The neutrinoless double-beta decay: A test for new physics

The neutrinoless double-beta decay is not allowed in the Standard Model (SM) but it is allowed in most Grand Unified Theories (GUTs). The neutrino must be a Majorana particle (identical with its antiparticle) and must have a mass to allow the neutrinoless double-beta decay. Apart of one claim that the neutrinoless double-beta decay in ⁷⁶Ge is measured, one has only upper limits for this transition probability. But even the upper limits allow to give upper limits for the electron Majorana neutrino mass and upper limits for parameters of GUTs and the minimal R-parity violating supersymmetric model. One further can give lower limits for the vector boson mediating mainly the right-handed weak interaction and the heavy mainly right-handed Majorana neutrino in left-right symmetric GUTs. For that, one has to assume that the specific mechanism is the leading one for the neutrinoless double-beta decay and one has to be able to calculate reliably the corresponding nuclear matrix elements. In the present contribution, one discusses the accuracy of the present status of calculating the nuclear matrix elements and the corresponding limits of GUTs and supersymmetric parameters.     

Suppression of the neutrinoless ββ decay?

The neutrinoless ββ decay rates of ⁷⁶Ge, ⁸²Se, ^{128, 130}Te are calculated in the quasi-particle random appproximation using a realistic effective NN interaction. The reduction of the 0νββ decay nuclear matrix elements due to ground-state correlations is much weaker than that of the 2νββ decay matrix elements, and we can deduce stringent limits on the Majorana neutrino mass and the right-handed leptonic currents from experimental data on νββ decay.     

First results of the search for neutrinoless double-beta decay with the NEMO 3 detector

The NEMO 3 detector, which has been operating in the Fréjus underground laboratory since February 2003, is devoted to the search for neutrinoless double-beta decay (beta beta 0v). The half-lives of the two neutrino double-beta decay (beta beta 2v) have been measured for 100Mo and 82Se. After 389 effective days of data collection from February 2003 until September 2004 (phase I), no evidence for neutrinoless double-beta decay was found from approximately 7 kg of 100Mo and approximately 1 kg of 82Se. The corresponding limits are T1/2(beta beta0v) > 4.6 x 10(23) yr for 100Mo and T1/2(beta beta 0v) > 1.0 x 10(23) yr for 82Se (90% C.L.). Depending on the nuclear matrix element calculation, the limits for the effective Majorana neutrino mass are < 0.7-2.8 e/v for 100Mo and < 1.7-4.9 eV for 82Se.     

Test of physics beyond the standard model in nuclei

The modern theories of Grand Unification (GUT) and SuperSymmetric (SUSY) extensions of Standard Model (SM) suppose that the conservation laws of the SM may be violated to some small degree. The nuclei are well-suited as a laboratory to test fundamental symmetries and fundamental interactions like lepton flavor (LF) and lepton number (LN) conservation. A prominent role between experiments looking for LF and total LN violation play not yet observed processes of neutrinoless double-beta decay (0νββ decay). The GUT and SUSY models offer a variety of mechanisms that allow 0νββ decay to occur. They are based on mixing of Majorana neutrinos and/or R-parity-violation hypothesis. Although the 0νββ-decay has not been seen, it is possible to extract from the lower limits of the lifetime upper limits for the effective electron Majorana neutrino mass, effective right-handed weak-interaction parameters, the effective Majoron coupling constant, R-parity-violating SUSY parameters, etc. A condition for obtaining reliable limits for these fundamental quantities is that the nuclear matrix elements governing this process can be calculated correctly. The nuclear structure wave functions can be tested by calculating the two-neutrino double-beta decay (2νββ decay) for which we have experimental data and not only lower limits as for the 0νββ decay. For open-shell nuclei, the method of choice has been the quasiparticle random-phase approximation (QRPA), which treats Fermion pairs as bosons. It has been found that, by extending the QRPA including fermion commutation relations, better agreement with 2νββ-decay experiments is achieved. This increases also the reliability of conclusions from the upper limits on the 0νββ-decay transition probability. In this work, the limits on the LN-violating parameters extracted from current 0νββ-decay experiments are listed. Studies in respect to future 0νββ-decay experimental projects are also presented.     

