Majorana CP-violating Research Articles

Majorana CP-violating phases and NSI effects in neutrino decay

In this work, we investigate the impact of neutrino decay in the presence of non-standard interactions (NSI) along with the effects of the Majorana phase on neutrino decay in matter in the context of two-flavor neutrino oscillations. These effects are studied on neutrino oscillation probabilities P α β ≡ P(ν α → ν β ), and the difference ΔPαβ≡P(να→νβ)−P(ν¯α→ν¯β) for several accelerator and reactor neutrino experiments. We find that for P α β , the influence of the Majorana phase on decay in matter can be replicated by the simultaneous presence of both decay and NSI. However, precise measurements of the P α β and ΔP α β observables have the potential to unequivocally identify the presence of the Majorana phase by discerning its effects from the concurrent presence of both decay and NSI.

Investigating CP Violating Majorana Phases of Neutrinos

Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix is a complex symmetric matrix consisting of three generations of neutrinos and 12 real parameters. Diagonalizing the neutrino mass matrix and expressing the same in terms of three neutrino masses, three mixing angles, one Dirac phase and two Majorana phases such that it removes all the unphysical phases. The absolute neutrino mass scale and two Majorana CP-violating phases cannot be determined by neutrino oscillation experiments and hence an attempt has been made to investigate Majorana phases by drawing a correlation between the elements of neutrino mass matrix under the conditions of simultaneity and equated them to zero. We obtain twenty-five neutrino mass matrix textures for inverted hierarchy of Majorana neutrinos. Finally, numerical values of Majorana phases have been calculated for these textures and other phenomenological quantities are in consistent with the oscillation data.

On minimal realization of topological Lorentz structures with one-loop seesaw extensions in A4 modular symmetry

The topological classification of one-loop Weinberg operator at dimension-5 leads to systematic categorization of one-loop neutrino mass models. All one-loop neutrino mass models must fall in one of these categories. Among these topological categories, loop extension of canonical seesaw scenarios is interesting in light of the current LHC run. Apart from one-loop contribution, these extensions result in dominant tree-level contribution to neutrino masses. The immediate remedy to obtain dominant one-loop contribution requires combination of flavor symmetries and enlarged field content. Alternatively, in this work, we propose a minimal way of realizing the topological structures with dominant one-loop contribution using modular variant of the permutation symmetries. In such a realization, no new fields are needed apart from those permitted by the topology itself. For the first time, we have realized one such topological Lorentz structure(T4-2-i) pertaining to one-loop extension of Type-II seesaw using modular A4 symmetry. Here, modular weights play an important role in suppressing tree-level terms and stabilizing the particles running in the loop(Ni , ρ and ϕ), thus, making them suitable dark matter candidates. In this work, we have explored the possibility of fermionic dark matter candidate where right-handed neutrino (N 1) is assumed to be lightest. We have, also, analyzed the compatibility of the model with neutrino oscillation data and obtained model predictions for effective Majorana mass Mee and CP violation. Furthermore, the predictions on relic density of dark matter and its direct detection considering bound on lepton flavor violating process, μ → eγ have, also, been investigated.

Comment on: “Geometric phase of neutrinos: Differences between Dirac and Majorana neutrinos” [Phys. Lett. B 780 (2018) 216

In [5] (2018), Capolupo et al. calculate the noncyclic geometric phases associated with neutrino flavor transitions in the two-neutrino scenario, and claim that the results depend on the choice of representations of neutrino mixing matrix thus can be used to distinguish between Dirac and Majorana neutrinos. In this paper, we show that their calculation is flawed due to incorrect application of the definition of noncyclic geometric phase and the omission of one term in Wolfenstein effective Hamiltonian. Their results are neither gauge invariant nor lepton field rephasing invariant. We present an alternative calculation, which is solely in order to demonstrate that the Majorana CP-violating phase enters the geometric phase essentially by lepton field rephasing transformation. We point out that the seemingly nontrivial dependence of geometric phase on Majorana CP-violating phase presented in Capolupo et al. (2018) [5] is unphysical and thus unmeasurable.

