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The neutrino sector offers one of the most sensitive probes of new physics beyond the Standard Model of Particle Physics (SM). The mechanism of neutrino mass generation is still unknown. The observed suppression of neutrino masses hints at a large scale, conceivably of the order of the scale of a rand unified theory (GUT), which is a unique feature of neutrinos that is not shared by the charged fermions. The origin of neutrino masses and mixing is part of the outstanding puzzle of fermion masses and mixings, which is not explained ab initio in the SM. Flavor model building for both quark and lepton sectors is important in order to gain a better understanding of the origin of the structure of mass hierarchy and flavor mixing, which constitute the dominant fraction of the SM parameters. Recent activities in neutrino flavor model building based on non-Abelian discrete flavor symmetries and modular flavor symmetries have been shown to be a promising direction to explore. The emerging models provide a framework that has a significantly reduced number of undetermined parameters in the flavor sector. In addition, such a framework affords a novel origin of C P violation from group theory due to the intimate connection between physical C P transformation and group theoretical properties of non-Abelian discrete groups. Model building based on non-Abelian discrete flavor symmetries and their modular variants enables the particle physics community to interpret the current and anticipated upcoming data from neutrino experiments. Non-Abelian discrete flavor symmetries and their modular variants can result from compactification of a higher-dimensional theory. Pursuit of flavor model building based on such frameworks thus also provides the connection to possible UV completions: in particular, to string theory. We emphasize the importance of constructing models in which the uncertainties of theoretical predictions are smaller than, or at most compatible with, the error bars of measurements in neutrino experiments. While there exist proof-of-principle versions of bottom-up models in which the theoretical uncertainties are under control, it is remarkable that the key ingredients of such constructions were discovered first in top-down model building. We outline how a successful unification of bottom-up and top-down ideas and techniques may guide us towards a new era of precision flavor model building in which future experimental results can give us crucial insights into the UV completion of the SM. [ABSTRACT FROM AUTHOR]

The fermion flavor structure is investigated by bilinear decomposition of the mass matrix after EW symmetry breaking, and the roles of factorized matrices in flavor mixing and mass generation are explored. On a new Yukawa basis, the minimal parameterization of flavor mixing is realized containing two relative phases and two free SO (2) L rotation angles. It is shown that flavor mixing can be addressed from four independent parameters. The validity of the flavor mixing structure is checked in both the lepton and quark sectors. Under the decomposition of flavor mixing, fermion mass matrices are reconstructed in the hierarchy limit. A flat mass matrix with all elements equal to 1 arises naturally from the requirement that homology exists between up-type and down-type fermion mass matrices. Some hints of a flat matrix and flavor breaking are also discussed. [ABSTRACT FROM AUTHOR]

The neutrino sector offers one of the most sensitive probes of new physics beyond the Standard Model of Particle Physics (SM). The mechanism of neutrino mass generation is still unknown. The observed suppression of neutrino masses hints at a large scale, conceivably of the order of the scale of a rand unified theory (GUT), which is a unique feature of neutrinos that is not shared by the charged fermions. The origin of neutrino masses and mixing is part of the outstanding puzzle of fermion masses and mixings, which is not explained ab initio in the SM. Flavor model building for both quark and lepton sectors is important in order to gain a better understanding of the origin of the structure of mass hierarchy and flavor mixing, which constitute the dominant fraction of the SM parameters. Recent activities in neutrino flavor model building based on non-Abelian discrete flavor symmetries and modular flavor symmetries have been shown to be a promising direction to explore. The emerging models provide a framework that has a significantly reduced number of undetermined parameters in the flavor sector. In addition, such a framework affords a novel origin of CP violation from group theory due to the intimate connection between physical CP transformation and group theoretical properties of non-Abelian discrete groups. Model building based on non-Abelian discrete flavor symmetries and their modular variants enables the particle physics community to interpret the current and anticipated upcoming data from neutrino experiments. Non-Abelian discrete flavor symmetries and their modular variants can result from compactification of a higher-dimensional theory. Pursuit of flavor model building based on such frameworks thus also provides the connection to possible UV completions: in particular, to string theory. We emphasize the importance of constructing models in which the uncertainties of theoretical predictions are smaller than, or at most compatible with, the error bars of measurements in neutrino experiments. While there exist proof-of-principle versions of bottom-up models in which the theoretical uncertainties are under control, it is remarkable that the key ingredients of such constructions were discovered first in top-down model building. We outline how a successful unification of bottom-up and top-down ideas and techniques may guide us towards a new era of precision flavor model building in which future experimental results can give us crucial insights into the UV completion of the SM.

