Large Lepton Mixing Research Articles

Leptonic CP violation from a vector-like lepton

Leptonic CP violation is yet to be confirmed as an additional source of CP violation in fundamental interactions. We study the case where leptonic CP violation is spontaneous and is induced by the mixing with a heavy charged vector-like lepton (VLL). We show that the non-decoupling of this VLL is linked with the presence of CP violation and its coupling with the SM leptons are partly fixed from the SM Yukawas. Due to the large leptonic mixing angles, these couplings are typically of the same order and there is no flavor preference. Strong but not definitive constraints come from charged lepton flavor violating processes because the VLL can decouple from one or two leptonic flavors in very special points of parameter space. These special points are very sensitive to the neutrino Majorana phases.

Fermion mass hierarchies, large lepton mixing and residual modular symmetries

In modular-invariant models of flavour, hierarchical fermion mass matrices may arise solely due to the proximity of the modulus τ to a point of residual symmetry. This mechanism does not require flavon fields, and modular weights are not analogous to Froggatt-Nielsen charges. Instead, we show that hierarchies depend on the decomposition of field representations under the residual symmetry group. We systematically go through the possible fermion field representation choices which may yield hierarchical structures in the vicinity of symmetric points, for the four smallest finite modular groups, isomorphic to S3, A4, S4, and A5, as well as for their double covers. We find a restricted set of pairs of representations for which the discussed mechanism may produce viable fermion (charged-lepton and quark) mass hierarchies. We present two lepton flavour models in which the charged-lepton mass hierarchies are naturally obtained, while lepton mixing is somewhat fine-tuned. After formulating the conditions for obtaining a viable lepton mixing matrix in the symmetric limit, we construct a model in which both the charged-lepton and neutrino sectors are free from fine-tuning.

Naturalising the third family hypercharge model for neutral current B{-}hbox {anomalies}

We consider a deformation of the Third Family Hypercharge Model, which arguably makes the model more natural. Additional non-zero charges of the spontaneously broken, family-dependent U(1)_F gauge symmetry are assigned to the second family leptons, and the third family leptons’ charges are deformed away from their hypercharges in such a way that the U(1)_F gauge symmetry remains anomaly-free. Second family U(1)_F lepton charges allow a Z^prime coupling to muons without having to assume large charged lepton mixing, which risks violating tight lepton flavour violation bounds. In this deformed version, only the bottom and top Yukawa couplings are generated at the renormalisable level, whereas the tauon Yukawa coupling is absent. The Z^prime mediates a beyond the Standard Model contribution to an effective ({bar{b}} s) (bar{mu }mu ) vertex in the combination C_9=-9C_{10} and is able to fit the apparent discrepancy between Standard Model predictions in flavour changing neutral-current B-meson decays and their measurements, whilst simultaneously avoiding current constraints from direct Z^prime searches and other measurements, when 0.8~text {TeV}< M_{Z^prime } < 12.5 ~text {TeV}.

Low scale left-right symmetry and naturally small neutrino mass

We consider the low scale (10-100 TeV) left-right symmetric model with “naturally” small neutrino masses generated through the inverse seesaw mechanism. The Dirac neutrino mass terms are taken to be similar to the masses of charged leptons and quarks in order to satisfy the quark-lepton similarity condition. The inverse seesaw implies the existence of fermion singlets S with Majorana mass terms as well as the “left” and “right” Higgs doublets. These doublets provide the portal for S and break the left-right symmetry. The inverse seesaw allows to realize a scenario in which the large lepton mixing originates from the Majorana mass matrix of S fields which has certain symmetry. The model contains heavy pseudo-Dirac fermions, formed by S and the right-handed neutrinos, which have masses in the 1 GeV-100 TeV range and can be searched for at current and various future colliders such as LHC, FCC-ee and FCC-hh as well as in SHiP and DUNE experiments. Their contribution to neutrinoless double beta decay is unobservable. The radiative corrections to the mass of the Higgs boson and the possibility for generating the baryon asymmetry of the Universe are discussed. Modification of the model with two singlets (SL and SR) per generation can provide a viable keV-scale dark matter candidate.

