Neutrino Majorana masses from string theory instanton effects

Assuming a Zee-like matrix for the right-handed neutrino Majorana masses in the see-saw mechanism, one gets maximal mixing for vacuum solar oscillations, a very small value for $U_{e3}$ and an approximate degeneracy for the two lower neutrino masses. The scale of right-handed neutrino Majorana masses is in good agreement with the value expected in a SO(10) model with Pati-Salam $SU(4)\ts SU(2)\ts SU(2)$ intermediate symmetry.

This paper investigates non-thermal leptogenesis from inflaton decays in the minimal extension of the canonical type-I seesaw model, where a complex singlet scalar ϕ is introduced to generate the Majorana masses of right-handed neutrinos (RHNs) and to play the role of inflaton. First, we systematically study non-thermal leptogenesis with the least model dependence. We give a general classification of the parameter space and find four characteristic limits by carefully examining the interplay between inflaton decay into RHNs and the decay of RHNs into the standard-model particles. Three of the four limits are truly non-thermal, with a final efficiency larger than that of thermal leptogenesis. Two analytic estimates for these three limits are provided with working conditions to examine the validity. In particular, we find that the strongly non-thermal RHNs scenario occupies a large parameter space, including the oscillation-preferred K range, and works well for a relatively-low reheating temperature TRH ≥ 103 GeV, extending the lower bound on the RHN mass to 2 × 107 GeV. The lepton flavor effects are discussed. Second, we demonstrate that such a unified picture for inflation, neutrino masses, and baryon number asymmetry can be realized by either a Coleman-Weinberg potential (for the real part of ϕ) or a natural inflation potential (for the imaginary part of ϕ). The allowed parameter ranges for successful inflation and non-thermal leptogenesis are much more constrained than those without inflationary observations. We find that non-thermal leptogenesis from inflaton decay offers a testable framework for the early Universe. It can be further tested with upcoming cosmological and neutrino data. The model-independent investigation of non-thermal leptogenesis should be useful in exploring this direction.

We consider the seesaw model with two right-handed neutrinos, $N_1$ and $N_2$, the masses of which are hierarchical, and investigate their contribution to the neutrinoless double beta ($0 \nu \beta \beta$) decay. Although the lepton number is broken by the Majorana masses of right-handed neutrinos, such decay processes can be absent in some cases. We present a possibility where the lighter $N_1$ gives a destructive contribution to the decay of active neutrinos by choosing the specific mixing elements of $N_1$, while $N_2$ is sufficiently heavy not to contribute to the $0 \nu \beta \beta$ decay. In this case the mixing elements of $N_1$ in the charged current interaction are determined by its mass and the Majorana phase of active neutrinos. We then study the impacts of such a possibility on the direct search for $N_1$. In addition, we discuss the consequence of the case when the $0 \nu \beta \beta$ decay in one specific nucleus is absent.

Neutrino mass requires new physics beyond the Standard Model: sterile neutrinos are one such example. In general the mass scale of such particles is unknown, so that different model building scenarios arise. The aim of this thesis is to accommodate light sterile neutrinos in working
\nmodels and study the phenomenological consequences. Indeed, sterile neutrinos at the eV scale could explain observed short-baseline anomalies, whereas keV-scale warm dark matter particles could resolve tensions in the standard cosmological model. Different A4 flavour symmetry models
\nare modified to include sterile neutrinos, with the Froggatt-Nielsen mechanism controlling their mass spectrum and higher-order effects explicitly taken into account. The resulting signatures in neutrinoless double beta decay are focussed on. In addition, the connection between that process and neutrino mass is studied in the left-right symmetric model: the multitude of contributions are categorised and various special cases are studied numerically. The role of mixed helicity diagrams is emphasised, and the inverse neutrinoless double beta decay process at a linear collider is analysed in detail. These and other experimental signatures will be crucial in deciphering the nature and origin of neutrino mass.

We present a new viable benchmark scenario under the current experimental data for the model which can explain tiny mass of active neutrinos and dark matter, as a summary of Ref. [1]. Majorana masses of right-handed neutrinos are given by the spontaneous breaking of the U(1)B−L gauge symmetry above the electroweak scale, and tiny neutrino masses are radiatively induced by quantum effects of particles of the dark sector including dark matter candidates. We first show benchmark points which satisfy current experimental data, and then give comments on how this model can be tested at collider experiments.

We explore the big-bang nucleosynthesis (BBN) constraint on heavy neutrino that is a mixture of gauge-singlet fermion and active neutrinos in the Standard Model. We work in the minimal model with only two parameters, the heavy neutrino mass m4 and the mixing parameter |Ua4|2, where a=e, μ, or τ stands for the active neutrino flavor. We show that both the early Universe production mechanism and decay products of the heavy neutrino are determined by m4 and |Ua4|2, with little room for further assumptions. This predictability allows us to present a portrait of the entire BBN excluded parameter space. As a novel result, we derive the lower boundary of the BBN exclusion in the |Ua4|2 versus m4 parameter space. Our analysis includes various effects including temporary matter domination, energy injections in the form of charged mesons, photons, and light neutrinos. The BBN constraint is complementary to the terrestrial search for heavy neutrinos (heavy neutral leptons) behind the origin of neutrino masses and a portal to the dark sector.