Neutrinoless double beta decay and a new limit on the lepton number violation

We have calculated the neutrinoless double beta decay rate of ⁷⁶Ge. We take into account for the first time a relativistic correction to the nuclear current including weak magnetism. Its effect is to cancel a considerable part of the decay amplitude and we obtain less stringent upper limits on the neutrino Majorana mass and the right-handed weak leptonic current compared with previous calculations.     

Do neutrinos have mass?

Limits on neutrino masses are discussed, both from kinematical considerations (3-body weak decays, etc.) and from dynamical neutrino mass effects (oscillations). The Dirac versus Majorana question is addressed as well and typical limits from neutrinoless double-beta decay are presented.     

Angular distribution of electrons in neutrinoless double-beta decay and new physics

For neutrinoless double-beta decay caused by the exchange of light Majorana neutrinos, an expression for the differential width with respect to the angle between the final-electron momenta is obtained on the basis of a Lorentz-invariant effective Lagrangian of the general form. The shape of this angular distribution is analyzed within various extensions of the Standard Model that allow this process—in particular, within theories that involve Majorana super partners and (or) right-handed currents. The angular correlation coefficient for electrons as a function of the mass of the right-handed W boson and the effective Majorana neutrino mass in the decay of the ⁷⁶Ge nucleus is considered within the model involving left—right symmetry.     

A large Hilbert space QRPA and RQRPA calculation of neutrinoless double beta decay

A large Hilbert space is used for the calculation of the nuclear matrix elements governing the light neutrino mass mediated mode of neutrinoless double beta decay (Ovββ-decay) of⁷⁶ Ge,¹⁰⁰ Mo,¹¹⁶ Cd,¹²⁸ Te, and¹³⁶ Xe within the proton-neutron quasiparticle random phase approximation (pn-QRPA) and the renormalized QRPA with proton-neutron pairing (full-RQRPA) methods. We have found that the nuclear matrix elements obtained with the standard pn-QRPA for several nuclear transitions are extremely sensitive to the renormalization of the particle-particle component of the residual interaction of the nuclear hamiltonian. Therefore the standard pn-QRPA does not guarantee the necessary accuracy to allow us to extract a reliable limit on the effective neutrino mass. This behavior already known from the calculation of the two-neutrino double beta decay matrix elements, manifests itself in the neutrinoless double-beta decay but only if a large model space is used. The full-RQRPA, which takes into account proton-neutron pairing and considers the Pauli principle in an approximate way, offers a stable solution in the physically acceptable region of the particle-particle strength. In this way more accurate values on the effective neutrino mass have been deduced from the experimental lower limits of the half-lifes of neutrinoless double beta decay.     

Neutrinoless double-beta decay and related topics

The fundamental importance of searching for neutrinoless double-beta decay (0νββ-decay) is widely recognized. Observation of the decay would tell us that the total lepton number is not conserved and that, consequently, neutrinos are massive Majorana fermions. A brief history of the double-beta decay is presented. The 0νββ-decay is discussed in context of neutrino oscillation data. The perspectives of the experimental 0νββ-decay searches are analyzed. The importance of reliable determination of the 0νββ-decay nuclear matrix elements is pointed out. The problem of distinguishing of the light-neutrino exchange, heavy-neutrino exchange and the trilinear R-parity breaking supersymmetric ( \not R_p \not R_p SUSY) mechanisms of the 0νββ-decay is addressed. Further, the process of resonant neutrinoless double-electron capture (0νɛɛ) is revisited. Arguments are presented that an experimental search for the 0νɛɛ might be feasible.     