Non-unitary lepton mixing in an inverse seesaw and its impact on the physics potential of long-baseline experiments

In this paper, we consider the low energy scale inverse seesaw mechanism in which the observed neutrino mass and lepton mixing are explained by introducing right-handed neutrinos and the gauge-singlet fermions with experimentally testable energy scale. Moreover, the presence of such new fermions leads to unitarity violation in lepton mixing due to significantly large mixing between active neutrinos and the heavy fermions. In addition to this, such large lepton mixing also gives rise to potentially large lepton flavor violation, which allows one to constrain the non-unitarity parameters via lepton flavor violating decays (li → lj γ). We make use of these constraints on non-unitarity parameters and investigate their effects on the determination of current unknown oscillation parameters at long-baseline experiments. We find that non-unitarity parameters are sensitive to the NOνA experiment. However, it is observed that the NOνA experiment is not expected to improve the current knowledge of non-unitarity parameter η21. We also find that the sensitivities to current unknowns are deteriorated significantly in the presence of non-unitary lepton mixing and these sensitivities crucially depend upon the new CP-violating phase in the non-unitary mixing. Further, we find that the degeneracy resolution capability of the NOνA experiment is reduced in the presence of non-unitarity parameters. However, the synergy between the currently running experiments T2K and NOνA can improve the parameter degeneracy resolution and hence there is enhancement in the sensitivities of unknowns.

Neutrino mixing and masses in SO(10) GUTs with hidden sector and flavor symmetries

We consider the neutrino masses and mixing in the framework of SO(10) GUTs with hidden sector consisting of fermionic and bosonic SO(10) singlets and flavor symmetries. The framework allows to disentangle the CKM physics responsible for the CKM mixing and different mass hierarchies of quarks and leptons and the neutrino new physics which produces smallness of neutrino masses and large lepton mixing. The framework leads naturally to the relation U PMNS ∼ V CKM † U 0, where structure of U 0 is determined by the flavor symmetry. The key feature of the framework is that apart from the Dirac mass matrices m D , the portal mass matrix M D and the mass matrix of singlets M S are also involved in generation of the lepton mixing. This opens up new possibilities to realize the flavor symmetries and explain the data. Using A 4 × Z 4 as the flavor group, we systematically explore the flavor structures which can be obtained in this framework depending on field content and symmetry assignments. We formulate additional conditions which lead to U 0 ∼ U TBM or U BM. They include (i) equality (in general, proportionality) of the singlet flavons couplings, (ii) equality of their VEVs; (iii) correlation between VEVs of singlets and triplet, (iv) certain VEV alignment of flavon triplet(s). These features can follow from additional symmetries or be remnants of further unification. Phenomenologically viable schemes with minimal flavon content and minimal number of couplings are constructed.

Constrained flavor breaking

We explore predictive flavor models based on subgroups of the standard-model $SU(3)^5$ flavor symmetry. Restricting to products of $SU(3)$, we find that a global $SU(3)^3$ flavor symmetry, broken only by two Yukawa spurions, leads to a relation among down-type quark, up-type quark and charged-lepton Yukawa matrices: $Y_d \propto Y_u Y_e^\dagger$. As a result, the charged-lepton mass ratios are expressed in terms of quark mass ratios and mixing angles. Large leptonic mixing angles appear to be natural and lead to contributions to flavor-changing neutral currents in the charged-lepton sector, which can be tested in future precision experiments.

