On the quantitative impact of the Schechter-Valle theorem

We give a review on neutrino models in which Majorana neutrino masses are generated radiatively through loop diagrams. In particular, we concentrate on the two-loop models which contain extra doubly charged singlet [Formula: see text] and triplet [Formula: see text] scalars beyond the Standard Model so that the new Yukawa [Formula: see text] and effective [Formula: see text] couplings can be induced. In these two-loop models, we find that the neutrino mass spectrum is a normal hierarchy and the rate of the neutrinoless double beta decay [Formula: see text] can be large as it is dominated by the short-distance tree contribution. In addition, by using the neutrino oscillation data and comparing with the global fitting result in the literature, we find a unique neutrino mass matrix and predict the Dirac and two Majorana CP phases to be [Formula: see text], [Formula: see text] and [Formula: see text] with [Formula: see text], respectively.

We study the general phenomenology of neutrinoless double beta decay in seesaw models. In particular, we focus on the dependence of the neutrinoless double beta decay rate on the mass of the extra states introduced to account for the Majorana masses of light neutrinos. For this purpose, we compute the nuclear matrix elements as functions of the mass of the mediating fermions and estimate the associated uncertainties. We then discuss what can be inferred on the seesaw model parameters in the different mass regimes and clarify how the contribution of the light neutrinos should always be taken into account when deriving bounds on the extra parameters. Conversely, the extra states can also have a significant impact, canceling the Standard Model neutrino contribution for masses lighter than the nuclear scale and leading to unobservable neutrinoless double beta decay amplitudes even if neutrinos are Majorana particles. In particular, the decay rate is reduced by at least six orders of magnitude for masses of the extra states below 1 MeV in absence of extra contributions. We also discuss how seesaw models could reconcile large rates of neutrinoless double beta decay with more stringent cosmological bounds on neutrino masses.

The effective Majorana mass which determines the rate of the neutrinoless double beta ((ββ)0ν-)decay, |<m> | , is considered in the case of three-neutrino mixing and massive Majorana neutrinos. Assuming a rather precise determination of the parameters characterizing the neutrino oscillation solutions of the solar and atmospheric neutrino problems has been made, we discuss the information a measurement of |<m> | ∼> (0.005−0.010) eV can provide on the value of the lightest neutrino mass and on the CP-violation in the lepton sector. The implications of combining a measurement of |<m> | with future measurement of the neutrino mass mνe in 3 H β−decay experiments for the possible determination of leptonic CP-violation are emphasized.

The rate of neutrinoless double beta decay between pairs of single-beta emitters is computed. The ejection of electrons with a kinetic energy higher than ${Q}_{\ensuremath{\beta}}$ is the experimental signature for this phenomenon. The probability of $\ensuremath{\beta}{\ensuremath{\beta}}_{0\ensuremath{\nu}}$ occurrence is proportional to the $\frac{4}{3}$ power of the volume of the radioactive source.

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 study of the neutrinoless double beta(0νββ)decay mode can provide us with important information on the neutrino properties, particularly on the electron neutrino absolute mass. In this work we revise the present constraints on the neutrino mass parameters derived from the0νββdecay analysis of the experimentally interesting nuclei. We use the latest results for the phase space factors (PSFs) and nuclear matrix elements (NMEs), as well as for the experimental lifetime limits. For the PSFs we use values computed with an improved method reported very recently. For the NMEs we use values chosen from the literature on a case-by-case basis, taking advantage of the consensus reached by the community on several nuclear ingredients used in their calculation. Thus, we try to restrict the range of spread of the NME values calculated with different methods and, hence, to reduce the uncertainty in deriving limits for the Majorana neutrino mass parameter. Our results may be useful to have an updated image on the present neutrino mass sensitivities associated with0νββmeasurements for different isotopes and to better estimate the range of values of the neutrino masses that can be explored in the future double beta decay (DBD) experiments.

