Theory of neutrinoless double-beta decay

Muon to Positron Conversion

Lepton-flavor violation (LFV) has been discovered in the neutrino sector by neutrino oscillation experiments. The minimal extension of the Standard Model (SM) to include neutrino masses allows LFV in the charged sector (CLFV) at the loop level, but at rates that are too small to be experimentally observed. Lepton-number violation (LNV) is explicitly forbidden even in the minimally extended SM, so the observation of an LNV process would be unambiguous evidence of physics beyond the SM. The search for the LNV and CLFV process μ−+N(A,Z)→e++N′(A,Z−2) (referred to as μ−→e+) complements 0νββ decay searches, and is sensitive to potential flavor effects in the neutrino mass-generation mechanism. A theoretical motivation for μ−→e+ is presented along with a review of the status of past μ−→e+ experiments and future prospects. Special attention is paid to an uncertain and potentially dominant background for these searches, namely, radiative muon capture (RMC). The RMC high energy photon spectrum is theoretically understudied and existing measurements insufficiently constrain this portion of the spectrum, leading to potentially significant impacts on current and future μ−→e+ work.

^{159}Dy Electron-Capture: A New Candidate for Neutrino Mass Determination

The ground state to ground state electron-capture Q value of ^{159}Dy (3/2^{-}) has been measured directly using the double Penning trap mass spectrometer JYFLTRAP. A value of 364.73(19) keV was obtained from a measurement of the cyclotron frequency ratio of the decay parent ^{159}Dy and the decay daughter ^{159}Tb ions using the novel phase-imaging ion-cyclotron resonance technique. The Q values for allowed Gamow-Teller transition to 5/2^{-} and the third-forbidden unique transition to 11/2^{+} state with excitation energies of 363.5449(14) keV and 362.050(40) keV in ^{159}Tb were determined to be 1.18(19) keV and 2.68(19) keV, respectively. The high-precision Q value of transition 3/2^{-}→5/2^{-} from this work, revealing itself as the lowest electron-capture Q value, is used to unambiguously characterize all the possible lines that are present in its electron-capture spectrum. We performed atomic many-body calculations for both transitions to determine electron-capture probabilities from various atomic orbitals and found an order of magnitude enhancement in the event rates near the end point of energy spectrum in the transition to the 5/2^{-} nuclear excited state, which can become very interesting once the experimental challenges of identifying decays into excited states are overcome. The transition to the 11/2^{+} state is strongly suppressed and found unsuitable for measuring the neutrino mass. These results show that the electron-capture in the ^{159}Dy atom, going to the 5/2^{-} state of the ^{159}Tb nucleus, is a new candidate that may open the way to determine the electron-neutrino mass in the sub-eV region by studying electron-capture. Further experimental feasibility studies, including coincidence measurements with realistic detectors, will be of great interest.

Scintillation in Low-Temperature Particle Detectors

Inorganic crystal scintillators play a crucial role in particle detection for various applications in fundamental physics and applied science. The use of such materials as scintillating bolometers, which operate at temperatures as low as 10 mK and detect both heat (phonon) and scintillation signals, significantly extends detectors performance compared to the conventional scintillation counters. In particular, such low-temperature devices offer a high energy resolution in a wide energy interval thanks to a phonon signal detection, while a simultaneous registration of scintillation emitted provides an efficient particle identification tool. This feature is of great importance for a background identification and rejection. Combined with a large variety of elements of interest, which can be embedded in crystal scintillators, scintillating bolometers represent powerful particle detectors for rare-event searches (e.g., rare alpha and beta decays, double-beta decay, dark matter particles, neutrino detection). Here, we review the features and results of low-temperature scintillation detection achieved over a 30-year history of developments of scintillating bolometers and their use in rare-event search experiments.

