Majorana Mass Terms Research Articles

Neutrino mass and nature through its mediation in atomic clock interference

The absolute mass of neutrinos and their nature are presently unknown. Aggregate matter has a coherent weak charge leading to a repulsive interaction mediated by a neutrino pair. The virtual neutrinos are non-relativistic at micron distances, giving a distinct behavior for Dirac versus Majorana mass terms. This effective potential allows for the disentanglement of the Dirac or Majorana nature of the neutrino via magnitude and distance dependence. We propose an experiment to search for this potential based on the concept that the density-dependent interaction of an atomic probe with a material source in one arm of an atomic clock interferometer generates a differential phase. The appropriate geometry of the device is selected using the saturation of the weak potential as a guide. The proposed experiment has the added benefit of being sensitive to gravity at micron distances. A strategy to suppress the competing Casimir–Polder interaction, depending on the electronic structure of the material source, as well as a way to compensate the gravitational interaction in the two arms of the interferometer is discussed.

Electroweak symmetry breaking by gravity

We consider a simple scale-invariant action coupling the Higgs field to the metric scalar curvature R and containing an R2 term that exhibits spontaneous breaking of scale invariance and electroweak symmetry. The coefficient of the R2 term in this case determines the self-coupling of the Higgs boson in the Einstein frame, and the scalaron becomes a dilaton weakly coupled to the Higgs boson. Majorana mass terms for right-handed neutrinos can be generated in a scale-invariant manner by using the Higgs-field invariant; in this case, the existing experimental limits on the Higgs-boson total width rule out Majorana mass values in a certain range. The model inherits the naturalness issues of general relativity connected with the smallness of the gravitational and cosmological constants.

Updated constraints and future prospects on majoron dark matter

Majorons are (pseudo-)Nambu-Goldstone bosons associated with lepton number symmetry breaking due to the Majorana mass term of neutrinos introduced in the seesaw mechanism. They are good dark matter candidates since their lifetime is suppressed by the lepton number breaking scale. We update constraints and discuss future prospects on majoron dark matter in the singlet majoron models based on neutrino, gamma-ray, and cosmic-ray telescopes in the mass region of MeV–10 TeV.

Toward the discovery of matter creation with neutrinoless ββ decay

Observation of neutrino oscillations implies that neutrinos have mass, but one does not know whether they are described by Dirac or Majorana mass terms. The discovery of a Majorana mass would provide a test of the global symmetries of the standard model, and would have implications for the origin of the number of baryons in the Universe. To achieve this one can search for neutrinoless double-beta decay, a rare nuclear decay where two new electrons are created with no antimatter. The next generation of experiments will explore large Majorana neutrino mass values, also testing alternative theoretical models. In this review, devoted to neutrinoless double-beta decay, the particle and nuclear physics aspects involved in predicting the decay rate and the experimental search methods are discussed.

Neutrinoless double beta decay in a left-right symmetric model with a double seesaw mechanism