Towards the meV limit of the effective neutrino mass in neutrinoless double-beta decays * * This work was supported in part by the National Key R&D Program of China (2018YFA0404100), the Strategic Priority Research Program of the Chinese Academy of Sciences (XDA10010100), the National Natural Science Foundation of China (11605081, 11775231, 11775232, 11835013, 11820101005) and the CAS Center for Excellence

We emphasize that it is extremely important for future neutrinoless double-beta ( ) decay experiments to reach the sensitivity to the effective neutrino mass . With such a sensitivity, it is highly possible to discover the signals of decays. If no signal is observed at this sensitivity level, then either neutrinos are Dirac particles or stringent constraints can be placed on their Majorana masses. In this paper, assuming the sensitivity of for future decay experiments and the precisions on neutrino oscillation parameters after the JUNO experiment, we fully explore the constrained regions of the lightest neutrino mass and two Majorana-type CP-violating phases . Several important conclusions in the case of normal neutrino mass ordering can be made. First, the lightest neutrino mass is severely constrained to a narrow range , which together with the precision measurements of neutrino mass-squared differences from oscillation experiments completely determines the neutrino mass spectrum and . Second, one of the two Majorana CP-violating phases is limited to , which cannot be obtained from any other realistic experiments. Third, the sum of three neutrino masses is found to be , while the effective neutrino mass for beta decays turns out to be . These observations clearly set up the roadmap for future non-oscillation neutrino experiments aiming to solve the fundamental problems in neutrino physics.

Constraining the Effective Mass of Majorana Neutrino with Sterile Neutrino Mass for Inverted Ordering Spectrum

Inspired by the experimental anomalies in neutrino physics and recent oscillation data from short baseline and another neutrino experiment, the realization of one extra neutrino flavor seems to be favoring. This extra flavor may change the observable, |mββ|, of current data taking and next-generation (ββ)0ν-decay experiments aim to probe and possibly look at the Inverted Ordering region (|mββ|≃10-2eV) of parameter space. This observation would allow establishing physics beyond the standard model and phenomena like lepton number violation and Majorana nature of neutrino. The range of this observable (|mββ|) is not very well defined for both the ordering of mass spectrum (Normal Ordering and Inverted Ordering). Several attempts have been made for defining exactly the range for three active neutrino states. For contrasting this range, I have worked with an extra mass state, ν4, and its effect on the observable with various combinations of CP violation Majorana phases by taking into account the updated data on the neutrino oscillation parameters for IO case. Based on the Monte Carlo technique, a parameter region is obtained using the fourth Majorana-Dirac phase of sterile parameters that lead to an effective mass below 0.01 eV or .05 eV for inverted mass ordering case which is planned to be observed in the near future experiment.

Modular S4 models of lepton masses and mixing

We investigate models of charged lepton and neutrino masses and lepton mixing based on broken modular symmetry. The matter fields in these models are assumed to transform in irreducible representations of the finite modular group Γ4 ≃ S4. We analyse the minimal scenario in which the only source of symmetry breaking is the vacuum expectation value of the modulus field. In this scenario there is no need to introduce flavon fields. Using the basis for the lowest weight modular forms found earlier, we build minimal phenomenologically viable models in which the neutrino masses are generated via the type I seesaw mechanism. While successfully accommodating charged lepton masses, neutrino mixing angles and mass-squared differences, these models predict the values of the lightest neutrino mass (i.e., the absolute neutrino mass scale), of the Dirac and Majorana CP violation (CPV) phases, as well as specific correlations between the values of the atmospheric neutrino mixing parameter sin2θ23 and i) the Dirac CPV phase δ, ii) the sum of the neutrino masses, and iii) the effective Majorana mass in neutrinoless double beta decay. We consider also the case of residual symmetries ℤ3ST and ℤ2S respectively in the charged lepton and neutrino sectors, corresponding to specific vacuum expectation values of the modulus.