Toward Complete Leading-Order Predictions for Neutrinoless Double β Decay

The amplitude for the neutrinoless double β (0νββ) decay of the two-neutron system nn→ppe^{-}e^{-} constitutes a key building block for nuclear-structure calculations of heavy nuclei employed in large-scale 0νββ searches. Assuming that the 0νββ process is mediated by a light-Majorana-neutrino exchange, a systematic analysis in chiral effective field theory shows that already at leading order a contact operator is required to ensure renormalizability. In this Letter, we develop a method to estimate the numerical value of its coefficient (in analogy to the Cottingham formula for electromagnetic contributions to hadron masses) and validate the result by reproducing the charge-independence-breaking contribution to the nucleon-nucleon scattering lengths. Our central result, while derived in dimensional regularization, is given in terms of the renormalized amplitude A_{ν}(|p|,|p^{'}|), matching to which will allow one to determine the contact-term contribution in regularization schemes employed in nuclear-structure calculations. Our results thus greatly reduce a crucial uncertainty in the interpretation of searches for 0νββ decay.

Measurement of the 2νββ Decay Half-Life of ^{130}Te with CUORE

We measured two-neutrino double beta decay of ^{130}Te using an exposure of 300.7 kg yr accumulated with the CUORE detector. Using a Bayesian analysis to fit simulated spectra to experimental data, it was possible to disentangle all the major background sources and precisely measure the two-neutrino contribution. The half-life is in agreement with past measurements with a strongly reduced uncertainty: T_{1/2}^{2ν}=7.71_{-0.06}^{+0.08}(stat)_{-0.15}^{+0.12}(syst)×10^{20}  yr. This measurement is the most precise determination of the ^{130}Te 2νββ decay half-life to date.

The NUMEN Project: Toward New Experiments with High-Intensity Beams

The search for neutrinoless double-beta (0νββ) decay is currently a key topic in physics, due to its possible wide implications for nuclear physics, particle physics, and cosmology. The NUMEN project aims to provide experimental information on the nuclear matrix elements (NMEs) that are involved in the expression of 0νββ decay half-life by measuring the cross section of nuclear double-charge exchange (DCE) reactions. NUMEN has already demonstrated the feasibility of measuring these tiny cross sections for some nuclei of interest for the 0νββ using the superconducting cyclotron (CS) and the MAGNEX spectrometer at the Laboratori Nazionali del Sud (LNS.) Catania, Italy. However, since the DCE cross sections are very small and need to be measured with high sensitivity, the systematic exploration of all nuclei of interest requires major upgrade of the facility. R&D for technological tools has been completed. The realization of new radiation-tolerant detectors capable of sustaining high rates while preserving the requested resolution and sensitivity is underway, as well as the upgrade of the CS to deliver beams of higher intensity. Strategies to carry out DCE cross-section measurements with high-intensity beams were developed in order to achieve the challenging sensitivity requested to provide experimental constraints to 0νββ NMEs.

Nuclear magnetic transitions in the relativistic energy density functional approach

Recently a novel theory framework has been established for description of magnetic dipole (M1) transitions in finite nuclei, based on relativistic nuclear energy density functional with point coupling interactions. The properties of M1 transitions have been studied, including the sum rules, spin, orbital, isoscalar and isovector M1 transition strengths in magic and open shell nuclei. It is shown that pairing correlations and spinorbit interaction plays an important role in the description of M1 transition strength distributions. The analysis of the evolution of M1 transition properties in the isotope chain 100-140 Sn shows the interplay between single and double-peak structures, determined by the evolution of single-particle states, their occupations governed by the pairing correlations, and two-quasiparticle transitions involved. Comparison of the calculated B(M1) transition strength with recent data from inelastic proton scattering on 112-124 Sn, shows that quenching of the g factors geff/gfree =0.80-0.93 is required to reproduce the experimental data. Further experimental investigations are needed to determine accurately the quenching factor.

Recent experimental activity on heavy-ion induced reactions within the NUMEN project

The possibility to use a special class of heavy-ion induced direct reactions, such as double charge exchange reactions, is discussed in view of their application to extract information that may be helpful to determinate the nuclear matrix elements entering in the expression of neutrinoless double beta decay half-life. The strategies adopted in the experimental campaigns performed at INFN - Laboratori Nazionali del Sud are briefly described, emphasizing the advantages of the multi-channel approach to nuclear reaction data analysis.