Observation of two-neutrino double-beta decay in 136Xe with the EXO-200 detector

We report the observation of two-neutrino double-beta decay in (136)Xe with T(1/2) = 2.11 ± 0.04(stat) ± 0.21(syst) × 10(21) yr. This second-order process, predicted by the standard model, has been observed for several nuclei but not for (136)Xe. The observed decay rate provides new input to matrix element calculations and to the search for the more interesting neutrinoless double-beta decay, the most sensitive probe for the existence of Majorana particles and the measurement of the neutrino mass scale.     

Recent results of the IGEX 76Ge double-beta decay experiment

The International Germanium Experiment (IGEX) has now analyzed 117 mol yr of data from its isotopically enriched (86% ⁷⁶Ge) germanium detectors. Applying pulse shape discrimination (PSD) to the more recent data, the lower bound on the half-life for neutrinoless double-beta decay of ⁷⁶Ge is deduced: T _1/2(0ν)>1.57×10²⁵ yr (90% C.L.). This corresponds to an upper bound on the Majorana neutrino mass parameter, 〈m _ν〉, between 0.33 eV and 1.35 eV depending on the choice of theoretical nuclear matrix elements used in the analysis.     

Investigation of double-beta decay at the Institute of Theoretical and Experimental Physics (ITEP, Moscow)

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.     

Nearly mass-degenerate Majorana neutrinos: Double-beta decay and neutrino oscillations

Assuming equal tree-level Majorana masses for the standard-model neutrinos, either from the canonical seesaw mechanism or from a heavy scalar triplet, I discuss how their radiative splitting may be relevant to neutrinoless double-beta decay and neutrino oscillations.     

Calculation of double beta decay rates and the neutrino mass

Predictions for 2v and 0v double beta decay rates are given for all nuclei with A ⩾ 70, for which double beta decay is energetically allowed. These predictions are based on detailed nuclear structure studies of the beta strength distribution and replace earlier estimates basing mostly on phase space considerations. New and more stringent limits on the Majorana neutrino mass are deduced from existing double beta decay experiments. Since the collective effects arising from spin-isospin as well as quadrupole-quadrupole forces are found to lead to a strong reduction of the nuclear matrix elements for two-neutrino double beta decay, but to have only minor influence on the matrix elements M^0v for the neutrinoless decay mode, the smaller limits for m_v result mainly from the fact that the widely used scaling procedure underestimates the 0_v matrix elements. It is further discussed to what extent interference between different neutrinos affects the obtained mass limits.     

Double-beta decay in gauge theories

Neutrinoless double-beta decay is a very important process both from the particle and nuclear physics point of view. From the elementary particle point of view, it pops up in almost every model, giving rise among others to the following mechanisms: (a) the traditional contributions like the light neutrino mass mechanism as well as the j _L –j _R leptonic interference (λ and η terms), (b) the exotic R-parity-violating supersymmetric (SUSY) contributions. Thus, its observation will severely constrain the existing models and will signal that the neutrinos are massive Majorana particles. From the nuclear physics point of view, it is challenging, because (1) the nuclei, which can undergo double-beta decay, have complicated nuclear structure; (2) the energetically allowed transitions are suppressed (exhaust a small part of all the strength); (3) since in some mechanisms the intermediate particles are very heavy one must cope with the short distance behavior of the transition operators (thus novel effects, like the double-beta decay of pions in flight between nucleons, have to be considered; in SUSY models, this mechanism is more important than the standard two-nucleon mechanism; and (4) the intermediate momenta involved are quite high (about 100 MeV/c). Thus one has to take into account possible momentum-dependent terms of the nucleon current, like modification of the axial current due to PCAC, weak magnetism terms, etc. We find that, for the mass mechanism, such modifications of the nucleon current for light neutrinos reduce the nuclear matrix elements by about 25%, almost regardless of the nuclear model. In the case of heavy neutrino, the effect is much larger and model-dependent. Taking the above effects into account, the needed nuclear matrix elements have been obtained for all the experimentally interesting nuclei A=76, 82, 96, 100, 116, 128, 130, 136, and 150. Then, using the best presently available experimental limits on the half-life of the 0νββ decay, we have extracted new limits on the various lepton-violating parameters. In particular, we find 〈m _ν〉 < 0.3 eV/c ², and, for reasonable choices of the parameters of SUSY models in the allowed SUSY parameter space, we get a stringent limit on the R-parity-violating parameter λ′₁₁₁<4.0×10^?4.     

