The non-unitarity effects in the leptonic flavor mixing are regarded as one of the generic features of the type-I seesaw model. Therefore, we explore these effects in the TeV-scale type-I seesaw model, and show that there exist non-trivial correlations among the non-unitarity parameters, stemming from the typical flavor structure of the low-scale seesaw model. In general, it follows from analytical discussions and numerical results that all the six non-unitarity parameters are related to three model parameters, while the widely studied parameters η_{eτ} and η_{μτ} cannot be phenomenologically significant
If neutrino masses are obtained via the canonical seesaw mechanism, based on an underlying 2X2 mass matrix, unitarity violation of the neutrino mixing matrix is unavoidable, but its effect is extremely small. On the other hand, in the inverse (and linear) seesaw mechanisms, based on an underlying 3X3 mass matrix, it can be significant and possibly observable. This 3X3 matrix is examined in more detail, and a NEW variation (the lopsided seesaw) is proposed which has features of both mechanisms. A concrete example based on U(1)_N is discussed.
Future experiments such as SHiP and high-intensity $e^+ e^-$ colliders will have a superb sensitivity to heavy Majorana neutrinos with masses below $M_Z$. We show that the measurement of the mixing to electrons and muons of one such state could imply the discovery of leptonic CP violation in the context of seesaw models. We quantify in the minimal model the CP discovery potential of these future experiments, and demonstrate that a 5$σ$ CL discovery of leptonic CP violation would be possible in a very significant fraction of parameter space.
We study the possibility of connecting leptonic Dirac CP phase $δ$, lightest neutrino mass and baryon asymmetry of the Universe within the framework of a model where both type I and type II seesaw mechanisms contribute to neutrino mass. Type I seesaw gives rise to Tri-Bimaximal (TBM) type neutrino mixing whereas type II seesaw acts as a correction in order to generate non-zero $θ_{13}$. We derive the most general form of type II seesaw mass matrix which can not only give rise to correct neutrino mixing angles but also can generate non-trivial value of $δ$. Considering both the cases where type…
A minimal version of the inverse seesaw model featuring only two pairs of TeV-scale singlet neutrinos is discussed from the perspective of non-standard neutrino interactions. A particular attention is paid to the non-standard patterns of flavour and CP violation emerging due to the possibly enhanced non-decoupling effects of the heavy sector and the associated non-unitarity of the effective lepton mixing matrix.
We show that a TeV scale inverse seesaw model for neutrino masses can be realized within the framework of a supersymmetric SO(10) model consistent with gauge coupling unification and observed neutrino masses and mixing. We present our expectations for non-unitarity effects in the leptonic mixing matrix some of which are observable at future neutrino factories as well as the next generation searches for lepton flavor violating processes such as μ--> e + γ. The model has TeV scale W_R and Z' bosons which are accessible at the Large Hadron Collider.
We address the question of deviations from $3\times 3$ unitarity of the leptonic mixing matrix showing that, contrary to conventional wisdom, one may have significant deviations from unitarity in the framework of type I seesaw mechanism. In order for this scenario to be feasible, at least one of the heavy neutrinos must have a mass at the TeV scale, while the other two may have much larger masses. We present specific examples where deviations from $3\times 3$ unitarity are sufficiently small to conform to all the present stringent experimental bounds but are sufficiently large to have the pote…
Following analogy of the `db' triangle in the quark mixing case, we have explored the construction of the `ν_2.ν_3' leptonic unitarity triangle using the Maki-Nakagawa-Sakata matrix obtained by Bjorken {\it et al.} through generalization of the tribimaximal scenario. In particular, for the U_{e3} range 0.05-0.15, the existence of the leptonic unitarity triangle indicates a fairly good possibility of having non zero CP violation.