The double mass hierarchy pattern: Simultaneously understanding quark and lepton mixing

The charged fermion masses of the three generations exhibit the two strong hierarchies m3≫m2≫m1. We assume that also neutrino masses satisfy mν3>mν2>mν1 and derive the consequences of the hierarchical spectra on the fermionic mixing patterns. The quark and lepton mixing matrices are built in a general framework with their matrix elements expressed in terms of the four fermion mass ratios, mu/mc, mc/mt, md/ms and ms/mb, and me/mμ, mμ/mτ, mν1/mν2 and mν2/mν3, for the quark and lepton sector, respectively. In this framework, we show that the resulting mixing matrices are consistent with data for both quarks and leptons, despite the large leptonic mixing angles. The minimal assumption we take is the one of hierarchical masses and minimal flavor symmetry breaking that strongly follows from phenomenology. No special structure of the mass matrices has to be assumed that cannot be motivated by this minimal assumption. This analysis allows us to predict the neutrino mass spectrum and set the mass of the lightest neutrino well below 0.01 eV. The method also gives the 1σ allowed ranges for the leptonic mixing matrix elements. Contrary to the common expectation, leptonic mixing angles are found to be determined solely by the four leptonic mass ratios without any relation to symmetry considerations as commonly used in flavor model building. Still, our formulae can be used to build up a flavor model that predicts the observed hierarchies in the masses — the mixing follows then from the procedure which is developed in this work.

Quasidegeneracy of Majorana neutrinos and the origin of large leptonic mixing

We propose that the observed large leptonic mixing may just reflect a quasidegeneracy of three Majorana neutrinos. The limit of exact degeneracy of Majorana neutrinos is not trivial, as leptonic mixing and even $CP$ violation may occur. We conjecture that the smallness of $|{U}_{13}|$, when compared to the other elements of ${U}_{PMNS}$, may be related to the fact that, in the limit of exact mass degeneracy, the leptonic mixing matrix necessarily has a vanishing element. We show that the lifting of the mass degeneracy can lead to the measured value of $|{U}_{13}|$ while at the same time accommodating the observed solar and atmospheric mixing angles. In the scenario we consider for the breaking of the mass degeneracy, there is only one $CP$ violating phase, already present in the limit of exact degeneracy, which upon the lifting of the degeneracy generates both Majorana and Dirac-type $CP$ violation in the leptonic sector. We analyze some of the correlations among physical observables and point out that, in most of the cases considered, the implied strength of leptonic Dirac-type $CP$ violation is large enough to be detected in the next round of experiments.

Neutrino mass and mixing: from theory to experiment

The origin of fermion mass hierarchies and mixings is one of the unresolved and most difficult problems in high-energy physics. One possibility to address the flavour problems is by extending the standard model to include a family symmetry. In the recent years it has become very popular to use non-Abelian discrete flavour symmetries because of their power in the prediction of the large leptonic mixing angles relevant for neutrino oscillation experiments. Here we give an introduction to the flavour problem and to discrete groups that have been used to attempt a solution for it. We review the current status of models in light of the recent measurement of the reactor angle, and we consider different model-building directions taken. The use of the flavons or multi-Higgs scalars in model building is discussed as well as the direct versus indirect approaches. We also focus on the possibility of experimentally distinguishing flavour symmetry models by means of mixing sum rules and mass sum rules. In fact, we illustrate in this review the complete path from mathematics, via model building, to experiments, so that any reader interested in starting work in the field could use this text as a starting point in order to obtain a broad overview of the different subject areas.

Probing the leptonic DiracCP-violating phase in neutrino oscillation experiments

The discovery of leptonic CP violation is one of the primary goals of next-generation neutrino oscillation experiments, which is feasible due to the recent measurement of a relatively large leptonic mixing angle \theta_{13}. We suggest two new working observables \Delta A^{\rm m}_{\alpha \beta} \equiv \max[A^{\rm CP}_{\alpha \beta}(\delta)] - \min[A^{\rm CP}_{\alpha \beta}(\delta)] and \Delta A^{\rm CP}_{\alpha \beta}(\delta) \equiv A^{\rm CP}_{\alpha \beta}(\delta) - A^{\rm CP}_{\alpha \beta}(0) to describe the CP-violating effects in long-baseline and atmospheric neutrino oscillation experiments. The former signifies the experimental sensitivity to the leptonic Dirac CP-violating phase $\delta$ and can be used to optimize the experimental setup, while the latter measures the intrinsic leptonic CP violation and can be used to extract $\delta$ directly from the experimental observations. Both analytical and numerical analyses are carried out to illustrate their main features. It turns out that an intense neutrino beam with sub-GeV energies and a baseline of a few 100 km may serve as an optimal experimental setup for probing leptonic CP violation.