Phenomenological implications of the Friedberg-Lee transformation in a neutrino mass model with \u03bc\u03c4-flavored CP symmetry

We propose a neutrino mass model with μτ-flavored CP symmetry, where the effective light neutrino Lagrangian enjoys an additional invariance under a Friedberg-Lee (FL) transformation on the left-handed flavor neutrino fields that leads to a highly predictive and testable scenario. While both types of the light neutrino mass ordering, i.e., Normal Ordering (NO) as well as the Inverted Ordering (IO) are allowed, the absolute scale of neutrino masses is fixed by the vanishing determinant of light Majorana neutrino mass matrix Mν. We show that for both types of mass ordering, whilst the atmospheric mixing angle θ23 is in general nonmaximal (θ23 ≠ π/4), the Dirac CP phase δ is exactly maximal (δ = π/2, 3π/2) for IO and nearly maximal for NO owing to cos δ ∝ sin θ13. For the NO, very tiny nonvanishing Majorana CP violation might appear through one of the Majorana phases β; otherwise the model predicts vanishing Majorana CP violation. Thus, despite the fact, that from the measurement of θ23, it is difficult to rule out the model, any large deviation of δ from its maximality, will surely falsify the scenario. For a comprehensive numerical analysis, beside fitting the neutrino oscillation global fit data, we also present a study on the νμ → νe oscillation which is expected to show up Dirac CP violation in different long baseline experiments. Finally, assuming purely astrophysical sources, we calculate the Ultra High Energy (UHE) neutrino flavor flux ratios at neutrino telescopes, such as IceCube, from which statements on the octant of θ23 could be made in our model.

CP transformed mixed μτ antisymmetry for neutrinos and its consequences

We propose a complex extension of mixed $\mu\tau$ antisymmetry in the neutrino Majorana mass matrix $M_\nu$. This can be implemented in the Lagrangian by a generalized CP transformation (labeled by a mixing parameter $\theta$) on the left-chiral flavor neutrino fields. We investigate its implications for leptonic CP violation and neutrino phenomenology in general. Interestingly, the $\mu\tau$ mixing parameter $\theta$ gets correlated with the Dirac CP phase $\delta$ and the atmospheric mixing angle $\theta_{23}$ through an analytical relation. In general, for arbitrary $\theta$, both $\theta_{23}$ and $\delta$ are nonmaximal. We discuss the corresponding results for the CP asymmetry parameter $A_{\mu e}$ in neutrino oscillation experiments. For a nonmaximal $\delta$, one of the two Majorana phases is different from $0$ or $\pi$, thereby leading to nonvanishing Majorana CP violation with observable consequences for the neutrinoless double beta ($\beta\beta0\nu$) decay process. We numerically work out in detail the predictions for that process in relation to various ongoing and forthcoming experiments. We also work out the predictions of our scheme on flavor flux ratios at neutrino telescopes. While exact CP transformed $\mu\tau$ interchange antisymmetry ($\theta=\pi/2$) leads to an exact equality among those ratios, taking a value $0.5$, a tiny deviation can cause a drastic change in them. Careful measurement of these flux ratios in future will further constrain the parameter $\theta$.

Combining texture zeros with a remnant CP symmetry in the minimal type-I seesaw

In the framework of the two right-handed neutrino seesaw model, we consider maximally-restrictive texture-zero patterns for the lepton Yukawa coupling and mass matrices, together with the existence of a remnant CP symmetry. Under this premise, we find that several textures are compatible with the most recent data coming from neutrino oscillation and neutrinoless double beta decay experiments. It is shown that, the maximum number of allowed texture zeros in the Dirac Yukawa coupling matrix is two, for an inverted neutrino mass spectrum. In contrast, for Yukawa coupling matrices with just one texture zero, both normal and inverted orderings of neutrino masses are compatible with data. In all cases, the predictions for the low-energy Dirac and Majorana CP-violating phases, and for the effective mass parameter relevant in neutrinoless double-beta decay experiments, are presented and discussed. We also comment on the impact of future experimental improvements in scrutinising texture-zero patterns with a remnant CP symmetry, within the minimal version of the seesaw mechanism considered here.

The 10−3 eV frontier in neutrinoless double beta decay

The observation of neutrinoless double beta decay would allow to establish lepton number violation and the Majorana nature of neutrinos. The rate of this process in the case of 3-neutrino mixing is controlled by the neutrinoless double beta decay effective Majorana mass |〈m〉|. For a neutrino mass spectrum with normal ordering, which is favoured over the spectrum with inverted ordering by recent global fits, |〈m〉| can be significantly suppressed. Taking into account updated data on the neutrino oscillation parameters, we investigate the conditions under which |〈m〉| in the case of spectrum with normal ordering exceeds 10−3(5×10−3)eV: |〈m〉|NO>10−3(5×10−3)eV. We analyse first the generic case with unconstrained leptonic CP violation Majorana phases. We show, in particular, that if the sum of neutrino masses is found to satisfy Σ>0.10eV, then |〈m〉|NO>5×10−3eV for any values of the Majorana phases. We consider also cases where the values for these phases are either CP conserving or are in line with predictive schemes combining flavour and generalised CP symmetries.