We discuss the leptonic flavor structure generated by a brane shifted extra dimensional seesaw model with a single right handed neutrino in the bulk. In contrast to previous works, no unitarity approximation for the $3 \times 3$ submatrix has been employed. This allows to study phenomenological signatures such as lepton flavor violating decays. A strong prediction of the model, assuming CP conservation, are the ratios of flavor violating charged lepton decay and Z decay branching ratios which are correlated with the neutrino mixing angles and the neutrino mass hierarchy. Furthermore, it is pos…
The non-unitarity of the leptonic mixing matrix is a generic signal of new physics aiming at the generation of the observed neutrino masses. We discuss the Minimal Unitarity Violation (MUV) scheme, an effective field theory framework which represents the class of extensions of the Standard Model (SM) by heavy neutral leptons, and discuss the present bounds on the non-unitarity parameters as well as estimates for the sensitivity of the Circular Electron Positron Collider (CEPC), based on the performance parameters from the preCDR.
The seesaw mechanism can play a key role in the generation of the leptonic mixing in unified models. We consider an unified model with a family symmetry and extended seesaw, and obtain viable fermion masses and mixing (leptonic mixing is close to tri-bi-maximal).
We provide an $A_4$ based flavor symmetric scenario to accommodate the inverse seesaw mechanism for explaining light neutrino masses and mixing. We find that the lepton mixing, in particular the tri-bimaximal mixing pattern and its deviation through nonzero $θ_{13}$, is originated solely from the flavor structure of the lepton number violating contribution of the neutral lepton mass matrix. Here we discuss in detail how a nonzero value of $θ_{13}$ is correlated with the other parameters in the framework and its impact on the Dirac CP phase $δ$. We also analyze the non-unitarity effects on lept…
In the Next-to-Minimal Supersymmetric Standard Model with the inverse seesaw mechanism to generate neutrino masses, the lightest sneutrino may act as a feasible dark matter candidate in vast parameter space. In this case, the smallness of the leptonic unitarity violation and the recent XENON-1T experiment can limit the dark matter physics. In particular, they set upper bounds of the neutrino Yukawa couplings $λ_ν$ and $Y_ν$. We study such effects by encoding the constraints in a likelihood function and carrying out elaborated scans over the parameter space of the theory with the Nested Samplin…
The non-unitarity of the effective leptonic mixing matrix at low energies is a generic signal of extensions of the Standard Model (SM) with extra fermionic singlet particles, i.e. sterile or right-handed neutrinos, to account for the observed neutrino masses. The low energy effects of such extensions can be described in a model-independent way by the Minimal Unitarity Violation (MUV) scheme, an effective field theory extension of the SM. We perform a global fit of the MUV scheme parameters to the present experimental data, which yields the up-to-date constraints on leptonic non-unitarity. Furt…
The latest measurements of the anomalous muon magnetic moment $a^{}_μ\equiv (g^{}_μ- 2)/2$ show a $4.2σ$ discrepancy between the theoretical prediction of the Standard Model and the experimental observations. In order to account for such a discrepancy, we consider a possible extension of the type-(I+II) seesaw model for neutrino mass generation with a gauged $L^{}_μ- L^{}_τ$ symmetry. By explicitly constructing an economical model with only one extra scalar singlet, we demonstrate that the gauge symmetry $U(1)^{}_{L^{}_μ- L^{}_τ}$ and its spontaneous breaking are crucially important not only f…
A low-energy non-unitary leptonic mixing matrix is a generic effect of some theories of new physics accounting for neutrino masses. We show how the extra CP-phases of a general non-unitary matrix allow for sizeable CP-asymmetries in the $ν_μ\to ν_τ$ channel. This CP-asymmetries turns out to be an excellent probe of such new physics.
In the light of the recent LHC data, we study precision tests sensitive to the violation of lepton universality, in particular the violation of unitarity in neutrino mixing. Keeping all data we find no satisfatory fit, even allowing for violations of unitarity in neutrino mixing. Leaving out sin$^2 θ_{\scriptsize \mbox{eff}}$ from the hadronic forward-backward asymmetry at LEP, we find a good fit to the data with some evidence of lepton universality violation at the $\mathcal{O}(10^{-3})$ level.