Neutrino-Mass Sensitivity and Nuclear Matrix Element for Neutrinoless Double Beta Decay

Neutrinoless double beta decay (DBD) is a useful probe to study neutrino properties such as the Majorana nature, the absolute neutrino mass, the CP phase and the others, which are beyond the standard model. The nuclear matrix element (NME) for DBD is crucial to extract the neutrino properties from the experimental transition rate. The neutrino-mass sensitivity, i.e., the minimum neutrino-mass to be measured by the DBD experiment, is very sensitive to the DBD NME. Actually, the NME is one of the key elements for designing the DBD experiment. Theoretical evaluation for the DBD NME, however, is very hard. Recently experimental studies of charge-exchange nuclear and leptonic reactions have shown to be used to get single-β NMEs associated with the DBD NME. Critical discussions are made on the neutrino-mass sensitivity and the NME for the DBD neutrino-mass study and on the experimental studies of the single-β NMEs and nuclear structures associated with DBD NMEs.

Cosmogenic Activation in Double Beta Decay Experiments

Double beta decay is a very rare nuclear process and, therefore, experiments intended to detect it must be operated deep underground and in ultra-low background conditions. Long-lived radioisotopes produced by the previous exposure of materials to cosmic rays on the Earth’s surface or even underground can become problematic for the required sensitivity. Here, the studies developed to quantify and reduce the activation yields in detectors and materials used in the set-up of these experiments will be reviewed, considering target materials like germanium, tellurium and xenon together with other ones commonly used like copper, lead, stainless steel or argon. Calculations following very different approaches and measurements from irradiation experiments using beams or directly cosmic rays will be considered for relevant radioisotopes. The effect of cosmogenic activation in present and future double beta decay projects based on different types of detectors will be analyzed too.

The NUMEN Heavy Ion Multidetector for a Complementary Approach to the Neutrinoless Double Beta Decay

Neutrinos are so far the most elusive known particles, and in the last decades many sophisticated experiments have been set up in order to clarify several questions about their intrinsic nature, in particular their masses, mass hierarchy, intrinsic nature of Majorana or Dirac particles. Evidence of the Neutrinoless Double-Beta Decay (NDBD) would prove that neutrinos are Majorana particles, thus improving the understanding of the universe itself. Besides the search for several large underground experiments for the direct experimental detection of NDBD, the NUMEN experiment proposes the investigation of a nuclear mechanism strongly linked to this decay: the Double Charge Exchange reactions (DCE). As such reactions share with the NDBD the same initial and final nuclear states, they could shed light on the determination of the Nuclear Matrix Elements (NMEs), which play a relevant role in the decay. The physics of DCE is described elsewhere in this issue, while the focus of this paper will be on the challenging experimental apparatus currently under construction in order to fulfil the requirements of the NUMEN experiment. The overall structure of the technological improvement to the cyclotron, along with the newly developed detection systems required for tracking and identifying the reaction products and their final excitation level are described.

Neutrinoless Double-Beta Decay and Realistic Shell Model

We report on the calculation of the neutrinoless double-ß decay nuclear matrix element for 76Ge within the framework of the realistic shell model. The effective shell-model Hamiltonian and the two-body transition operator describing the decay are derived by way of many-body perturbation theory. Particular attention is focused on the role played by the so-called Pauli blocking effect in the derivation of the effective operator.

