Neutrinoless double beta decay

The physics potential of neutrinoless double beta decay is discussed. Furthermore, experimental considerations as well as the current status of experiments are presented. Finally, an outlook towards the future, work on nuclear matrix elements and alternative processes is given.     

Non-collapsing QRPA for neutrinoless double beta decay

The standard quasiparticle random phase approximation(QRPA) is widely used to describe the neutrinoless double beta decay process. Although it has been quite successful in many cases of interest, it has some shortcomings. The most important one is that its solutions collapse for physical values of the particle-particle strength. We shall show that modifications can be done which can extend the validity of this standard QRPA beyond the point of collapse. Such modifications are: The introduction of proton-neutron pairing, the inclusion of the Pauli principle and the extension of the Hilbert space. If all these modifications are introduced into the standard QRPA then the collapse does not occur for physical values of the particle-particle strengths. Thus, one might be able to extract more accurate values on the effective neutrino mass by using the best available experimental limits on the half life of neutrinoless double beta decay. Presented by G. Pantis at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997.     

Constraining neutrinoless double beta decay

A class of discrete flavor-symmetry-based models predicts constrained neutrino mass matrix schemes that lead to specific neutrino mass sum-rules (MSR). We show how these theories may constrain the absolute scale of neutrino mass, leading in most of the cases to a lower bound on the neutrinoless double beta decay effective amplitude.     

Neutrino-less double beta decay experiments

The observation of neutrinoless double beta decay would unambiguosly demonstrate that neutrinos are Majorana particles and would provide unique information about the ordering and absolute scale of neutrino masses. This very rare decay is actively searched for in a number of candidate isotopes. It violates lepton-number and is predicted by many extensions of the standard model. The most recent experimental results are reviewed. The technological advances and the most compelling requirements for the new generation of experiments are discussed.     

Nuclear moments for the neutrinoless double beta decay

A derivation of the neutrinoless double beta decay rate, specially adapted for nuclear structure calculations, is presented. It is shown that the Fourier-Bessel expansion of the hadronic currents, jointly with angular momentum recoupling, leads to very simple final expressions for the nuclear form factors. This greatly facilitates the theoretical estimate of the half-life. Our approach does not require the closure approximation, which, however, can be implemented if desired. The method is exemplified for ββ decay ⁴⁸Ca → ⁴⁸Ti, both within the QRPA and a shell-model like model.     

Search for double beta decay of 106Cd

A search for the β⁺β⁺, β⁺/EC, and EC/EC decays of ¹⁰⁶Cd was performed at the Modane Underground Laboratory (France) located at a depth of 4800 m w.e. using a TGV-2 multidetector germanium spectrometer. A preliminary evaluation is performed of the experimental data accumulated during the measurements (12 900 h) of ～13.6 g of ¹⁰⁶Cd (with an enrichment of 75%) and the spectrometer background without samples and with samples of natural Cd. New limits (at a 90% confidence level) of half-lives are obtained: T _1/2 ? 1.7 × 10²⁰ yr and T _1/2 ? 1.6 × 10²⁰ yr for the 0νEC/EC resonant decay of ¹⁰⁶Cd to the 2741 keV and 2718 keV excited states of the daughter nucleus ¹⁰⁶Pd and T _1/2 ? 4.2 × 10²⁰ yr for the 2νEC/EC decay to the ground state of ¹⁰⁶Pd (0⁺ → 0⁺, g.s.). The limits for other branches of the double beta decay of ¹⁰⁶Cd with transitions to the ground and excited states of ¹⁰⁶Pd are improved.     

Nuclear reactions and the double beta decay

Charge-exchange reactions of (n,p) and (p,n) types at intermediate energies are introduced as a tool for the study of nuclear matrix element in ββ decay. Here, the (n,p) type reactions are realized through , where ²He refers to two protons in a singlet ¹S₀ state and where both of these are momentum analyzed and detected by the same spectrometer and detector. These reactions have been developed and performed exclusively at KVI, Groningen (NL), using an incident deuteron energy of 183 MeV. The  reaction is of (p,n) type and was developed at the RCNP facility in Osaka (JP) at incident energies of 420 MeV. Using both reaction types one can extract the Gamow-Teller transition strengths B(GT⁺) and , which define the two “legs” of the ββ decay matrix elements for the 2νββ decay. The high resolution available in both reactions allows a detailed insight into the excitations of the intermediate odd-odd nuclei and, as will be shown, some unexpected features are being unveiled.     

Present and future strategies for neutrinoless double beta decay searches

The renewed interest shown in these days towards neutrinoless double beta decay, a lepton number violating process which can take place only if neutrinos are Majorana particles (ν = \(\bar \nu \)) with a nonvanishing mass, is justified by the fact that the Majorana nature of neutrinos is expected in many theories beyond the Standard Model. We also now know, thanks to the neutrino oscillation experiments, that neutrinos are in fact massive, as expected in these theories and not requested in the Standard Model. Moreover, since neutrino oscillation experiments measure only the absolute value of the difference of the square of the neutrino masses, the discovery of neutrinoless double beta decay would help to disentangle questions that still remain unsolved: what is the absolute mass scale of the neutrinos and which mass hierarchy (normal, inverted or quasi-degenerate) is the correct one?The scope of this paper is not only to review the present results reached in the field by the different groups and technologies worldwide, but also to illustrate and comment on the (near and long-term) future strategies that experimentalists are trying to pursue to reach the needed sensitivity required to explore the inverted hierarchy neutrino mass scale.     