In this paper, we examine the leptonic flavor invariants in the minimal seesaw model (MSM), in which only two right-handed neutrino singlets are added into the Standard Model in order to accommodate tiny neutrino masses and explain cosmological matter-antimatter asymmetry via leptogenesis mechanism. For the first time, we calculate the Hilbert series (HS) for the leptonic flavor invariants in the MSM. With the HS we demonstrate that there are totally 38 basic flavor invariants, among which 18 invariants are CP-odd and the others are CP-even. Moreover, we explicitly construct these basic invari…
We analyze the structure of the non-unitary leptonic mixing matrix in the inverse seesaw model with heavy singlets accessible at the LHC. In this model, unlike in the usual TeV seesaw scenarios, thelow-scale right-handed neutrinos do not suffer from naturalness issues. Underlying correlations among various parameters governing the non-unitarity effects are established, which leads to a considerable improvement of the generic non-unitarity bounds. In view of this, we study the discovery potential of the non-unitarity effects at future experiments, focusing on the sensitivity limits at a neutrin…
We show that, in the low-scale type-I seesaw model, renormalization group running of neutrino parameters may lead to significant modifications of the leptonic mixing angles in view of so-called seesaw threshold effects. Especially, we derive analytical formulas for radiative corrections to neutrino parameters in crossing the different seesaw thresholds, and show that there may exist enhancement factors efficiently boosting the renormalization group running of the leptonic mixing angles. We find that, as a result of the seesaw threshold corrections to the leptonic mixing angles, various flavor …
We estimate the effect of leptonic CP violating phases in the minimal seesaw model with two heavy neutrinos $N$ by imposing the approximately $μ-τ$ symmetry on the model. For $N$ subject to the $μ-τ$ symmetry, we find that neutrinos show the normal mass hierarchy and obtain the general phase structure that contains only two phases which arise from $μ-τ$ symmetry breaking terms. To perform similar consideration for $N$ blind to the $μ-τ$ symmetry necessarily giving the inverted mass hierarchy, we assume the same phase structure. Our phases consist of six phases that need to take care of generic…
We propose a theory based on the $A_5$ discrete group which successfully accounts for lepton masses and mixings. In the proposed model, the neutrino masses arise from an inverse seesaw mechanism. The leptonic mixing consists in a perturbed golden ratio mixing pattern with a strong correlation arising between the leptonic mixing observables, which can be expressed as $θ_{13}$ predicting the other mixing angles and the Dirac CP phase.
We consider a model for a Z'-boson coupled only to baryon minus lepton number and hypercharge. Besides the usual right-handed neutrinos, we add a pair of fermions with a fractional lepton charge, which we therefore call leptinos. One of the leptinos is taken to be odd under an additional Z_2 charge, the other even. This allows for a natural (inverse) seesaw mechanism for neutrino masses. The odd leptino is a candidate for dark matter, but has to be resonantly annihilated by the Z'-boson or the Higgs-boson responsible for giving mass to the former. Considering collider and cosmological bounds o…
The area of the unitarity triangle is a measure of CP-violation. We introduce the leptonic unitarity triangles and study their properties. We consider the possibility of reconstructing the unitarity triangle in future oscillation and non-oscillation experiments. A set of measurements is suggested which will, in principle, allow us to measure all sides of the triangle, and consequently to establish CP-violation. For different values of the CP-violating phase, $δ_D$, the required accuracy of measurements is estimated. The key elements of the method include determination of $|U_{e3}|$ and studies…
We study a CP and T violating triple (spin) correlation in the muon to electron conversion in nuclei in the context of the seesaw mechanism. After concluding that the results are negative for all three seesaw types, we turn to the left-right symmetric theories as the original source of seesaw. We find that in general this correlation is of order one which offers a hope of observing CP violation in lepton flavor violating processes for a L-R scale below around 10-30 TeV. We discuss the conditions that could render to (unlikely) conspiracies as to suppress the CP violating effects.