S3model for lepton mass matrices with nearly minimal texture

We propose a simple extension of the electroweak standard model based on the discrete ${S}_{3}$ symmetry that is capable of realizing a nearly minimal Fritzsch-type texture for the Dirac mass matrices of both charged leptons and neutrinos. This is achieved with the aid of additional ${Z}_{5}$ and ${Z}_{3}$ symmetries, one of which can be embedded in $U(1{)}_{B\ensuremath{-}L}$. Five complex scalar singlet fields are introduced in addition to the standard model with right-handed neutrinos. Although more general, the modified texture of the model retains the successful features of the minimal texture without fine-tuning; namely, it accommodates the masses and mixing of the leptonic sector and relates the emergence of large leptonic mixing angles with the seesaw mechanism. For large deviations of the minimal texture, both quasidegenerate spectrum or inverted hierarchy are allowed for neutrino masses.

Large mixing angles from many right-handed neutrinos

A beautiful understanding of the smallness of the neutrino masses may be obtained via the seesaw mechanism, whereby one takes advantage of the key qualitative distinction between the neutrinos and the other fermions: right-handed neutrinos are gauge singlets, and may therefore have large Majorana masses. The standard seesaw mechanism, however, does not address the apparent lack of hierarchy in the neutrino masses compared to the quarks and charged leptons, nor the large leptonic mixing angles compared to the small angles of the CKM matrix. In this paper, we will show that the singlet nature of the right-handed neutrinos may be taken advantage of in one further way in order to solve these remaining problems: Unlike particles with gauge interactions, whose numbers are constrained by anomaly cancellation, the number of gauge singlet particles is essentially undetermined. If large numbers of gauge singlet fermions are present at high energies - as is suggested, for example, by various string constructions - then the effective low energy neutrino mass matrix may be determined as a sum over many distinct Yukawa couplings, with the largest ones being the most important. This can reduce hierarchy, and lead to large mixing angles. Assuming a statistical distribution of fundamental parameters, we will show that this scenario leads to a good fit to low energy phenomenology, with only a few qualitative assumptions guided by the known quark and lepton masses. The scenario leads to predictions of a normal hierarchy for the neutrino masses, and a value for the |m_ee| mass matrix element of about 1-6 meV.

Neutrino mass: From LHC to grand unification

The tiny neutrino masses and the associated large lepton mixings provide an interesting puzzle and a likely window to the physics beyond the standard model. This is certainly true if neutrinos are Majorana particles, since then, unlike in the Dirac case, the standard model is not a complete theory. The Majorana case leads to lepton number violation manifested through neutrinoless-double-beta decay and same-sign dileptons potentially accessible to colliders such as the LHC. This is covered at length. I discuss in these lectures possible theories of neutrino mass whose predictions are dictated by their structure only and this points strongly to grand unification. I cover in detail both SU(5) and SO(10) grand unified theories, and study the predictions of their minimal versions. The main message I wish to bring across is a serious hope of probing the origin of neutrino mass in near future, through the combined effort of high-energy collider and low-energy lepton number and lepton flavor violation experiments.

Lepton flavor violation in complex SUSY seesaw models with nearly tribimaximal mixing

We survey the lepton flavor violation branching ratios Br(mu->e,gamma), Br(tau->mu,gamma), and Br(tau->e,gamma) in mSUGRA for a broad class of lepton mass matrix textures that give nearly tribimaximal lepton mixing. Small neutrino masses are generated by the type-I seesaw mechanism with non-degenerate right-handed neutrino masses. The textures exhibit a hierarchical mass pattern and can be understood from flavor models giving rise to large leptonic mixing. We study the branching ratios for the most general CP-violating forms of the textures. It is demonstrated that the branching ratios can be enhanced by 2-3 orders of magnitude as compared to the CP-conserving case. The branching ratios exhibit, however, a strong dependence on the choice of the phases in the Lagrangian which affects the significance of flavor models. In particular, for general CP-phases, the lepton flavor violating rates appear to be essentially uncorrelated with the possible high- and low-energy lepton mixing parameters, such as the reactor angle.

