The effect of weak magnetism and induced pseudoscalar coupling in neutrinoless double-beta decay

In calculating the amplitude of the majorana neutrino-mass mechanism of neutrinoless double-beta decay (0νββ-decay), several approximations of the nucleon current have been done. for example, effects from induced current such as weak magnetism and pseudoscalar coupling have been neglected. we shall show in this work that, although such terms do not contribute significantly to the 2νββ-decay amplitude, they are important in the case of 0νββ decay. performing calculations within the renormalized quasiparticle random phase approximation (pn-rqrpa) for all nuclei undergoing double-beta decay in the region a=76 to a=150, we have found that these additional contributions of the nucleon current reduce considerably the matrix elements in all cases for the light neutrino as well as for the heavy neutrino mass. in the light-neutrino mass, we find reductions up to thirty percent, while in the heavy-neutrino mass, up to almost a factor of five. these reductions make the limits on the lepton-number-violating parameters 〈m _ν〉 and η_N less stringent.     

Theory of neutrinoless double beta decay—A brief review

Neutrinoless double decay (0νββ-decay) is a unique probe for lepton number conservation and neutrino properties. This is a process with long and interesting history with important implications for particle physics and cosmology, but its observation is still elusive. The search for the 0νββ-decay represents the new frontiers of neutrino physics, allowing to determine the Majorana nature of neutrinos and to fix the neutrino mass scale and possible CP violation effects, which could explain the matter-antimatter asymmetry in the Universe. At present a complete theory is missing and, thus, to motivate and guide the experiments the mechanism mediated by light neutrinos is mostly considered. The subject of interest is an effective mass of Majorana neutrinos, which can be deduced from the measured half-life, once this process is definitely observed. The accuracy of the determination of this quantity is mainly determined by our knowledge of the nuclear matrix elements. There is a request to evaluate them with high precision, accuracy and reliability. Recently, there is an increased interest to the resonant neutrinoless double electron capture, which may also establish the Majorana nature of neutrinos. This possibility is considered as alternative and complementary to searches for the 0νββ-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.     

Renormalized proton- neutron QRPA and double beta decay of 82Se to excited states in 82Kr

We apply the self-consistent renormalized proton-neutron QRPA (RQRPA) method to calculate the two-neutrino double beta (2νββ) decay matrix elements associated with the ground-state and excited-state transitions of the ⁸²Se → ⁸²Kr decay. The RQRPA method is an extension of the pnQRPA method and promotes the Pauli exclusion principle violated by the pnQRPA ground state and yields more stable nuclear matrix elements with increasing strength of the proton-neutron interaction. In the present work the RQRPA wave functions are also used to evaluate 2νββ-decay rates to excited final states. The resulting theoretical half lives are compared with the new stringent experimental limits obtained by using a HPGe detector and external sources of enriched selenium.     

Chiral two-body currents in nuclei: Gamow-Teller transitions and neutrinoless double-beta decay

We show that chiral effective field theory (EFT) two-body currents provide important contributions to the quenching of low-momentum-transfer Gamow-Teller transitions, and use chiral EFT to predict the momentum-transfer dependence that is probed in neutrinoless double-beta (0νββ) decay. We then calculate for the first time the 0νββ decay operator based on chiral EFT currents and study the nuclear matrix elements at successive orders. The contributions from chiral two-body currents are significant and should be included in all calculations.     

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.     

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.     

Towards the meV limit of the effective neutrino mass in neutrinoless double-beta decays

We emphasize that it is extremely important for future neutrinoless double-beta(0νββ)decay experiments to reach the sensitivity to the effective neutrino mass|mββ|≈1 meV.With such a sensitivity,it is highly possible to discover the signals of 0νββ 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|mββ|≈1 meV for future 0νββ decay experiments and the precisions on neutrion oscillation parameters after the JUNO experiment,we fully explore the constrained regions of the lightest neutrino mass m1 and two Majorana-type CP-violating phases{ρ,σ}.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 m1∈[0.7,8]meV,which together with the precision measurements of neutrino mass-squared differences from oscillation experiments completely determines the neutrino mass spectrum m2∈[8.6,11.7]meV ing phases is limited to ρ∈[130°,230°],which cannot be obtained from any other realistic experiments.Third,the sum of three neutrino masses is found to beΣ≡m1+m2+m3∈[59.2,72.6]meV,while the effective neutrino mass for beta decays turns out to be mβ≡(|Ue1|2m1^2+|Ue2|2m2^2+|Ue3|2m3^2)1/2∈[8.9,12.6]meV.These observations clearly set up the roadmap for future non-oscillation neutrino experiments aiming to solve the fundamental problems in neutrino physics.     