Neutrino oscillation phenomenology is briefly reviewed, and the impact of the late Professor Masatoshi Koshiba on research on the neutrino oscillation is discussed from the viewpoint of phenomenology. [ABSTRACT FROM AUTHOR]

The observed pattern of fermion masses and mixing is an outstanding puzzle in particle physics, generally known as the flavor problem. Over the years, guided by precision neutrino oscillation data, discrete flavor symmetries have often been used to explain the neutrino mixing parameters, which look very different from the quark sector. In this review, we discuss the application of non-Abelian finite groups to the theory of neutrino masses and mixing in the light of current and future neutrino oscillation data. We start with an overview of the neutrino mixing parameters, comparing different global fit results and limits on normal and inverted neutrino mass ordering schemes. Then, we discuss a general framework for implementing discrete family symmetries to explain neutrino masses and mixing. We discuss CP violation effects, giving an update of CP predictions for trimaximal models with nonzero reactor mixing angle and models with partial μ − τ reflection symmetry, and constraining models with neutrino mass sum rules. The connection between texture zeros and discrete symmetries is also discussed. We summarize viable higher-order groups, which can explain the observed pattern of lepton mixing where the non-zero θ 13 plays an important role. We also review the prospects of embedding finite discrete symmetries in the Grand Unified Theories and with extended Higgs fields. Models based on modular symmetry are also briefly discussed. A major part of the review is dedicated to the phenomenology of flavor symmetries and possible signatures in the current and future experiments at the intensity, energy, and cosmic frontiers. In this context, we discuss flavor symmetry implications for neutrinoless double beta decay, collider signals, leptogenesis, dark matter, as well as gravitational waves. [ABSTRACT FROM AUTHOR]

The flavor mixing of the quarks is described by the CKM matrix, which is parametrized by three mixing angles and one phase parameter. We discuss a new texture for the two mass matrices of the six quarks. The three flavor mixing angles can be calculated — they are functions of the ratios of the quark masses. The third mixing angle is given by the CKM matrix element | V c b |. We find: | V c b | ≃ 2 (m s / m b). The calculated mixing angles agree with the mixing angles, measured in many experiments. [ABSTRACT FROM AUTHOR]

To obtain the equation of state of quark matter and construct hybrid stars, we calculate the thermodynamic potential in the three-flavor Nambu–Jona-Lasinio model including the tensor-type four-point interaction and the Kobayashi–Maskawa–'t Hooft interaction. To construct the hybrid stars, it is necessary to impose the β equilibrium and charge neutrality conditions on the system. It is shown that tensor condensed phases appear at large chemical potential. Under the possibility of the existence of the tensor condensates, the relationship between the radius and mass of hybrid stars is estimated. [ABSTRACT FROM AUTHOR]

The possible formation of tensor condensates originated from a tensor-type interaction between quarks is investigated in the three-flavor Nambu–Jona–Lasinio model including the Kobayashi–Maskawa–'t Hooft interaction, which leads to flavor mixing. It is shown that independent two tensor condensates appear and a tensor condensate related to the strange quark easily occurs by the effect of the flavor mixing compared with one related to light quarks. Also, it is shown that the tensor condensate related to the strange quark appears at a slightly smaller chemical potential if the Kobayashi–Maskawa–'t Hooft interaction is included, due to the flavor mixing effect. It is also shown that the two kinds of tensor condensates may coexist in a certain quark chemical potential due to the flavor mixing. [ABSTRACT FROM AUTHOR]