Origin of quark-lepton flavor in SO(10) with type II seesaw mechanism

Diverse mass and mixing patterns between the quarks and leptons makes it challenging to construct a simple grand unified theory of flavor. We show that SO(10) SUSY GUTs with type II seesaw mechanism giving neutrino masses provide a natural framework for addressing this issue. A simple ansatz that the dominant Yukawa matrix (the 10-Higgs coupling to matter) has rank one, appears to simultaneously explain both the large lepton mixings as well as the observed quark flavor hierarchy in these models. A testable prediction of this ansatz is the neutrino mixing, U_{e3}, which should be observable in planned long baseline experiments.

WMAP dark matter constraints onb−τ Yukawa unification with massive neutrinos

We revisit the WMAP dark matter constraints on Yukawa Unification in the presence of massive neutrinos. The large lepton mixing indicated by the data may modify the predictions for the bottom quark mass, enabling Yukawa unification also for large $\tan\beta$, and for positive $\mu$ that was previously disfavoured. As a result, the allowed parameter space for neutralino dark matter increases for positive $\mu$, particularly for areas with resonant enhancement of the neutralino relic density. On the contrary, a negative $\mu$ is not easily compatible with large lepton mixing and Dirac neutrino Yukawa couplings, and the WMAP allowed parameter space is in this case strongly constrained.

Neutrino mixing and mass hierarchy in Gaussian landscapes

The flavor structure of the Standard Model may arise from random selection on a landscape. In a class of simple models, called "Gaussian landscapes," Yukawa couplings derive from overlap integrals of Gaussian zero-mode wavefunctions on an extra-dimensional space. Statistics of vacua are generated by scanning the peak positions of these wavefunctions, giving probability distributions for all flavor observables. Gaussian landscapes can account for all of the major features of flavor, including both the small electroweak mixing in the quark sector and the large mixing observed in the lepton sector. We find that large lepton mixing stems directly from lepton doublets having broad wavefunctions on the internal manifold. Assuming the seesaw mechanism, we find the mass hierarchy among neutrinos is sensitive to the number of right-handed neutrinos, and can provide a good fit to neutrino oscillation measurements.

Embedding A4 into SU(3) × U(1) flavor symmetry: large neutrino mixing and fermion mass hierarchy in the SO(10) GUT

We give an explanation of both the fermion mass hierarchy and the large lepton mixing angles in the context of a grand unified flavor and gauge theory (GUTF). Starting from an (SU(3) × U(1))F flavor symmetry and an SO(10) GUT, the main ingredient of our model is that two different breaking patterns of the flavor symmetry are at work. On the one hand, the dynamical breaking of (SU(3) × U(1))F flavor symmetry into (U(2) × Z3)F explains why one family is much heavier than the others. On the other hand, an explicit symmetry breaking of SU(3)F into a discrete flavor symmetry, A4, leads to the observed tri-bimaximal mixing for the leptons. Naturalness of the charged fermion mass hierarchy appears as a consequence of the continuous SU(3)F symmetry. Moreover, the same discrete SO(10) × A4 invariant operators are the root of the large lepton mixing, small Cabibbo angle and neutrino masses.

Fermion masses, leptogenesis, and supersymmetric SO(10) unification

Current neutrino oscillation data indicate the existence of two large lepton mixing angles, while Kobayashi-Maskawa matrix elements are all small. Here we show how supersymmetric SO(10) with extra chiral singlets can easily reconcile large lepton mixing angles with small quark mixing angles within the framework of the successful Fritzsch ansatz. Moreover, we show how this is fully consistent with the thermal leptogenesis scenario, avoiding the so-called gravitino problem. A sizable asymmetry can be generated at scales as low as possible within the leptogenesis mechanism. We present our results in terms of the leptonic $CP$ violation parameter that characterizes neutrino oscillations.