We discuss a left-right (L-R) symmetric model with the double seesaw mechanism at the TeV scale generating Majorana masses for the active left-handed (LH) flavour neutrinos $\nu_{\alpha L}$ and the heavy right-handed (RH) neutrinos $N_{\beta R}$, $\alpha,\beta = e,\mu,\tau$, which in turn mediate lepton number violating processes, including neutrinoless double beta decay. The Higgs sector is composed of two Higgs doublets $H_L$, $H_R$, and a bi-doublet $\Phi$. The fermion sector has the usual for the L-R symmetric models quarks and leptons, along with three $SU(2)$ singlet fermion $S_{\gamma L}$. The choice of bare Majorana mass term for these sterile fermions induces large Majorana masses for the heavy RH neutrinos leading to two sets of heavy Majorana particles $N_j$ and $S_k$, $j,k=1,2,3$, with masses $m_{N_j} \ll m_{S_k}$. Working with a specific version of the model in which the $\nu_{\alpha L} - N_{\beta R}$ and the $N_{\beta R} - S_{\gamma L}$ Dirac mass terms are diagonal, and assuming that $m_{N_j} \sim (1 - 1000)$ GeV and ${\rm max}(m_{S_k}) \sim (1 - 10)$ TeV, $m_{N_j} \ll m_{S_k}$, we study in detail the new ``non-standard'' contributions to the $0\nu\beta\beta$ decay amplitude and half-life arising due to the exchange of virtual $N_j$ and $S_k$. We find that in both cases of NO and IO light neutrino mass spectra, these contributions are strongly enhanced and are dominant at relatively small values of the lightest neutrino mass $m_{1(3)} \sim (10^{-4} - 10^{-2})$ eV over the light Majorana neutrino exchange contribution. In large part of the parameter space, the predictions of the model for the $0\nu\beta\beta$ decay generalised effective Majorana mass and half-life are within the sensitivity range of the planned next generation of neutrinoless double beta decay experiments LEGEND-200 (LEGEND-1000), nEXO, KamlAND-Zen-II, CUPID, NEXT-HD.

A new viable mass region of dark matter and dirac neutrino mass generation in a scotogenic extension of SM

In this paper, we propose a scotogenic extension of the Standard Model (SM) which can provide a scalar dark matter (DM) candidate in the new, theoretically previously unaddressed, intermediate region ([Formula: see text][Formula: see text]GeV) and also generate light Dirac neutrino masses. In this framework, the SM is extended by three gauge singlet fermions, two singlet scalar fields and one additional scalar doublet along with a continuous global symmetry [Formula: see text] and discrete symmetries [Formula: see text] and [Formula: see text]. These additional symmetries prevent the singlet fermions from obtaining Majorana mass terms along with providing the stability to the DM candidate. It is known that in the case of the scalar singlet DM model, the only region which is not yet excluded is a narrow region close to the Higgs resonance [Formula: see text] — others ruled out from different experimental and theoretical bounds. In the case of the inert doublet model, the mass region ([Formula: see text]–80[Formula: see text]GeV) and the high-mass region (heavier than 550[Formula: see text]GeV) are allowed. This motivates us to explore a parameter range in the intermediate-mass region [Formula: see text][Formula: see text]GeV, which we do in a scotogenic extension of SM with a scalar doublet and scalar singlets. The DM in our model is a mixture of singlet and doublet scalars, in the freeze-out scenario. We constrain the allowed parameter space of the model using the Planck bound on present DM relic abundance, neutrino mass and the latest bound on spin-independent DM-nucleon scattering cross-section from the XENON1T experiment. Further, we constrain the DM parameters from the indirect detection bounds arising from the global analysis of the Fermi-LAT observations of dwarf spheroidal satellite (dSphs) galaxies, Higgs invisible decay and Electroweak Precision Test (EWPT) as well. We find that our model findings may provide a viable DM candidate satisfying all the constraints on DM parameters in the new, previously unexplored mass range ([Formula: see text][Formula: see text]GeV). This new window for the DM candidate could be searched in future experiments along with an explanation of the Dirac mass of neutrinos since so far there is no strong evidence in support of the Majorana nature of neutrino mass.

Preparations for quantum simulations of quantum chromodynamics in 1+1 dimensions. II. Single-baryon β -decay in real time

A framework for quantum simulations of real-time weak decays of hadrons and nuclei in a two-flavor lattice theory in one spatial dimension is presented. A single generation of the Standard Model is found to require 16 qubits per spatial lattice site after mapping to spin operators via the Jordan-Wigner transformation. Both quantum chromodynamics and flavor-changing weak interactions are included in the dynamics, the latter through four-Fermi effective operators. Quantum circuits that implement time evolution in this lattice theory are developed and run on Quantinuum's H1-1 20-qubit trapped ion system to simulate the $\ensuremath{\beta}$-decay of a single baryon on one lattice site. These simulations include the initial state preparation and are performed for both one and two Trotter time steps. The potential intrinsic error-correction properties of this type of lattice theory are discussed, and the leading lattice Hamiltonian required to simulate $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay of nuclei induced by a neutrino Majorana mass term is provided.