Assuming 3-ν mixing and massive Majorana neutrinos, we analyze the possibility of establishing the existence of CP violation associated with Majorana neutrinos in the lepton sector by (i) measuring of the effective Majorana mass |〈m〉| in neutrinoless double beta decay with a sufficient precision and (ii) by measuring of, or obtaining a stringent upper limit on, the lightest neutrino mass m1. Information on m1 can be obtained in the 3H β-decay experiment KATRIN and from astrophysical and cosmological observations. Proving that the indicated CP violation takes place requires, in particular, a relative experimental error on the measured value of |〈m〉| not bigger than 20%, a “theoretical uncertainty” in the value of |〈m〉| due to an imprecise knowledge of the corresponding nuclear matrix elements smaller than a factor of 2, a value of tan2θ⊙≳0.55, and values of the relevant Majorana CP-violating phases typically within the intervals of ∼(π2–3π4) and ∼(5π4–3π2). In the case of, e.g., quasi-degenerate neutrino mass spectrum it requires also that the neutrino masses have values not smaller than ∼0.7 eV.

Investigation of neutrinoless double-beta (2β0ν) decay is presently being considered as one of the most important problems in particle physics and cosmology Interest in the problem was quickened by the observation of neutrino oscillations. The results of oscillation experiments determine the mass differences between different neutrino flavors, and the observation of neutrinoless decay may fix the absolute scale and the hierarchy of the neutrino masses. Investigation of 2β0ν decay is the most efficient method for solving the problem of whether the neutrino is a Dirae or a Majorana particle, Physicists from the Institute of Theoretical and Experimental Physics (ITEP, Moscow) have been participating actively in solving this problem. They initiated and pioneered the application of semiconductor detectors manufactured from enriched germanium to searches for the double-beta decay of 76Ge. Investigations with 76Ge provided the most important results. At present, ITEP physicists are taking active part in four very large projects, GERDA. Majorana, EXO, and NEMO, which are capable of recording 2β0ν decay at a Majorana neutrino mass of 〈m ν〉 ≈ 10−2 eV.

Recent results from neutrino oscillation experiments have convincingly demonstrated that neutrinos have mass and they can mix. The neutrinoless double beta decay is the most sensitive process to determine the absolute scale of the neutrino masses, and the only one that can distinguish whether neutrino is a Dirac or a Majorana particle. A key ingredient for extracting the absolute neutrino masses from neutrinoless double beta decay experiments is a precise knowledge of the nuclear matrix elements (NME) for this process. Newly developed shell model approaches for computing the NME and half‐lifes for the two‐neutrino and neutrinoless double beta decay modes using modern effective interactions are presented. The implications of the new results on the experimental limits of the effective neutrino mass are discussed by comparing the decays of 48Ca and 76Ge.

The νM SM is defined as the SM extended to include dimension-5 operators. In this model neutrino masses violate lepton number, and two parameters of the lepton mixing matrix, the Majorana phases, are yet to be constrained. One combination of these phases and the neutrino masses, often denoted by mee, is probed by neutrinoless double beta decays (0νββ). We explore what information may be obtained beyond 0νββ, and how it depends on the lightest neutrino mass. We point out that with current central values of the mixing parameters, ∆Le = 2 and ∆Le = ∆Lμ = 1 (or ∆Le = 2 and ∆Lμ = 2) processes cannot simultaneously vanish, providing a no-lose theorem, in principle, for excluding the νM SM, even in the case of normal mass ordering.

An interesting mass relation between down type quarks and charged leptons has been recently predicted within a supersymmetric SU(3)_c \times SU(2)_L \times U(1)_Y model based on the A4 flavor symmetry. Here we propose a simple extension which provides an adequate full description of the quark sector. By adding a pair of vector-like up-quarks we show how the CKM entries Vub, Vcb, Vtd and Vts arise from deviations of the unitarity. We perform an analysis including the most relevant observables in the quark sector, such as oscillations and rare decays of Kaons, Bd and Bs mesons. In the lepton sector, model predicts an inverted hierarchy for the neutrino masses leading to a potentially observable rate of neutrinoless double beta decay.

The present state of the problem of the double neutrinoless beta decay, 2β(0ν), and related questions is reviewed. Various mechanisms for ΔL = 2 transitions in models with spontaneous violation of lepton number (L) conservation are discussed. From the standpoint of unified gauge theories, a Majorana neutrino mass would be the most probable reason for processes with ΔL = 2 (if they occur). The 2β(0ν) decay is compared with other phenomena which are sensitive to the neutrino mass. It follows from this comparison that the 2β(0ν) decay is essentially the only process which could be detected at the present level of experimental capabilities and which might tell us about the nature of the neutrino mass, if this mass is some tens of electron volts.