Status and prospects of searches for neutrinoless double beta decay

The simultaneous beta decay of two neutrons in a nucleus without the emission of neutrinos (called neutrinoless double beta decay) is a lepton number violating process which is not allowed in the Standard Model of particle physics. More than a dozen experiments using different candidate isotopes and a variety of detection techniques are searching for this decay. Some (EXO‐200, Kamland‐Zen, and GERDA) started to take data recently. EXO and Kamland‐Zen have reported first limits of the half life for ¹³⁶Xe. After a decade of little progress in this field, these results start to scrutinize the claim from part of the Heidelberg–Moscow collaboration to have observed this decay. The sensitivities of the different proposals are reviewed.     

Extended operator expansion method for neutrinoless double beta decay

Reliable calculations of nuclear matrix elements are a prerequisite for the determination of the effective neutrino mass and other particle physics parameters from neutrinoless double beta decay. Here, the operator expansion method is improved by including Coulomb, tensor and central interactions simultaneously. Furthermore, the formalism of the OEM is extended to those matrix elements necessary to extract the right-handed parameters and from 0 decay. OEM includes the dependence of the nuclear matrix elements on the intermediate states implicitly and can therefore be understood as a step beyond the closure approximation. Numerical studies are carried out for the isotope⁷⁶Ge combining the OEM expressions with ground-state wave functions calculated within a proton-neutron quasiparticle Random Phase Approximation (pn-QRPA) model. The influence and relative importance of central, tensor and Coulomb interactions is investigated. Within the OEM, contributions from the Coulomb force are found to be negligible in 0 decay, while the tensor force leads to a moderate change of the results, of the order of (10–30)%, giving a better agreement between sets of calculations which employ different NN-interactions. Generally, results of the OEM+QRPA calculation are similar to previous calculations of 0 decay matrix elements, indicating that 0 decay is not sensitive to model approximations and might therefore be more accurately calculated than the strongly suppressed 2 decay matrix elements.     

无中微子双贝塔衰变：寻找马约拉纳中微子之路

无中微子双贝塔衰变是目前粒子物理与核物理学家积极寻找的一种极其稀有的原子核衰变模式。它的发现将验证中微子是否是其本身的反粒子,也就是通常指的马约拉纳费米子。同时这一物理过程破坏轻子数守恒,也可以为宇宙初期的正反物质不对称性提供重要的条件。鉴于其极重要的物理意义,国际上多个实验组利用不同的探测器技术,在多种不同的目标同位素中寻找这一突破粒子物理标准模型的稀有衰变。目前主流实验还未发现确定的无中微子双贝塔衰变信号,但对其半衰期的限制已经达到了10²⁶年量级。国内近期也开展了一系列预研实验,期望在未来几年内可以确定一到两个切实可行的实验方案,开展吨级实验。     

Neutrinoless double beta decay and heavy sterile neutrinos

The experimental rate of neutrinoless double beta decay can be saturated by the exchange of virtual sterile neutrinos, that mix with the ordinary neutrinos and are heavier than 200 MeV. Interestingly, this hypothesis is subject only to marginal experimental constraints, because of the new nuclear matrix elements. This possibility is analyzed in the context of the Type I seesaw model, performing also exploratory investigations of the implications for heavy neutrino mass spectra, rare decays of mesons as well as neutrino-decay search, LHC, and lepton flavor violation. The heavy sterile neutrinos can saturate the rate only when their masses are below some 10 TeV, but in this case, the suppression of the light-neutrino masses has to be more than the ratio of the electroweak scale and the heavy-neutrino scale; i.e., more suppressed than the naive seesaw expectation. We classify the cases when this condition holds true in the minimal version of the seesaw model, showing its compatibility (1) with neutrinoless double beta rate being dominated by heavy neutrinos and (2) with any light neutrino mass spectra. The absence of excessive fine-tunings and the radiative stability of light neutrino mass matrices, together with a saturating sterile neutrino contribution, imply an upper bound on the heavy neutrino masses of about 10 GeV. We extend our analysis to the Extended seesaw scenario, where the light and the heavy sterile neutrino contributions are completely decoupled, allowing the sterile neutrinos to saturate the present experimental bound on neutrinoless double beta decay. In the models analyzed, the rate of this process is not strictly connected with the values of the light neutrino masses, and a fast transition rate is compatible with neutrinos lighter than 100 meV.     

Effective Majorana mass and neutrinoless double beta decay

The probability distribution for the effective Majorana mass as a function of the lightest neutrino mass in the standard three neutrino scheme is computed via a random sampling from the distributions of the involved mixing angles and squared mass differences. A flat distribution in the \([0,2\pi ]\) range for the Majorana phases is assumed, and the dependence of small values of the effective mass on the Majorana phases is highlighted. The study is then extended with the addition of the cosmological bound on the sum of the neutrino masses. Finally, the prospects for \(0\nu \beta \beta \) decay search with \(^{76}\)Ge, \(^{130}\)Te and \(^{136}\)Xe are discussed, as well as those for the measurement of the electron neutrino mass.     

Nuclear moments for the neutrinoless double beta decay II

The recently developed formalism for the evaluation of nuclear form factors in neutrinoless double beta decay is applied to ⁴⁸Ca, ⁷⁶Ge, ⁸²Se, ¹⁰⁰Mo, ¹²⁸Te and ¹³⁰Te nuclei. Explicit analytical expressions that follows from this theoretical development, in the single-mode model for the decay of ⁴⁸Ca, have been worked out. They are useful both for testing the full numerical calculations, and for analytically checking the consistency with other formalisms. Large configuration space calculations are compared with previous studies, where alternative formulations were used. Yet, besides using the G-matrix as residual interaction, we here use a simple δ-force. Attention is paid to the connected effects of the short range nuclear correlations and the finite nucleon size. Constraints on lepton number violating terms in the weak Hamiltonian (effective neutrino Majorana mass and effective right-handed current coupling strengths) are deduced.