Most of the free parameters in the Standard Model (SM) — a quantum field theory which has successfully elucidated the behaviors of strong, weak and electromagnetic interactions of all the known fundamental particles, come from the lepton and quark flavors. The discovery of neutrino oscillations has proved that the SM is incomplete, at least in its lepton sector; and thus the door of opportunity is opened to exploring new physics beyond the SM and solving a number of flavor puzzles. In this review article we give an overview of important progress made in understanding the mass spectra, flavor mixing patterns, CP-violating effects and underlying flavor structures of charged leptons, neutrinos and quarks in the past twenty years. After introducing the standard pictures of fermion mass generation, flavor mixing and CP violation in the SM extended with the presence of massive Dirac or Majorana neutrinos, we briefly summarize current experimental knowledge about the flavor parameters of quarks and leptons. Various ways of describing flavor mixing and CP violation are discussed, the renormalization-group evolution of flavor parameters is illuminated, and the matter effects on neutrino oscillations are interpreted. Taking account of possible extra neutrino species, we propose a standard parametrization of the 6 × 6 flavor mixing matrix and comment on the phenomenological aspects of heavy, keV-scale and light sterile neutrinos. We pay particular attention to those novel and essentially model-independent ideas or approaches regarding how to determine the Yukawa textures of Dirac fermions and the effective mass matrix of Majorana neutrinos, including simple discrete and continuous flavor symmetries. An outlook to the future development in unraveling the mysteries of flavor structures is also given. [ABSTRACT FROM AUTHOR]

We discuss the mass matrices with texture zeros for the quarks and leptons. The flavor mixing angles for the quarks are functions of the quark masses and can be calculated. The results agree with the experimental data. The texture zero mass matrices for the leptons and the see-saw mechanism are used to derive relations between the matrix elements of the lepton mixing matrix and the ratios of the neutrino masses. Using the measured neutrino mass differences, the neutrino masses can be calculated. The neutrinoless double beta decay is discussed. The effective Majorana neutrino mass, describing the neutrinoless double beta decay, can be calculated—it is about 4.6 meV. The present experimental limit is at least twenty times larger.

In the light of several recent analyses pointing toward texture 4-zero Fritzsch-like quark mass matrices as the only viable structures for quark mass matrices, this work adopts a model independent approach to reconstruct an alternate and simplified structure of texture specific quark mass matrices in a generalized '-diagonal' basis within the Standard Model framework using the unitarity of CKM matrix and the observed hierarchies in quark mass spectra and mixing angles. It is observed that the measured values of the three physical parameters namely , and naturally lead to the vanishing of (11) element in the down type quark mass matrix and that the single measurable CP violating phase in the CKM matrix is sufficient enough in to explain the observed mixing pattern in a suitable basis. The leading order as well as exact analytic phenomenological solutions are addressed for the modest pattern of quark mass matrices derived from CKM matrix and precision measurements of mixing parameters. [ABSTRACT FROM AUTHOR]

The observed pattern of lepton flavor mixing and CP violation strongly indicates the possible existence of a simple flavor symmetry in the neutrino sector-the effective Majorana neutrino mass term keeps invariant when the three left-handed neutrino fields transform asνeL→(νeL)c,νμL→(ντL)candντL→(νμL)c. A direct application of such a µ - τ reflection symmetry to the canonical seesaw mechanism can help a lot to constrain the flavor textures of active and sterile Majorana neutrinos. The present article is intended to summarize the latest progress made in exploring the properties of this minimal flavor symmetry, its translational and rotational extensions, its soft breaking effects via radiative corrections from a superhigh energy scale to the electroweak scale, and its various phenomenological implications., (© 2023 IOP Publishing Ltd.)

In this review, we present a derivation of the on-shell renormalization conditions for scalar and fermionic fields in theories with and without parity conservation. We also discuss the specifics of Majorana fermions. Our approach only assumes a canonical form for the renormalized propagators and exploits the fact that the inverse propagators are nonsingular in , where is the external four-momentum and is a pole mass. In this way, we obtain full agreement with commonly used on-shell conditions. We also discuss how they are implemented in renormalization. [ABSTRACT FROM AUTHOR]

In this paper, we propose a simple model based on the S3 flavor symmetry, in which a perturbation ansatz is suggested that the flavor symmetry is explicitly broken down via S3 Z2 in the up-quark sector and via S3 Z3 in the down-quark sector. Our model is successful in obtaining the strong hierarchy of mass matrices of both up-type quarks and down-type quarks, but unsuccessful in obtaining the realistic mixing between the third generation and the first two, as in other models based on S3 flavor symmetry proposed in the literature. Through detailed analysis, we find the reason for the unsuccesses in our model which is related to the reducibility of the three-dimensional representation of the S3 group. We conclude that any perturbations in mass matrices preserving the partial symmetry of S3 cannot help getting realistic mixing between the third generation and first two without fine-tuning. [ABSTRACT FROM AUTHOR]