Barium Chemosensors with Dry-Phase Fluorescence for Neutrinoless Double Beta Decay

The nature of the neutrino is one of the major open questions in experimental nuclear and particle physics. The most sensitive known method to establish the Majorana nature of the neutrino is detection of the ultra-rare process of neutrinoless double beta decay. However, identification of one or a handful of decay events within a large mass of candidate isotope, without obfuscation by backgrounds is a formidable experimental challenge. One hypothetical method for achieving ultra- low-background neutrinoless double beta decay sensitivity is the detection of single 136Ba ions produced in the decay of 136Xe ("barium tagging"). To implement such a method, a single-ion-sensitive barium detector must be developed and demonstrated in bulk liquid or dry gaseous xenon. This paper reports on the development of two families of dry-phase barium chemosensor molecules for use in high pressure xenon gas detectors, synthesized specifically for this purpose. One particularly promising candidate, an anthracene substituted aza-18-crown-6 ether, is shown to respond in the dry phase with almost no intrinsic background from the unchelated state, and to be amenable to barium sensing through fluorescence microscopy. This interdisciplinary advance, paired with earlier work demonstrating sensitivity to single barium ions in solution, opens a new path toward single ion detection in high pressure xenon gas.

Search for Neutrinoless Double-β Decay with the Complete EXO-200 Dataset

A search for neutrinoless double-β decay (0νββ) in ^{136}Xe is performed with the full EXO-200 dataset using a deep neural network to discriminate between 0νββ and background events. Relative to previous analyses, the signal detection efficiency has been raised from 80.8% to 96.4±3.0%, and the energy resolution of the detector at the Q value of ^{136}Xe 0νββ has been improved from σ/E=1.23% to 1.15±0.02% with the upgraded detector. Accounting for the new data, the median 90% confidence level 0νββ half-life sensitivity for this analysis is 5.0×10^{25}  yr with a total ^{136}Xe exposure of 234.1 kg yr. No statistically significant evidence for 0νββ is observed, leading to a lower limit on the 0νββ half-life of 3.5×10^{25}  yr at the 90% confidence level.

Recent results on heavy-ion induced reactions of interest for neutrinoless double beta decay at INFN-LNS

The possibility to use a special class of heavy-ion induced direct reactions, such as double charge exchange reactions, is discussed in view of their application to extract information that may be helpful to determinate the nuclear matrix elements entering in the expression of neutrinoless double beta decay half-life. The methodology of the experimental campaign presently running at INFN - Laboratori Nazionali del Sud is reported andthe experimental challenges characterizing such activity are described.

Heavy Ion Charge Exchange Reactions as Probes for Beta–Decay

Peripheral heavy ion single and double charge reactions are described by fully quantum mechanical distorted wave methods. A special class of nuclear double charge exchange (DCE) reactions proceeding as a one-step reaction through a two-body process are shown to proceed by nuclear matrix elements of a diagrammatic structure as found also in 0ν2ß decay. These hadronic Majorana-type DCE reactions (MDCE) have to be distinguished from second order DCE reactions, given by double single charge exchange (DSCE) processes, resembling 2ν2ß decay. The theoretical concepts of MDCE are discussed. First results show that ion-ion DCE reactions are the ideal testing grounds for investigations of rare second order nuclear processes, giving insight into nuclear in-medium two-body correlation.

Variation of NMEs of 0νββ for 48Ca with different components of NN interaction

We examine the sensitivity of nuclear matrix elements (NMEs) for light-neutrino exchange mechanism of neutrinoless double beta decay (0νββ) for 48Ca to the various components of two-nucleon interaction, GXPF1A, in fp model space. It is found that the contribution in NMEs coming from the central component is close to contribution from total interaction. The spin-orbit and tensor components are found canceling the contribution of each other.

Two neutrino double-beta decay and effective axial-vector coupling constant

The theoretical and experimental study of the two-neutrino double-beta decay (2νββ-decay) is of crucial importance for reliable calculation of matrix elements governing the neutrinoless double-beta decay (0νββ-decay). That will allow to determine masses of neutrinos once the 0νββ-decay, which occurs if the neutrino is a massive Majorana particle and the total lepton number is not onserved, will be observed. Experiments studying the 2νββ-decay are currently approaching a qualitatively new level, where high-precision measurements are performed not only for half-lives but for all other observables of the process. In this context an improved formula for the 2νββ-decay is presented. Further, a novel approach for determining the effective axial-vector coupling constant is proposed.