Double-beta-decay experiments: Present status and prospects for the future

The present status of experiments seeking double-beta decay is surveyed. The results of the most sensitive experiments are discussed. Particular attention is given to describing the NEMO-3 detector, which is intended for seeking the neutrinoless double-beta decay of various isotopes (¹⁰⁰Mo, ⁸²Se, etc.) with a sensitivity as high as T _1/2 ～ 10²⁵ yr, which corresponds to a sensitivity to the Majorana neutrino mass at a level of 0.1 to 0.3 eV. The first results obtained with the NEMO-3 detector are presented. A review of the existing projects of double-beta-decay experiments where it is planned to reach a sensitivity to the Majorana neutrino mass at a level of 0.01 to 0.1 eV is given.     

Structure of nuclear transition matrix elements for neutrinoless double-<Emphasis Type="Italic">β</Emphasis> decay

The structure of nuclear transition matrix elements (NTMEs) required for the study of neutrinoless double-β decay within light Majorana neutrino mass mechanism is disassembled in the PHFB model. The NTMEs are calculated using a set of HFB intrinsic wave functions, the reliability of which has been previously established by obtaining an overall agreement between the theoretically calculated spectroscopic properties and the available experimental data. Presently, we study the role of short-range correlations, radial evolution of NTMEs and deformation effects due to quadrupolar correlations. In addition, limits on effective light neutrino mass 〈m _ν 〉 are extracted from the observed limits on half-lives T ₁^2/0ν of neutrinoless double-β decay.     

Neutrinoless double beta decay in the LHC era

Once neutrinoless double beta decay is discovered, the question which mechanism triggers the decay becomes crucial for drawing any conclusion about the concrete physics underlying the process, like the neutrino Majorana mass. For example, in the minimal supersymmetric extension with R-parity violation both neutrino Majorana masses and superpartners can trigger the decay. We show that in this case, if the decay is triggered by superpartners, there exist good prospects to observe single slepton production at the LHC. Resonant single slepton production at the LHC can therefore discriminate between the neutrinoless double beta decay mechanism and others.     

Mechanisms of neutrinoless double-beta decay: A comparative analysis of several nuclei

The neutrinoless double beta decay of several nuclei that are of interest from the experimental point of view (⁷⁶Ge, ⁸²Se, ¹⁰⁰Mo, ¹³⁰Te, and ¹³⁶Xe) is investigated on the basis of a general Lorentzinvariant effective Lagrangian describing physics effects beyond the Standard Model. The half-lives and angular-correlation coefficients for electrons are calculated for various decay mechanisms associated, in particular, with the exchange of Majorana neutrinos, supersymmetric particles (with R-parity violation), leptoquarks, and right-handed W _R bosons. The effect of theoretical uncertainties in the values of relevant nuclear matrix elements on decay features is considered.     

Neutrinoless double-beta decay—status of evidence and future

Double-beta decay is indispensable to solve the question of the neutrino mass matrix together with ν oscillation experiments. Recent analysis of the most sensitive experiment in the last eight years—the Heidelberg-Moscow experiment in Gran Sasso—yields evidence for the neutrinoless decay mode at a 97% C.L. This result is the first indication for lepton number violation and for the neutrino to be a Majorana particle. We give the present status of the analysis in these proceedings. It excludes several of the neutrino mass scenarios allowed from present neutrino oscillation experiments—essentially only degenerate and partially degenerate mass scenarios survive. To improve the present result, considerably enlarged experiments are required, such as GENIUS. A GENIUS Test Facility has just been funded and will come into operation by the end of 2002.