The new results on the muon anomalous magnetic moment (AMM) published by Fermilab in 2021, did not lead to a reduction of its long-pending deviation from the Standard Model (SM) value by more than 4$σ$. The explanation of this discrepancy by adding new particles to the theory puts many new physics models under tension when combined with the null results of the LHC direct searches for new particles. In this paper, we investigate the CP-violating Next-to-Minimal Supersymmetric extension of the SM (NMSSM) with and without an inverse seesaw mechanism. We compute the one-loop supersymmetric contrib…
Assuming a minimal seesaw model with two heavy neutrinos (N), we examine effects of leptonic CP violation induced by approximate mu-tau symmetric interactions. As long as N is subject to the mu-tau symmetry, we can choose CP phases of Dirac mass terms without loss of generality in such a way that these phases arise from mu-tau symmetry breaking interactions. In the case that no phase is present in heavy neutrino mass terms, leptonic CP phases are controlled by two phases alpha and beta. The similar consideration is extended to N blind to the mu-tau symmetry. It is argued that N subject (blind)…
We study the linking between the CP violating phase of the lepton sectors and the unitarity triangle of the B0 meson system. Antusch, King, Malinsky and Spinrath have shown that the quark mass matrices with the negligible 1-3 mixing give an interesting relation between the phase of the quark mixing matrices and CP violating measure phi_2(alpha). This approach is extended by considering the SO(10) GUT including the Pati-Salam symmetry, which links the Yukawa matrices of the quark sector to the one of the lepton sector. We discuss the relation of the CP violating phases between both quark and le…
After the observation of non-zero $θ_{13}$ the goal has shifted to observe $CP$ violation in the leptonic sector. Neutrino oscillation experiments can, directly, probe the Dirac $CP$ phases. Alternatively, one can measure $CP$ violation in the leptonic sector using Leptonic Unitarity Quadrangle(LUQ). The existence of Standard Model (SM) gauge singlets - sterile neutrinos - will provide additional sources of $CP$ violation. We investigate the connection between neutrino survival probability and rephasing invariants of the $4\times4$ neutrino mixing matrix. In general, LUQ contain eight geometri…
We present a geometric description of lepton flavor mixing and CP violation in matter by using the language of leptonic unitarity triangles. The exact analytical relations for both sides and inner angles are established between every unitarity triangle in vacuum and its effective counterpart in matter. The typical shape evolution of six triangles with the terrestrial matter density is illustrated for a realistic long-baseline neutrino oscillation experiment.
We present a comprehensive analysis of leptonic unitarity triangles, using both current neutrino oscillation data and projections of next-generation oscillation measurements. Future experiments, sensitive to the degree of CP violation in the lepton sector, will enable the construction of precise triangles. We show how unitarity violation could manifest in the triangles and discuss how they serve as unitarity tests. We also propose the use of Jarlskog factors as a complementary means of probing unitarity. This analysis highlights the importance of testing the unitarity of the leptonic mixing ma…
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 to constrain the non-unitarity parameters via lepton …
The octant of the atmospheric mixing angle $θ_{23}$ is still undetermined by neutrino oscillation experiments. Long-baseline experiments like NO$ν$A, T2K and DUNE offer good prospects for determining the octant of $θ_{23}$. However, their capability to do so may be compromised by the possible presence of non-unitarity in the leptonic mixing matrix. In this paper, we study in detail the octant degeneracy with and without non-unitarity at the level of oscillation probabilities and events for these experiments. We also analyze their octant sensitivity and discovery reach and show that they are ha…
We determine the elements of the leptonic mixing matrix, without assuming unitarity, combining data from neutrino oscillation experiments and weak decays. To that end, we first develop a formalism for studying neutrino oscillations in vacuum and matter when the leptonic mixing matrix is not unitary. To be conservative, only three light neutrino species are considered, whose propagation is generically affected by non-unitary effects. Precision improvements within future facilities are discussed as well.
We derive a new set of sum rules between the neutrino mass and mixing parameters in vacuum and their effective counterparts in matter. The moduli of nine genuine lepton mixing matrix elements can then be calculated in terms of the matter-corrected ones, and the latter can directly be determined from a variety of long-baseline neutrino oscillations. We show that it is possible to reconstruct the leptonic unitarity triangles and CP violation in a similar parametrization-independent way.
We present a Grand Unified model based on SO(10) with a Delta(27) family symmetry. Fermion masses and mixings are fitted and agree well with experimental values. An extended seesaw mechanism plays a key role in the generation of the leptonic mixing, which is approximately tri-bi-maximal.