Effects of Leptonic Nonunitarity on Lepton Flavor Violation, Neutrino Oscillation, Leptogenesis, and Lightest Neutrino Mass

Neutrino physics is a mature branch of science with all the three neutrino mixing angles and two mass squared differences determined with high precision. In spite 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 nonunitarity effects. Deriving the bounds on these nonunitarity parameters from existing experimental constraints, on cLFV decays such as μ→eγ, μ→τγ, and τ→eγ, we study their effects on the generation of baryon asymmetry through leptogenesis and neutrino oscillation probabilities. We consider a model where see-saw is extended by an additional singlet S which is very light but can give rise to nonunitarity effects without affecting the form on see-saw formula. We do a parameter scan of a minimal see-saw model in a type I see-saw framework satisfying the Planck data on baryon to photon ratio of the Universe, which lies in the interval 5.8×10-10<YB<6.6×10-10(BBN). We predict values of lightest neutrino mass and Dirac and Majorana CP-violating phases δCP, α, and β, for normal hierarchy and inverted hierarchy for one-flavor leptogenesis. It is worth mentioning that all these four quantities are unknown yet, and future experiments will be measuring them.

Neutrino mixing and leptonic CP violation from S4 flavour and generalised CP symmetries

We consider a class of models of neutrino mixing with S4 lepton flavour symmetry combined with a generalised CP symmetry, which are broken to residual Z2 and Z2 × HCPν symmetries in the charged lepton and neutrino sectors, respectively, HCPν being a remnant CP symmetry of the neutrino Majorana mass term. In this set-up the neutrino mixing angles and CP violation (CPV) phases of the neutrino mixing matrix depend on three real parameters — two angles and a phase. We classify all phenomenologically viable mixing patterns and derive predictions for the Dirac and Majorana CPV phases. Further, we use the results obtained on the neutrino mixing angles and leptonic CPV phases to derive predictions for the effective Majorana mass in neutrinoless double beta decay.

Renormalization group running of fermion observables in an extended non-supersymmetric SO(10) model

We investigate the renormalization group evolution of fermion masses, mixings and quartic scalar Higgs self-couplings in an extended non-supersymmetric SO(10) model, where the Higgs sector contains the 10H, 120H, and 126H representations. The group SO(10) is spontaneously broken at the GUT scale to the Pati-Salam group and subsequently to the Standard Model (SM) at an intermediate scale MI. We explicitly take into account the effects of the change of gauge groups in the evolution. In particular, we derive the renormalization group equations for the different Yukawa couplings. We find that the computed physical fermion observables can be successfully matched to the experimental measured values at the electroweak scale. Using the same Yukawa couplings at the GUT scale, the measured values of the fermion observables cannot be reproduced with a SM-like evolution, leading to differences in the numerical values up to around 80%. Furthermore, a similar evolution can be performed for a minimal SO(10) model, where the Higgs sector consists of the 10H and 126H representations only, showing an equally good potential to describe the low-energy fermion observables. Finally, for both the extended and the minimal SO(10) models, we present predictions for the three Dirac and Majorana CP-violating phases as well as three effective neutrino mass parameters.

Predictions for the Majorana CP violation phases in the neutrino mixing matrix and neutrinoless double beta decay