We discuss mass matrices with four texture zeros for the quarks and leptons. The three mixing angles for the quarks and leptons are functions of the fermion masses. The results agree with the experimental data. The ratio of the masses of the first two neutrinos is given by the solar mixing angle. The neutrino masses are calculated: , and . [ABSTRACT FROM AUTHOR]

The fact that quarks of the same electric charge possess a mass hierarchy is a big puzzle in particle physics, and it must be highly correlated with the hierarchy of quark flavor mixing. This chapter is intended to provide a brief description of some important issues regarding quark masses, flavor mixing and CP-violation. A comparison between the salient features of quark and lepton flavor mixing structures is also made. [ABSTRACT FROM AUTHOR]

Abstract: We investigate the idea that the double cover of the rotational icosahedral symmetry group is the family symmetry group in the quark sector. The icosahedral () group was previously proposed as a viable family symmetry group for the leptons. To incorporate the quarks, it is highly advantageous to extend the group to its double cover, as in the case of tetrahedral () symmetry. We provide the basic group theoretical tools for flavor model-building based on the binary icosahedral group and construct a model of the quark masses and mixings that yields many of the successful predictions of the well-known quark texture models. [Copyright &y& Elsevier]

Abstract: We show that non-Hermitian and nearest-neighbor-interacting perturbations to the Fritzsch textures of lepton and quark mass matrices can make both of them fit current experimental data very well. In particular, we obtain for the atmospheric neutrino mixing angle and predict to 6° for the smallest neutrino mixing angle when the perturbations in the lepton sector are at the 20% level. The same level of perturbations is required in the quark sector, where the Jarlskog invariant of CP violation is about . In comparison, the strength of leptonic CP violation is possible to reach about in neutrino oscillations. [Copyright &y& Elsevier]

Abstract: We propose a left–right symmetric model to simultaneously give natural inflation and flavor mixing from a Peccei–Quinn symmetry breaking at the Planck scale. Our model can be embedded into grand unification theories. [Copyright &y& Elsevier]

Abstract: We apply the discrete flavor symmetry to both lepton and quark sectors of the Standard Model extended by introducing one Higgs triplet and realizing the type-II seesaw mechanism for finite neutrino masses. The resultant mass matrices of charged leptons (), neutrinos (), up-type quarks () and down-type quarks () have a universal form consisting of two terms: one is proportional to the identity matrix I and the other is proportional to the democracy matrix D. We argue that the textures of , and are dominated by the D term, while that of is dominated by the I term. This hypothesis implies a near mass degeneracy of three neutrinos and can naturally explain why the mass matrices of charged fermions are strongly hierarchical, why the quark mixing matrix is close to I and why the lepton mixing matrix contains two large angles. We discuss a rather simple perturbation ansatz to break the symmetry and obtain more realistic mass spectra of leptons and quarks as well as their flavor mixing patterns. We stress that the I term, which used to be ignored from , and , is actually important because it can significantly modify the smallest lepton flavor mixing angle or three quark flavor mixing angles. [Copyright &y& Elsevier]

Abstract: If the ultrahigh-energy (UHE) cosmic neutrinos produced from a distant astrophysical source can be measured at a -size neutrino telescope such as the IceCube or KM3NeT, they will open a new window to understand the nature of flavor mixing and to probe possible new physics. Considering the conventional UHE cosmic neutrino source with the flavor ratio , I point out two sets of conditions for the flavor democracy to show up at neutrino telescopes: either and (CP invariance) or and (CP violation) in the standard parametrization of the neutrino mixing matrix V. Allowing for slight – symmetry breaking effects characterized by , I find as a good approximation. Another possibility to constrain is to detect the flux of via the Glashow resonance channel . I also give some brief comments on (1) possible non-unitarity of V in the seesaw framework and its effects on the flavor distribution at neutrino telescopes and (2) a generic description and determination of the cosmic neutrino flavor composition at distant astrophysical sources. [Copyright &y& Elsevier]