The Progress of Investigation on Neutrino Properties

Generally, particle physics plays an important role in the whole modern physics system. Thereinto, neutrino, as an elementary particle found from beta decay, is of great importance to discover its properties and mechanics. With the help of information retrieve and literature review, this paper aims at helping recollecting sorts of knowledge, e.g., the developing history of the principle, different kinds of matrix expressions, field theories etc. Additionally, some possible future developing directions have been proposed. Moreover, plenty of analytical models and experimental approaches for generating massive neutrinos are demonstrated, e.g., Lagrangian and beta decay. More experiments need to be carried out for the sake of verifying the theoretical predictions. Overall, these results offer a guideline for completing the Standard Model and hopefully the Grand Unified Theory, such as Majorana mass term.

Relic challenges for vector-like fermions as connectors to a dark sector

New dark sectors consisting of exotic fields that couple only very feebly to the Standard Model (SM) have strong theoretical motivation and may be relevant to explaining the abundance of dark matter (DM). An important question for such sectors is how they connect to the SM. For a dark sector with a new gauge interaction, a natural connection arises from heavy vector-like fermions charged under both the visible and dark gauge groups. The gauge charges of such fermions imply that one or more of them is stable in the absence of additional sources of dark symmetry breaking. A generic challenge for such connectors is that they can produce too much dark matter or interact too strongly with nuclei if they were ever thermalized in the early universe. In this paper we study this challenge in a simple connector theory consisting of new vector-like electroweak doublet and singlet fermions that also transform under the fundamental representation of a new Abelian gauge force, and we show that these connectors in their minimal form are almost always ruled out by existing direct DM searches. To address this challenge, we investigate two solutions. First, we study mitigating scattering on nuclei by introducing a Majorana mass term for the singlet. And second, we investigate a mixing with SM leptons that allows the connectors to decay while remaining consistent with cosmological tests and searches for charged lepton flavour violation. Both solutions rely on the presence of a dark Higgs field with a specific charge.

Majorana Neutrinos and Clockworked Yukawa Couplings Contribution to Nonobservation of the Rare Leptonic Decayli→ljγ, Clockwork Photon and Clockwork Graviton

The clockwork is an extra-dimensional set-up for generating light particles with exponentially suppressed or hierarchical couplings of light particles with N massive states having comparable masses near the threshold scale of the mechanism in theories which contain no small parameters at the fundamental level. We explore the prospect of charged lepton flavour violation (cLFV) in a clockwork framework which encompasses Dirac mass terms as well as Majorana mass terms for the new clockwork fermions. We deive the masses of the non zero clockwork Majorana masses, and new particles in a clockwork framework and for their Yukawa couplings to the lepton doublets, in the framework where the clockwork parameters are universal. When the new clockwork Majorana masses are non zero, neutrino masses are generated as a result from the exchange of heavy messenger particles such as right handed iso$-$singlet neutrinos or iso$ - $triplet scalar bosons known as the seesaw mechanism. In the case of non zero clockwork Majorana masses, owing to the sizable effective Yukawa couplings of the higher mass modes neutrino masses can only be made tiny by conjecturing large Majorana mass in the teraelectron volt range for allthe clockwork gears. This is apparent from the constraints on the mass scale of the clockwork fermions due to the non-observation of the rare cLFV decay $ \mu\rightarrow e\gamma $, $ \tau \rightarrow \mu \gamma $, $ \tau\rightarrow e\gamma $. A general description of the clockwork mechanism valid for fermions, gauge bosons, and gravitons is discussed here. This mechanism can be implemented with a discrete set of new fields or, in its continuum version, through an extra spatial dimension.