Neutrino Physics is a mature branch of science with all the three neutrino mixing angles and two mass squared differences determined with high precision. Inspite of several experimental verifications of neutrino oscillations and precise measurements of two mass squared differences and the three mixing angles, the unitarity of the leptonic mixing matrix is not yet established, leaving room for the presence of small non-unitarity effects. Deriving the bounds on these non-unitarity parameters from existing experimental constraints, on cLFV decays such as, $ μ\rightarrow eγ$, $ μ\rightarrow τγ$, $…
The recent IceCube observation of ultra-high-energy astrophysical neutrinos has begun the era of neutrino astronomy. In this work, using the unitarity of leptonic mixing matrix, we derive nontrivial unitarity constraints on the flavor composition of astrophysical neutrinos detected by IceCube. Applying leptonic unitarity triangles, we deduce these unitarity bounds from geometrical conditions, such as triangular inequalities. These new bounds generally hold for three flavor neutrinos, and are independent of any experimental input or the pattern of leptonic mixing. We apply our unitarity bounds …
We explore the possibility of resolving simultaneously the $W$-boson mass shift reported by the CDF collaboration and the apparent deviation from unitarity in the first row of the CKM mixing matrix in a class of left-right symmetric models. The fermion masses are generated in these models through a universal seesaw mechanism, utilizing vector-like partners of the usual fermions. We find a unique solution to the two anomalies where the mixing of the down quark with a vector-like quark (VLQ) resolves the CKM unitarity puzzle, and the mixing of the top quark with a VLQ partner explains the $W$ bo…
We explore generic features of the leptonic CP violation in the framework of the seesaw type I mechanism with similarity of the Dirac lepton and quarks mass matrices $m_D$. For this, we elaborate on the standard parametrization conditions which allow to simultaneously obtain the Dirac and Majorana phases. If the only origin of CP violation is the left-handed (LH) transformation which diagonalizes $m_D$ (similar to quarks), the leptonic CP violation is suppressed and the Dirac phase is close to $π$ or to $0$ with $\sin δ_{CP} \approx (\sin θ_{13}^q /\sin θ_{13}) \cos θ_{23} \sin δ_q \sim λ^2 \s…
The historical discovery of neutrino oscillations using solar and atmospheric neutrinos, and subsequent accelerator and reactor studies, has brought neutrino physics to the precision era. We note that CP effects in oscillation phenomena could be difficult to extract in the presence of unitarity violation. As a result upcoming dedicated leptonic CP violation studies should take into account the non-unitarity of the lepton mixing matrix. Restricting non-unitarity will shed light on the seesaw scale, and thereby guide us towards the new physics responsible for neutrino mass generation.
In terms of flavor invariants, we establish the intimate connection between leptonic CP violation in the canonical seesaw model for neutrino masses and that in the seesaw effective field theory (SEFT). For the first time, we calculate the Hilbert series and explicitly construct the primary flavor invariants in the SEFT by considering both the dimension-five Weinberg operator ${\cal O}^{αβ}_5 = \overline{\ell^{}_{α\rm L}} \widetilde{H} \widetilde{H}^{\rm T} \ell^{\rm C}_{β\rm L}$ and the dimension-six operator ${\cal O}^{αβ}_6 = \overline{\ell^{}_{α\rm L}} \widetilde{H} {\rm i} \not\!\partial \…
In the framework of seesaw models with only two heavy Majorana neutrinos, nonzero leptonic asymmetries can be radiatively generated when exact heavy neutrino mass degeneracy ($M_1=M_2=M$) is imposed at a scale $Λ_D > M$. For a specific case, we show that an acceptable value for the baryon asymmetry of the Universe can be obtained considering thermal leptogenesis.
There are six leptonic unitarity triangles (LUTs) defined by six orthogonality conditions of the three-family lepton flavor mixing matrix in the complex plane. In the framework of the standard model or the minimal supersymmetric standard model, the evolutions of sides and inner angles of the six LUTs from a superhigh energy scale $Λ_{\rm H}^{}$ to the electroweak scale $Λ_{\rm EW}^{}$ due to the renormalization-group equation (RGE) running are derived in the integral form for both Dirac and Majorana neutrinos. Furthermore, the LUTs as an intuitively geometrical language are applied to the desc…
Within the seesaw type-I leptogenesis, we formulate $CPT$ and unitarity constraints for the equilibrium reaction rate $CP$ asymmetries and consider thermal mass and quantum statistics. We demonstrate that including higher-order perturbative corrections in the classical Boltzmann equation remarkably induces quantum effects into the kinetic theory.