Double beta decay, the conversion of a nucleus changing the atomic number Z by two units while leaving the atomic mass A constant, is an extremely rare nuclear decay. It can occur via the emission of two electrons or two positrons, double electron capture or a mixed mode depending on the available Q-value. Furthermore, the neutrino-less mode is of major importance for neutrino physics. This mode violates the lepton number by two units and its observation would point towards physics beyond the Standard Model. The standard interpretation is via the exchange of a light Majorana neutrino, the mass of which could be measured via a half-life determination of double beta decay. There exist 11 isotopes for the double electron mode with a Q-value above 2 MeV, and for those considered for experimental searches, the neutrino-accompanied mode has been measured in the last decade. In recent years various new developments have occurred in almost all aspects related to double beta decay. With all the mixing angles of the PMNS leptonic mixing matrix measured, the regions of interest are well determined. Furthermore, with the launch of the LHC the existence of possible TeV particles contributing to neutrino-less double beta decays can be explored, complementing the searches in underground experiments. Nuclide pairs with the potential of degenerate nuclear states which would lead to a resonance enhancement of neutrino-less double electron capture were intensively searched for with Penning traps and caused a revival of this process. Last but not least, massive progress has been made in the involved conversion factors from the experimentally accessible half-life to the quantity of interest, the neutrino mass. New phase space factors were calculated and new approaches like the interacting boson model or energy density functional approaches joined the nuclear shell model and QRPA calculations to determine the involved nuclear transitions matrix elements. This is accompanied by a massive experimental program to improve the input parameters for these calculations using charge-exchange reactions, nucleon transfer reactions and muon capture. Furthermore, Penning traps have measured almost all relevant Q-values to sub-keV precision. All these exciting new developments over the last few years triggered the idea of a focus section in Journal of Physics G: Nuclear and Particle Physics on double beta decay during a workshop on the topic held in Dresden in July 2010. In addition to the research topics mentioned before, this focus section also covers the implication of double beta decay for current particle physics and theories beyond the Standard Model.

Nuclear double beta decay is one of the most promising tools for probing beyond-the-standard-model physics on beyond-accelerator energy scales. It is already now probing the TeV scale, on which new physics should manifest itself according to theoretical expectations. Only in the early 1980s was it known that double beta decay yields information on the Majorana mass of the exchanged neutrino. At present, the sharpest bound for the electron neutrino mass arises from this process. It is only in the last 10 years that the much more far-reaching potential of double beta decay has been discovered. Today, the potential of double beta decay includes a broad range of topics that are equally relevant to particle physics and astrophysics, such as masses of heavy neutrinos, of sneutrinos, as SUSY models, compositeness, leptoquarks, left-right symmetric models, and tests of Lorentz symmetry and equivalence principle in the neutrino sector. Double beta decay has become indispensable nowadays for solving the problem of the neutrino mass spectrum and the structure of the neutrino mass matrix - together with present and future solar and atmospheric neutrino oscillation experiments. Some future double beta experiments (like Genius) will be capable to be simultaneously neutrino observatories for double beta decay and low-energy solar neutrinos, and observatories for cold dark matter of ultimate sensitivity. This invaluable book outlines the development of double beta research from its beginnings until its most recent achievements, and also presents the outlook for its highly exciting future.

The renormalizable couplings of the Standard Model are invariant under two accidental global symmetries, which correspond to conserved baryon and lepton numbers. In this thesis, we discuss possible roles of these symmetries in extension of the Standard Model. Two approaches are considered: explicit violation of lepton number by two units in the renormalizable couplings of the Lagrangian, and promotion of the global symmetries to local gauge symmetries that are spontaneously broken. The former approach directly leads to Majorana neutrino masses and neutrinoless double beta decay. We discuss the interplay of the contributions to this decay in a one-loop neutrino mass model, the colored seesaw mechanism. We find that, depending on the parameters of the model, both the light Majorana neutrino exchange and the contribution of the new colored particles may be dominant. Additionally, an experimental test is presented, which allows for a discrimination of neutrinoless double beta decay from unknown nuclear background using only one isotope. In the latter approach, fascinating implications originate from the attempt to write down an anomaly-free and spontaneously broken gauge theory for baryon and lepton numbers, such as an automatically stable dark matter candidate. When gauging the symmetries in a left–right symmetric setup, the same fields that allow for an anomaly-free theory generate neutrino masses via the type III seesaw mechanism.