We show a TeV-scale seesaw model where Majorana neutrino masses, the dark\nmatter mass, and stability of the dark matter can be all originated from the\nU(1)_{B-L} gauge symmetry. Dirac mass terms for neutrinos are forbidden at the\ntree level by U(1)_{B-L}, and they are induced at the one-loop level by\nspontaneous U(1)_{B-L} breaking. The right-handed neutrinos can be naturally at\nthe TeV-scale or below because of the induced Dirac mass terms with loop\nsuppression. Such right-handed neutrinos would be discovered at the CERN Large\nHadron Collider (LHC). On the other hand, stability of the dark matter is\nguaranteed without introducing an additional Z_2 symmetry by a remaining global\nU(1) symmetry after the U(1)_{B-L} breaking. A Dirac fermion Psi_1 or a complex\nneutral scalar s^0_1 is the dark matter candidate in this model. Since the dark\nmatter (Psi_1 or s^0_1) has its own B-L charge, the invisible decay of the\nU(1)_{B-L} gauge boson Z' is enhanced. Experimental constraints on the model\nare considered, and the collider phenomenology at the LHC as well as future\nlinear colliders is discussed briefly.\n

“If we accept the view of complete symmetry between positive and negative electric charge so far as concerns the fundamental laws of Nature, we must regard it rather as an accident that the Earth (and presumably whole solar system), contains a preponderance of negative electrons and positive protons. . ..” This is a sentence in the Nobel Lecture given by Paul A. M. Dirac in 1933. 1) This is the first proposal for baryon-anti-baryon symmetric universe. However, astrophysical observations have ruled out the presence of antimatter in the present universe up to the scale of clusters of galaxies. If our universe indeed began baryon symmetric, those imbalances in numbers of baryons and anti-baryons must be generated by some physical processes in the early universe. I show, in this talk, that decays of the heavy (right-handed) Majorana neutrinos in the early universe generate the imbalances between baryon and anti-baryon numbers. The presence of super heavy (right-handed) Majorana neutrinos is an important prediction of unified theories beyond the standard model. An integration of the heavy Majorana neutrinos induces very small masses for neutrinos via the seesaw mechanism. 2) Thus, small neutrino masses is a reflection of unification at very high energy scale. It is quite natural to consider that the heavy Majorana neutrinos are produced thermally in the early universe. When the temperature of the universe cools down to the masses of the heavy Majorana neutrinos, the heavy neutrinos begin to decay into Higgs boson and lepton or Higgs boson and anti-lepton. The decay may produce the lepton-number asymmetry if CP invariance is violated in the decay processes. The CP invariance can be easily violated by phases in new complex Yukawa coupling of Higgs boson to the right-handed neutrinos and left-handed leptons. The decay processes can easily be out of thermal equilibrium. Thus, the decay processes of heavy Majorana neutrinos can satisfy three Sakharov conditions 3) for baryogenesis. This produced lepton-number asymmetry is converted into the baryon-number asymmetry in the present universe through non-perturbation effects of the electroweak gauge theory. 5) This is called “leptogenesis”. 4) I show that the neutrino masses observed in various neutrino-oscillation experiments are just in the range predicted by the thermal leptogenesis. 6)

We evaluate the Schechter-Valle (Black Box) theorem quantitatively by considering the most general Lorentz invariant Lagrangian consisting of point-like operators for neutrinoless double beta decay. It is well known that the Black Box operators induce Majorana neutrino masses at four-loop level. This warrants the statement that an observation of neutrinoless double beta decay guarantees the Majorana nature of neutrinos. We calculate these radiatively generated masses and find that they are many orders of magnitude smaller than the observed neutrino masses and splittings. Thus, some lepton number violating New Physics (which may at tree-level not be related to neutrino masses) may induce Black Box operators which can explain an observed rate of neutrinoless double beta decay. Although these operators guarantee finite Majorana neutrino masses, the smallness of the Black Box contributions implies that other neutrino mass terms (Dirac or Majorana) must exist. If neutrino masses have a significant Majorana contribution then this will become the dominant part of the Black Box operator. However, neutrinos might also be predominantly Dirac particles, while other lepton number violating New Physics dominates neutrinoless double beta decay. Translating an observed rate of neutrinoless double beta decay into neutrino masses would then be completely misleading. Although the principal statement of the Schechter-Valle theorem remains valid, we conclude that the Black Box diagram itself generates radiatively only mass terms which are many orders of magnitude too small to explain neutrino masses. Therefore, other operators must give the leading contributions to neutrino masses, which could be of Dirac or Majorana nature.

Sterile massive neutrinos are a natural extension of the standard model of elementary particles. The energy density of the extra sterile massive states affects cosmological measurements in an analogous way to that of active neutrino species. We perform here an analysis of current cosmological data and derive bounds on the masses of the active and the sterile neutrino states, as well as on the number of sterile states. The so-called (3 + 2) models, with three sub-eV active massive neutrinos plus two sub-eV massive sterile species, is well within the 95% CL allowed regions when considering cosmological data only. If the two extra sterile states have thermal abundances at decoupling, big bang nucleosynthesis bounds compromise the viability of (3 + 2) models. Forecasts from future cosmological data on the active and sterile neutrino parameters are also presented. Independent measurements of the neutrino mass from tritium beta-decay experiments and of the Hubble constant could shed light on sub-eV massive sterile neutrino scenarios.