Search for Neutrinoless Double-Beta Decay in ^{136}Xe with EXO-200

We report on a search for neutrinoless double-beta decay of ^{136}Xe with EXO-200. No signal is observed for an exposure of 32.5?kg?yr, with a background of ～1.5×10^{-3} kg^{-1}?yr^{-1}?keV^{-1} in the ±1σ region of interest. This sets a lower limit on the half-life of the neutrinoless double-beta decay T_{1/2}^{0νββ}(^{136}Xe)>1.6×10^{25} yr (90% C.L.), corresponding to effective Majorana masses of less than 140-380?meV, depending on the matrix element calculation.     

Neutrinoless double-beta decay and double-electron capture

The fundamental importance of searching for neutrinoless double-beta 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. The same statement could be made in the case of observing neutrinoless double-electron capture. We address the question of the sensitivity of the 0νεε decay to the effective mass of the Majorana neutrino. According to our estimates, in the case of ¹⁵²Gd and ¹⁶⁴Er the sensitivity can be comparable to the favored 0νββ decays of nuclei. The main uncertainty in the prediction of half-lives of the 0νεε decay stems from the lack of sufficient precision in measuring the mass difference between the parent and daughter atoms. More accurate measurements can be accomplished using the modern high-precision ion traps.     

Majorana neutrino masses and the neutrinoless double-beta decay

Neutrinoless double-beta decay is forbidden in the Standard Model of electroweak and strong interaction but allowed in most Grand Unified Theories (GUTs). Only if the neutrino is a Majorana particle (identical with its antiparticle) and if it has a mass is neutrinoless double-beta decay allowed. Apart from 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 one 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 neutrinoless double-beta decay and one has to be able to calculate reliably the corresponding nuclear matrix elements. In the present work, one discusses the accuracy of the present status of calculating of the nuclear matrix elements and the corresponding limits of GUTs and supersymmetric parameters. The text was submitted by the author in English.     

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.     

Matrix elements for 0νββ decay calculated with the operator expansion method and QRPA wave functions

Matrix elements for 0νββ decay of⁷⁶Ge,⁸²Se,¹¹⁶Cd,^128,130Te,¹³⁶Xe and¹⁵⁰Nd are calculated combining proton-neutron quasiparticle RPA wave functions with the operator expansion method (OEM). The differences between OEM and earlier QRPA calculations, using the closure approximation, are investigated in detail. Special emphasis is put on the discussion on the differences between the 2νββ and the 0νββ mode, since currently 0ν matrix elements can only indirectly be tested. By a comparison with experimental data upper limits on the effective neutrino mass are derived.     

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.     

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.     

Limits of Majorana neutrino mass from combined analysis of data from <Superscript>76</Superscript>Ge and <Superscript>136</Superscript>Xe neutrinoless double beta decay experiments

We present effective Majorana neutrino mass limits <m _ββ> obtained from the joint analysis of the recently published results of ⁷⁶Ge and ¹³⁶Xe neutrinoless double beta decay (0νββ) experiments, which was carried out by using the Bayesian calculations. Nuclear matrix elements (NMEs) used for the analysis are taken from the works, in which NMEs of ⁷⁶Ge and ¹³⁶Xe were simultaneously calculated. This reduced systematic errors connected with NME calculation techniques. The new effective Majorana neutrino mass limits <m _ββ> less than [85.4–197.0] meV are much closer to the inverse neutrino mass hierarchy region.     

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.     

Bimaximal mixing in an SO(10) minimal Higgs model

An SO(10) SUSY GUT model was previously presented based on a minimal set of Higgs fields. The quark and lepton mass matrices derived fitted the data extremely well and led to large ν_μ−ν_τ mixing in agreement with the atmospheric neutrino data and to the small-angle MSW solution for the solar neutrinos. Here we show how a slight modification leading to a non-zero up quark mass can result in bimaximal mixing for the atmospheric and solar neutrinos. The “just-so” vacuum solution is slightly favored over the large-angle MSW solution on the basis of the hierarchy required for the right-handed Majorana matrix and the more nearly-maximal mixing angles obtained.     

Majorana neutrinos, <Emphasis Type="Italic">CP</Emphasis> violation,neutrinoless double beta and tritium beta decays

If the present or upcoming searches for neutrinoless double beta ((ββ)_0ν) decay give a positive result, the Majorana nature of massive neutrinos will be established. From the determination of the value of the (ββ)_0ν-decay effective Majorana mass parameter (|〈m〉|), it would be possible to obtain information on the type of neutrino mass spectrum. Assuming 3-ν mixing and massive Majorana neutrinos, we discuss the information that a measurement of, or an upper bound on, |〈m〉| can provide on the value of the lightest neutrino mass m₁. With additional data on the neutrino masses obtained in ³H β-decay experiments, it might be possible to establish whether the CP symmetry is violated in the lepton sector. This would require very high precision measurements. If CP invariance holds, the allowed patterns of the relative CP parities of the massive Majorana neutrinos would be determined.