We obtain predictions for the Majorana phases α21/2 and α31/2 of the 3×3 unitary neutrino mixing matrix U=Ue†Uν, Ue and Uν being the 3×3 unitary matrices resulting from the diagonalisation of the charged lepton and neutrino Majorana mass matrices, respectively. We focus on forms of Ue and Uν permitting to express α21/2 and α31/2 in terms of the Dirac phase δ and the three neutrino mixing angles of the standard parametrisation of U, and the angles and the two Majorana-like phases ξ21/2 and ξ31/2 present, in general, in Uν. The concrete forms of Uν considered are fixed by, or associated with, symmetries (tri-bimaximal, bimaximal, etc.), so that the angles in Uν are fixed. For each of these forms and forms of Ue that allow to reproduce the measured values of the three neutrino mixing angles θ12, θ23 and θ13, we derive predictions for phase differences (α21/2−ξ21/2), (α31/2−ξ31/2), etc., which are completely determined by the values of the mixing angles. We show that the requirement of generalised CP invariance of the neutrino Majorana mass term implies ξ21=0 or π and ξ31=0 or π. For these values of ξ21 and ξ31 and the best fit values of θ12, θ23 and θ13, we present predictions for the effective Majorana mass in neutrinoless double beta decay for both neutrino mass spectra with normal and inverted ordering.

Maximal CP violation in flavor neutrino masses

Since flavor neutrino masses [Formula: see text] can be expressed in terms of [Formula: see text], mutual dependence among [Formula: see text] is derived by imposing some constraints on [Formula: see text]. For appropriately imposed constraints on [Formula: see text] giving rise to both maximal CP violation and the maximal atmospheric neutrino mixing, we show various specific textures of neutrino mass matrices including the texture with [Formula: see text] derived as the simplest solution to the constraint of [Formula: see text], which is required by the constraint of [Formula: see text] for [Formula: see text]. It is found that Majorana CP violation depends on the phase of [Formula: see text].

Formulas for flavor neutrino masses and their application to texture two zeros

We demonstrate the usefulness of flavour neutrino masses expressed in terms of $M_{ee},M_{e\mu}$ and $M_{e\tau}$. The analytical expressions for the flavour neutrino masses, mass eigenstates and physical CP-violating Majorana phases for texture two zeros are obtained exactly.

Theory prospective on leptonic CP violation

The phenomenology of 3-neutrino mixing, the current status of our knowledge about the 3-neutrino mixing parameters, including the absolute neutrino mass scale, and of the Dirac and Majorana CP violation in the lepton sector are reviewed. The problems of CP violation in neutrino oscillations and of determining the nature – Dirac or Majorana – of massive neutrinos are discussed. The seesaw mechanism of neutrino mass generation and the related leptogenesis scenario of generation of the baryon asymmetry of the Universe are considered. The results showing that the CP violation necessary for the generation of the baryon asymmetry of the Universe in leptogenesis can be due exclusively to the Dirac and/or Majorana CP-violating phase(s) in the neutrino mixing matrix U are briefly reviewed. The discrete symmetry approach to understanding the observed pattern of neutrino mixing and the related predictions for the leptonic Dirac CP violation are also reviewed.

Oscillation of heavy sterile neutrino in decay ofB→μeπ

In a scenario with two almost mass degenerate heavy sterile Majorana neutrinos with a mass $\sim 1$ GeV, we present the semileptonic decay widths of heavy charged pseudoscalars such as $B$ mesons, either lepton-number-violating ($B^{\pm} \to \mu^{\pm} e^{\pm} \pi^{\mp}$), or lepton-number-conserving ($B^{\pm} \to \mu^{\pm} e^{\mp} \pi^{\pm}$), mediated by such on-shell neutrinos. It had been explained in the literature that such decays may be eventually detected, and that they can present even detectable CP violation effects. In this work we point out that, in addition, such decays may present detectable effects of heavy neutrino oscillation, allowing us to extract the oscillation length and thus the heavy neutrino mass difference $\Delta M_N$, as well as a CP-violating Majorana phase.

Neutrino mass matrices with one texture zero and a vanishing neutrino mass

Assuming Majorana nature of neutrinos, we investigate the singular one texture zero neutrino mass matrices in the flavor basis. We find that for the normal mass ordering with $m_1=0$, all the six one texture zero classes are now ruled out at 3$\sigma$ confidence level, whereas for inverted mass ordering with $m_3=0$ only four classes out of total six can accommodate the latest neutrino oscillation data at 3$\sigma$ confidence level. Moreover, only two classes can accommodate the present data at 1$\sigma$ confidence level. We examine the phenomenological implications of the allowed classes for the effective Majorana mass, Dirac and Majorana CP-violating phases. Working within the framework of type-I seesaw mechanism, we present simple discrete Abelian symmetry models leading to all the phenomenologically allowed classes.