Seesaw mechanism in the R-parity-violating supersymmetric standard model with the gauged flavor U(1)X symmetry

Abstract We study the seesaw mechanism in the supersymmetric standard model (SSM) with the ${\mathbb {Z}}_3$ symmetry called matter triality (M3). The Abelian discrete symmetry prohibits the baryon number violation operators at the (non-)renormalizable level, which ensures proton longevity. The cubic coupling by right-handed neutrinos generates the Majorana mass term after the right-handed sneutrinos develop into the vacuum expectation values. Due to the R-parity violation, the active neutrino masses can be generated not only from the mixings with the right-handed neutrinos but also from those with the minimal SSM neutralinos. We propose a model where M3 is embedded in the gauged flavor symmetry. The flavor charges are constrained by the anomaly cancellation conditions and the requirements to realize the fermion masses and mixing angles in the quark and lepton sectors. We analyze the assignments of the flavor charge, and show that the sterile neutrino mass is allowed to be below the soft supersymmetry-breaking scale, which is constrained by the half-lifetime of the neutrinoless double beta decay.

Modular symmetry anomaly and nonperturbative neutrino mass terms in magnetized orbifold models

We study the modular symmetry anomaly in magnetized orbifold models. The non-perturbative effects such as D-brane instanton effects can break tree-level symmetry. We study which part of the modular symmetry is broken explicitly by Majorana mass terms with three generations of neutrinos. The modular weight of neutrino mass terms does not match with other coupling terms in tree-level Lagrangian. In addition, the $Z_N$ symmetry of the modular flavor symmetry is broken and a certain normal subgroup of the modular flavor symmetry remains in neutrino mass terms.

$$\text {TM}_1$$ neutrino mixing with $$\sin \theta _{13}=\frac{1}{\sqrt{3}}\sin \frac{\pi }{12}$$

We construct a neutrino model using the flavour group \(S_4\times C_4 \times C_3{ \times C_2}\) under the type 1 seesaw mechanism. The vacuum alignments of the flavons in the model lead to \(\text {TM}_1\) mixing with \(\sin \theta _{13}=\frac{1}{\sqrt{3}}\sin \frac{\pi }{12}\). The mixing also exhibits \(\mu \text {-}\tau \) reflection symmetry. By fitting the eigenvalues of the effective seesaw mass matrix with the observed neutrino mass-squared differences, we predict the individual light neutrino masses. The vacuum alignment of the \(S_4\) triplet appearing in the Majorana mass term plays a key role in obtaining the aforementioned \(\text {TM}_1\) scenario. Since the symmetries of the flavour group are not sufficient to define this alignment, we apply the recently proposed framework of the auxiliary group in our model. Using this framework, the \(S_4\) triplet is obtained by coupling together several irreducible multiplets that transform under an expanded flavour group consisting of the original flavour group as well as an auxiliary group. The vacuum alignment of each of these multiplets is uniquely defined in terms of its residual symmetries under the expanded flavour group. As a result, the \(S_4\) triplet constructed from these multiplets also becomes uniquely defined.

Two-body lepton-flavour-violating decays in a 2HDM with soft family-lepton-number breaking

We evaluate the decays {ell}_1^{pm } → {ell}_2^{pm}gamma , Z → {ell}_1^{+}{ell}_2^{-} , and h → {ell}_1^{+}{ell}_2^{-} , where ℓ1 and ℓ2 are charged leptons with different flavours and h is the scalar particle with mass 125.25 GeV, in a two-Higgs-doublet model where all the Yukawa-coupling matrices conserve the lepton flavours but the Majorana mass terms of the right-handed neutrinos break the flavour lepton numbers. We find that (1) the decays {ell}_1^{pm } → {ell}_2^{pm}gamma require large Yukawa couplings and very light right-handed neutrinos in order to be visible, (2) the decays Z → {ell}_1^{+}{ell}_2^{-} will be invisible in all the planned experiments, except in a very restricted range of circumstances, but (3) the decays h → {ell}_1^{+}{ell}_2^{-} may be detected in future experiments for rather relaxed sets of input parameters.

