seesaw. We point out how the viability of textures depends on the absolute neutrino mas…