I give an overview of some basic properties of massive neutrinos. The first part of this talk is devoted to three fundamental questions about three known neutrinos and to their flavor issues — the mass spectrum, mixing pattern and CP violation. The second part of this talk is to highlight a few hot topics at the frontiers of neutrino physics and neutrino astrophysics, including the naturalness and testability of TeV seesaw mechanisms at the LHC, effects of nonstandard interactions on neutrino oscillations, flavor distributions of ultrahigh-energy cosmic neutrinos at neutrino telescopes, collective flavor oscillations of supernova neutrinos, flavor effects in thermal leptogenesis, the GSI anomaly and Mössbauer neutrino oscillations, and so on. I finally make some concluding remarks for the road ahead. [ABSTRACT FROM AUTHOR]

Abstract: We address the time-to-space conversion in quantum field theory of mixing. In the general theory of quantum field mixing (with an arbitrary number of mixed fields with either boson or fermion statistics) the mixing relations for flavor states are derived directly from the definition of mixing for quantum fields and the unitary inequivalence of the Fock space of energy- and flavor-eigenstates is found. The time dynamics of the interacting fields can be explicitly solved and the flavor time oscillation formulas can be derived in a general form. In this work, we analyze the conversion of these results to space-oscillations with a generalized method of wave-packets. Emphasizing the antiparticle content, we work entirely within the canonical formalism of creation and annihilation operators that allows us to include the effect due to the nontrivial flavor vacuum. [Copyright &y& Elsevier]

Abstract: After making brief comments on the Kamioka–Korea two-detector setting, I delivered a pedagogical seminar on perturbation theory of neutrino oscillations with and without nonstandard interactions. I also described a general property of neutrino flavor transformation of such a system which includes useful relationships between S matrix elements and a phase reduction theorem. [Copyright &y& Elsevier]

Given its briefness and predictability, the minimal seesaw-a simplified version of the canonical seesaw mechanism with only two right-handed neutrino fields-has been studied in depth and from many perspectives, and now it is being pushed close to a position of directly facing experimental tests. This article is intended to provide an up-to-date review of various phenomenological aspects of the minimal seesaw and its associated leptogenesis mechanism in neutrino physics and cosmology. Our focus is on possible flavor structures of such benchmark seesaw and leptogenesis scenarios and confronting their predictions with current neutrino oscillation data and cosmological observations. In this connection particular attention will be paid to the topics of lepton number violation, lepton flavor violation, discrete flavor symmetries, CP violation and antimatter of the Universe., (© 2021 IOP Publishing Ltd.)

Este trabalho é uma introdução ao modelo da oscilação de neutrinos para estudantes de física. Apresentamos o modelo de mistura de neutrinos baseado no conceito de superposição de estados. Em particular, consideraremos o caso onde os neutrinos se propagam exclusivamente no vácuo. A hipótese de mistura entre os sabores de neutrinos leva à oscilação de sabor induzida por diferença de massa, ou simplesmente oscilação de sabor. Neste processo o neutrino é convertido sucessivamente entre os três sabores possíveis durante o trajeto entre sua fonte e o detector. Pretende-se que este fenômeno seja capaz de solucionar o aparente desaparecimento dos neutrinos provenientes do Sol, conhecido como o problema do neutrino solar. Por motivos didáticos, consideramos apenas o caso de mistura entre dois sabores (um deles é uma mistura de outros dois) e derivamos assim a probabilidade de um neutrino do tipo eletrônico ''sobreviver" em seu trajeto até a Terra. Uma simples verificação nos revela que o modelo não é capaz de explicar os dados do experimento Super-Kamiokande (um dos principais relacionado aos neutrinos solares) mas que por outro lado é capaz de explicar o desaparecimento de neutrinos provenientes dos reatores nucleares localizados no Japão e observados pelo experimento de KamLAND. Como a diferença entre os dois casos é a existência da densa matéria solar, no primeiro caso, segue-se que um modelo satisfatório deve levar em consideração a interação do neutrino com a matéria para uma proposta completa de solução ao problema do neutrino solar.

Abstract: We study a model for the mass matrices of the leptons, based on texture zero elements. We are able to relate the mass eigenvalues of the charged leptons and of the neutrinos to the mixing angles, and can predict the masses of the neutrinos. We find a normal hierarchy—the masses are 0.005 eV, 0.01 eV and 0.05 eV. Predictions for the double beta decay and the reactor neutrino experiments are made. [Copyright &y& Elsevier]