Flavour and CP symmetries in the inverse seesaw

We consider an inverse seesaw mechanism of neutrino mass generation in which the Standard Model is extended by 3+3 (heavy) sterile states, and endowed with a flavour symmetry G_f, G_f=Delta (3 , n^2) or G_f=Delta (6 , n^2), and a CP symmetry. These symmetries are broken in a peculiar way, so that in the charged lepton sector a residual symmetry G_ell is preserved, while the neutral fermion sector remains invariant under the residual symmetry G_nu =Z_2 times CP. We study the concrete setup, where the Majorana mass term for three of the sterile states conserves G_nu , while the remaining mass terms (i.e. couplings of left-handed leptons and heavy sterile states, as well as the Dirac-type couplings among the latter) do not break the flavour or CP symmetry. We perform a comprehensive analysis of lepton mixing for different classes of residual symmetries, giving examples for each of these, and study in detail the impact of the additional sterile states on the predictions for lepton mixing. We further confront our results with those obtained in the model-independent scenario, in which the light neutrino mass matrix leaves the residual symmetry G_nu intact. We consider the phenomenological impact of the inverse seesaw mechanism endowed with flavour and CP symmetries, in particular concerning effects of non-unitarity of the lepton mixing matrix (which strongly constrain the parameter space of the scenario), prospects for neutrinoless double beta decay and for charged lepton flavour violating processes.

Origin of neutrino masses and disappearance ofprimordial antimatter

<p indent="0mm">The standard model (SM) of particle physics has proved to be a huge success in describing the microscopic structures of matter and the behaviors of strong, weak and electromagnetic forces, but it is incomplete in some aspects. For example, the SM itself provides no answer about the origin of tiny neutrino masses, and it fails in accounting for the observed matter-antimatter asymmetry of the Universe. To go beyond the SM, one may wonder whether there exists an intrinsic connection between the solutions to these two fundamental issues in particle physics and cosmology. It is argued that the seesaw mechanism for neutrino mass generation and the associated leptogenesis mechanism for cosmological baryogenesis may pave a way for our deeper understanding of the origin of neutrino masses and mysterious disappearance of primordial antimatter of the Universe. Behind these two mechanisms is the existence of heavy and sterile Majorana neutrinos, which interact with the known (light and active) neutrinos via the Yukawa interactions. The SM contains no right-handed neutrino fields, and hence there is no way to write out a Dirac neutrino mass term. The simplest way to go beyond the SM is to introduce the right-handed neutrino fields and allow for lepton number violation. In this case the right-handed neutrino fields and their charge-conjugate counterparts may constitute a Majorana mass term which, together with the Yukawa interactions between left- and right-handed neutrino fields via the Higgs field, leads us to the origin of tiny Majorana masses for three active neutrinos. Such a seesaw mechanism attributes the smallness of active neutrino masses to the largeness of sterile neutrino masses as compared with the electroweak scale. The lepton-number-violating and CP-violating decays of those heavy degrees of freedom in the early Universe may produce a net lepton-antilepton asymmetry, and the latter may be partly converted into a net baryon-antibaryon asymmetry via the sphaleron process. This is just the leptogenesis mechanism, and it has attracted a lot of attention thanks to the observations of neutrino oscillations in the past decades. The seesaw and leptogenesis scenarios are correlated with each other, and they provide an elegant way of accounting for the cosmological baryon-antibaryon asymmetry and tiny neutrino masses. A pressing question is how to test such a “killing two birds with one stone” picture at low-energy experiments. It seems that a direct test of this picture is extremely difficult or even impossible, but one may always collect various “fossils” of heavy Majorana neutrinos which might have played a crucial role in the early Universe. In this connection it will be greatly helpful to verify the Majorana nature of massive neutrinos by observing the neutrinoless double-beta decays, to measure CP violation in neutrino oscillations and to test unitarity of the 3×3 flavor mixing matrix of three active neutrinos.