The nuclear matrix elements of 0νββ decay and the NUMEN project at INFN-LNS

The goal of NUMEN project is to access experimentally driven information on Nuclear Matrix Elements (NME) involved in the neutrinoless double beta decay (0νββ), by high-accuracy measurements of the cross sections of Heavy Ion (HI) induced Double Charge Exchange (DCE) reactions. The knowledge of the nuclear matrix elements is crucial to infer the neutrino average masses from the possible measurement of the half-life of 00νββ decay and to compare experiments on different isotopes. In particular, the (18O, 18Ne) and (20Ne, 20O) reactions are performed as tools for β+β+ and β-β- decays, respectively. The experiments are performed at INFN - Laboratory Nazionali del Sud (LNS) in Catania using the Superconducting Cyclotron (CS) to accelerate the beams and the MAGNEX magnetic spectrometer to detect the reaction products. The measured cross sections are very low, limiting the present exploration to few selected isotopes of interest in the context of typically low-yield experimental runs. In order to make feasible a systematic study of all the candidate nuclei, a major upgrade of the LNS facility is foreseen to increase the experimental yield of about two orders of magnitude. To this purpose, frontier technologies are going to be developed for both the accelerator and the detection systems. In parallel, advanced theoretical models will be developed to extract the nuclear structure information from the measured cross sections.

The Majorana Demonstrator Status and Preliminary Results

The Majorana Collaboration is using an array of high-purity Ge detectors to search for neutrinoless double-beta decay in 76Ge. Searches for neutrinoless double-beta decay are understood to be the only viable experimental method for testing the Majorana nature of the neutrino. Observation of this decay would imply violation of lepton number, that neutrinos are Majorana in nature, and provide information on the neutrino mass. The Majorana Demonstrator comprises 44.1 kg of p-type point-contact Ge detectors (29.7 kg enriched in 76Ge) surrounded by a low-background shield system. The experiment achieved a high efficiency of converting raw Ge material to detectors and an unprecedented detector energy resolution of 2.5 keV FWHM at Qββ. The Majorana collaboration began taking physics data in 2016. This paper summarizes key construction aspects of the Demonstrator and shows preliminary results from initial data.

Search for Neutrinoless Double-β Decay in ^{76}Ge with the Majorana Demonstrator

The Majorana Collaboration is operating an array of high purity Ge detectors to search for neutrinoless double-β decay in ^{76}Ge. The Majorana Demonstrator comprises 44.1 kg of Ge detectors (29.7 kg enriched in ^{76}Ge) split between two modules contained in a low background shield at the Sanford Underground Research Facility in Lead, South Dakota. Here we present results from data taken during construction, commissioning, and the start of full operations. We achieve unprecedented energy resolution of 2.5 keV FWHM at Q_{ββ} and a very low background with no observed candidate events in 9.95 kg yr of enriched Ge exposure, resulting in a lower limit on the half-life of 1.9×10^{25}  yr (90% C.L.). This result constrains the effective Majorana neutrino mass to below 240-520 meV, depending on the matrix elements used. In our experimental configuration with the lowest background, the background is 4.0_{-2.5}^{+3.1}  counts/(FWHM t yr).

Realistic shell model description of beta decay

In this paper, we extend our previous realistic shell-model study of Gamow-Teller strengths and double-β decay properties for nuclei around 132Sn to lighter mass nuclei. The effective shell-model Hamiltonian and transition operators are microscopically derived by way of many-body perturbation theory, without resorting to empirical parameters. Our main aim is to further check the reliability of our approach and verify its stability in other mass regions. Calculated energy spectra as well as electric-quadrupole and β-decay properties are presented for 76Ge and 82Se and compared with the experimental data, together with some results for 130Te and 136Xe already reported in our previous paper. Finally, some preliminary results of nuclear matrix elements responsible for the neutrinoless double beta decay, calculated by using the bare operator, are shown.