We investigate the relation between non-unitarity of the leptonic mixing matrix and leptogenesis. We discuss how all parameters of the canonical type-I seesaw mechanism can, in principle, be reconstructed from the neutrino mass matrix and the deviation of the effective low-energy leptonic mixing matrix from unitary. When the mass M' of the lightest right-handed neutrino is much lighter than the masses of the others, we show that its decay asymmetries within flavour-dependent leptogenesis can be expressed in terms of two contributions, one depending on the unique dimension five (d=5) operator g…
We consider a new Weinberg operator for neutrino mass of the form $H_u\tilde{H_d}L_iL_j$ involving two different Higgs doublets $H_u, H_d$ with opposite hypercharge, where $\tilde{H_d}$ is the charge conjugated doublet. It may arise from a model where the two Higgs doublets carry the same charge under a $U(1)'$ gauge group which forbids the usual Weinberg operator but allows the mixed one. The new Weinberg operator may be generated via two right-handed neutrinos oppositely charged under the $U(1)'$, which may be identified as components of a fourth vector-like family in a complete model. Such …
With the motivation of simultaneously explaining dark matter and neutrino masses, mixing angles, we have invoked the Type-II seesaw model extended by an extra $SU(2)$ doublet $Φ$. Moreover, we have imposed a $\mathbb{Z}_2$ parity on $Φ$ which remains unbroken as the vacuum expectation value of $Φ$ is zero. Consequently, the lightest neutral component of $Φ$ becomes naturally stable and can be a viable dark matter candidate. On the other hand, light Majorana masses for neutrinos have been generated following usual Type-II seesaw mechanism. Further in this framework, for the first time, we have …
The unitarity of the lepton mixing matrix is a critical assumption underlying the standard neutrino-mixing paradigm. However, many models seeking to explain the as-yet-unknown origin of neutrino masses predict deviations from unitarity in the mixing of the active neutrino states. Motivated by the prospect that future experiments may provide a precise measurement of the lepton mixing matrix, we revisit current constraints on unitarity violation from oscillation measurements and project how next-generation experiments will improve our current knowledge. With the next-generation data, the normali…
The possible existence of light and heavy sterile neutrinos may give rise to direct and indirect unitarity violation of the $3\times3$ lepton mixing matrix respectively. In the current work we study the potential of future accelerator neutrino facilities in probing the unitarity violation effects. Taking DUNE, T2HK and a low-energy Neutrino Factory (LENF) as working examples of future accelerator neutrino facilities, we study the distinct effects of direct and indirect unitarity violation on the discovery reach of the leptonic CP violation and precision measurements of $θ_{23}$ in the three ne…
In this work we implement the type II seesaw mechanism into the framework of the $U(1)_{B-L}$ gauge model. As main gain, the right-handed neutrinos of the model get free to play the role of the dark matter of the universe. As side effect, the model realizes Higgs inflation without problem with loss of unitarity.
We investigate, within the Type I seesaw framework, the physical implications of zero textures in the Yukawa couplings which generate the neutrino Dirac mass matrix $m_D$. It is shown that four is the maximal number of texture zeroes compatible with the observed leptonic mixing and the assumption that no neutrino mass vanishes. We classify all allowed four-zero textures of $m_D$ into two categories with three classes each. We show that the different classes, in general, admit CP violation both at low and high energies. We further present the constraints obtained for low energy physics in each …
If leptonic unitarity is violated by new physics at an energy scale much lower than the electroweak scale, which we call low-scale unitarity violation, it has different characteristic features from those expected in unitarity violation at high-energy scales. They include maintaining flavor universality and absence of zero-distance flavor transition. We present a framework for testing such unitarity violation at low energies by neutrino oscillation experiments. Starting from the unitary 3 active plus $N$ (arbitrary integer) sterile neutrino model we show that by restricting the active-sterile a…