Flavored neutrinoless double beta decay

We discuss a mechanism of neutrinoless double beta decay, where neutrinos of different flavours come into play. This is realized by effective flavour-violating scalar interactions. As one consequence, we find that within the normal mass ordering the neutrino effective mass may no longer vanish due to contributions from other flavours. We evaluate the necessary nuclear matrix elements, consider the interference between the standard diagram and the new scalar one, and analyze a UV-complete model that realizes the scalar interaction. Tests of the complete model are possible at colliders and future neutrino experiments. Our scenario represents an alternative mechanism for neutrinoless double beta decay, where nevertheless lepton number violation resides only in Majorana mass terms of light neutrinos.

A dark clue to seesaw and leptogenesis in a pseudo-Dirac singlet doublet scenario with (non)standard cosmology

We propose an appealing alternative scenario of leptogenesis assisted by dark sector which leads to the baryon asymmetry of the Universe satisfying all theoretical and experimental constraints. The dark sector carries a non minimal set up of singlet doublet fermionic dark matter extended with copies of a real singlet scalar field. A small Majorana mass term for the singlet dark fermion, in addition to the typical Dirac term, provides the more favourable dark matter of pseudo-Dirac type, capable of escaping the direct search. Such a construction also offers a formidable scope to radiative generation of active neutrino masses. In the presence of a (non)standard thermal history of the Universe, we perform the detailed dark matter phenomenology adopting the suitable benchmark scenarios, consistent with direct detection and neutrino oscillations data. Besides, we have demonstrated that the singlet scalars can go through CP-violating out of equilibrium decay, producing an ample amount of lepton asymmetry. Such an asymmetry then gets converted into the observed baryon asymmetry of the Universe through the non-perturbative sphaleron processes owing to the presence of the alternative cosmological background considered here. Unconventional thermal history of the Universe can thus aspire to lend a critical role both in the context of dark matter as well as in realizing baryogenesis.

Time evolution of lepton number carried by Majorana neutrinos

Abstract We revisit the time evolution of the lepton family number for an SU(2) doublet consisting of a neutrino and a charged lepton. The lepton family number is defined through the weak basis of the SU(2) doublet, where the charged lepton mass matrix is real and diagonal. The lepton family number carried by the neutrino is defined by the left-handed current of the neutrino family. For this work we assume that the neutrinos have Majorana mass. This Majorana mass term is switched on at time $t=0$ and the lepton family number evolves. Since the operator in the flavor eigenstate is continuously connected to that of the mass eigenstate, the creation and annihilation operators for the two eigenstates are related to each other. We compute the time evolution of all lepton family numbers by choosing a specific initial flavor eigenstate for a neutrino. The evolution is studied for relativistic and non-relativistic neutrinos. The non-relativistic region is of particular interest for the cosmic neutrino background predicted from Big Bang models. In that region we find that the lepton family numbers are sensitive to the Majorana and Dirac phases, the absolute mass, and the mass hierarchy of neutrinos.

Dirac neutrino mass models with a modular S4 symmetry

In this paper, we investigate lepton mass spectra, flavor mixing and CP violation with a modular S4 symmetry under the assumption that neutrinos are Dirac fermions. We find that the Majorana mass term can be forbidden by adjusting the weight of the right-handed neutrino superfields. We study the scenarios where modular forms in the neutrino sector take the lowest non-trivial weight two, while those in the charged-lepton sector vary from two to six. The corrections from renormalization-group running effects to our model have also been discussed in detail. We totally obtain twelve different classes of models and find that ten of them can accommodate current neutrino oscillation data.