We present an alternative formulation of the left-right symmetric theory\nwhere the scalar sector consists of two Higgs doublets which differs from the\nstandard version of the left-right model that makes use of $L-$ and $R-$ Higgs\ntriplets and a Higgs bi-doublet. The basic idea is to consider few extra\ncharged iso-singlet fields and the fermion masses can be realized by\nintegrating out these heavy isosinglet fields. We also give a detailed\ndiscussion on neutrinoless double beta decay in this particular left-right\nsymmetric theory where the right-handed Majorana neutrino can be of MeV range.\nWith this right-handed Majorana mass around MeV scale, the contribution to\nneutrinoless double beta decay coming from the right-handed current can be\ncomparable with the contributions coming from the standard left-handed sector\nonly if the right-handed gauge boson mass is around 5 TeV, and with this\noperative scale of $W_R$ around few TeV, it is possible to probe at LHC. We\nhave briefly commented on cosmological constraints coming from the big-bang\nnucleosynthesis and Universe cosmology to the right-handed neutrinos involved\nin this discussion.\n

We demonstrate how a class of non-supersymmetric SO(10) GUT with asymmetric left–right theory SU(2)L × U(1)R × U(1)B−L × SU(3)C and Pati–Salam theory SU(2)L × SU(2)R × SU(4)C as intermediate symmetry breaking steps leads to successful gauge coupling unification satisfying proton decay constraints. The motivation behind this work is two fold: firstly to study the renormalization group evolution equations for gauge couplings by keeping right-handed neutral gauge boson ZR around LHC energy range leading interesting dilepton searches at collider while fixing charge partner of the gauge boson WR at very high scale; secondly to explain neutrino masses and associated lepton number violating process like neutrinoless double beta decay in three possible cases depending on how SU(2)L × U(1)R × U(1)B−L × SU(3)C breaks down to SM. The presence of Pati–Salam symmetry and Pati–Salam symmetry with D-parity (discrete left–right symmetry leading to gL = gR) at highest scale is to allow two gauge couplings and thereby ensuring precision unification for gauge couplings. We focus on neutrino mass and neutrinoless double beta decay for one particular case where TeV scale asymmetric left–right theory is spontaneously broken down to SM with non-zero VEV of both Higgs doublets with B − L = −1 and Higgs triplets with B − L = 2. We include one extra fermion singlet per generation in order to implement gauged extended seesaw where light neutrino mass is governed by dominant type-II seesaw mechanism whereas type-I seesaw contribution is cancelled out. Since light neutrino mass formula is independent of Dirac neutrino mass matrix, the value of Dirac neutrino mass is taken to be up-type quark mass matrix which is a characteristics of Pati–Salam symmetry relating quarks with leptons. This can lead to non-unitarity effects in leptonic sector and induce lepton flavor violation. We present analytic relation for effective Majorana mass parameter and corresponding half-life arising from new physics contributions due to purely left-handed currents through exchange of heavy right-handed neutrinos and sterile neutrinos. We numerically estimate effective Majorana mass parameter and half-life versus lightest neutrino mass and derive lower bound on lightest neutrino mass by saturating with experimental bounds like GERDA Phase-II, KamLANDZen and EXO.

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.

We investigate cosmological predictions on the early universe based on the noncommutative geometry (NCG) models of gravity coupled to matter. Using the renormalization group analysis for the standard model with right-handed neutrinos and Majorana mass terms, which is the particle
\nphysics content of the most recent NCG models, we analyze the behavior of the coefficients of the gravitational and cosmological terms in the Lagrangian derived from the asymptotic expansion of the spectral action functional of NCG. We find emergent Hoyle–Narlikar and conformal
\ngravity at the see-saw scales and a running effective gravitational constant, which affects the propagation of gravitational waves and the evaporation law of primordial black holes and provides Linde models of negative gravity in the early universe. The same renormalization group
\nanalysis also governs the running of the effective cosmological constant of the model. The model also provides a Higgs-based slow-roll inflationary mechanism, for which one can explicitly compute the slow-roll parameters.
\nThe particle physics content allows for dark matter models based on sterile neutrinos with Majorana mass terms.

Neutrinos can gain mass from coupling to an ultralight field in slow roll. When such a field is displaced from its minimum, its vev acts just like the Higgs vev in spontaneous symmetry breaking. Although these masses may eventually vanish, they do it over a very long time. The theory is technically natural, with the ultralight field-dependent part being the right-handed Majorana mass. The mass variation induced by the field correlates with the cosmological evolution. The change of the mass term changes the mixing matrix, and therefore suppresses the fraction of sterile neutrinos at earlier times and increases it at later times. Since the issue of quantum gravity corrections to field theories with large field variations remains open, this framework may give an observational handle on the Weak Gravity Conjecture.