Status and future of nuclear matrix elements for neutrinoless double-beta decay: a review

The nuclear matrix elements that govern the rate of neutrinoless double beta decay must be accurately calculated if experiments are to reach their full potential. Theorists have been working on the problem for a long time but have recently stepped up their efforts as ton-scale experiments have begun to look feasible. Here we review past and recent work on the matrix elements in a wide variety of nuclear models and discuss work that will be done in the near future. Ab initio nuclear-structure theory, which is developing rapidly, holds out hope of more accurate matrix elements with quantifiable error bars.

Nuclear structure aspects of neutrinoless double-β decay

We decompose the neutrinoless double-β decay matrix elements into sums of products over the intermediate nucleus with two less nucleons. We find that the sum is dominated by the J(π)=0(+) ground state of this intermediate nucleus for both the light and heavy neutrino decay processes. This provides a new theoretical tool for comparing and improving nuclear structure models. It also provides the connection to two-nucleon transfer experiments.

Neutrino propagation in nuclear medium and neutrinoless double-β decay

We discuss a novel effect in neutrinoless double-β (0νββ) decay related with the fact that its underlying mechanisms take place in the nuclear matter environment. We study the neutrino exchange mechanism and demonstrate the possible impact of nuclear medium via lepton-number-violating (LNV) four-fermion interactions of neutrinos with quarks from a decaying nucleus. The net effect of these interactions is the generation of an effective in-medium Majorana neutrino mass matrix. The enhanced rate of the 0νββ decay can lead to the apparent incompatibility of observations of the 0νββ decay with the value of the neutrino mass determined or restricted by the β-decay and cosmological data. The effective neutrino masses and mixing are calculated for the complete set of the relevant four-fermion neutrino-quark operators. Using experimental data on the 0νββ decay in combination with the β-decay and cosmological data, we evaluate the characteristic scales of these operators: ΛLNV≥2.4  TeV.

Neutrinoless double-β decay and QCD corrections

We consider one-loop QCD corrections and renormalization group running of the neutrinoless double-β decay amplitude focusing on the short-range part of the amplitude (without the light neutrino exchange) and find that these corrections can be sizeable. Depending on the operator under consideration, there can be moderate to large cancellations or significant enhancements. We discuss several specific examples in this context. Such large corrections will lead to significant shifts in the half-life estimates, which currently are known to be plagued with the uncertainties due to nuclear physics inputs to the physical matrix elements.

Results on neutrinoless double-β decay of 76Ge from phase I of the GERDA experiment

Neutrinoless double beta decay is a process that violates lepton number conservation. It is predicted to occur in extensions of the standard model of particle physics. This Letter reports the results from phase I of the Germanium Detector Array (GERDA) experiment at the Gran Sasso Laboratory (Italy) searching for neutrinoless double beta decay of the isotope (76)Ge. Data considered in the present analysis have been collected between November 2011 and May 2013 with a total exposure of 21.6 kg yr. A blind analysis is performed. The background index is about 1 × 10(-2) counts/(keV kg yr) after pulse shape discrimination. No signal is observed and a lower limit is derived for the half-life of neutrinoless double beta decay of (76)Ge, T(1/2)(0ν) >2.1 × 10(25) yr (90% C.L.). The combination with the results from the previous experiments with (76)Ge yields T(1/2)(0ν)>3.0 × 10(25) yr (90% C.L.).

Shell-model analysis of the 136Xe double beta decay nuclear matrix elements

Neutrinoless double beta decay, if observed, could distinguish whether the neutrino is a Dirac or a Majorana particle, and it could be used to determine the absolute scale of the neutrino masses. 136Xe is one of the most promising candidates for observing this rare event. However, until recently there were no positive results for the allowed and less rare two-neutrino double beta decay mode. The small nuclear matrix element associated with the long half-life represents a challenge for nuclear structure models used for its calculation. We report a new shell-model analysis of the two-neutrino double beta decay of 136Xe, which takes into account all relevant nuclear orbitals necessary to fully describe the associated Gamow-Teller strength. We further use the new model to analyze the main contributions to the neutrinoless double beta decay matrix element, and show that they are also diminished.