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

First Result on the Neutrinoless Double-β Decay of ^{82}Se with CUPID-0

We report the result of the search for neutrinoless double beta decay of ^{82}Se obtained with CUPID-0, the first large array of scintillating Zn^{82}Se cryogenic calorimeters implementing particle identification. We observe no signal in a 1.83 kg yr ^{82}Se exposure, and we set the most stringent lower limit on the 0νββ ^{82}Se half-life T_{1/2}^{0ν}>2.4×10^{24}  yr (90% credible interval), which corresponds to an effective Majorana neutrino mass m_{ββ}<(376-770)  meV depending on the nuclear matrix element calculations. The heat-light readout provides a powerful tool for the rejection of α particles and allows us to suppress the background in the region of interest down to (3.6_{-1.4}^{+1.9})×10^{-3}  counts/(keV kg yr), an unprecedented level for this technique.

New Leading Contribution to Neutrinoless Double-β Decay

Within the framework of chiral effective field theory, we discuss the leading contributions to the neutrinoless double-beta decay transition operator induced by light Majorana neutrinos. Based on renormalization arguments in both dimensional regularization with minimal subtraction and a coordinate-space cutoff scheme, we show the need to introduce a leading-order short-range operator, missing in all current calculations. We discuss strategies to determine the finite part of the short-range coupling by matching to lattice QCD or by relating it via chiral symmetry to isospin-breaking observables in the two-nucleon sector. Finally, we speculate on the impact of this new contribution on nuclear matrix elements of relevance to experiment.

Double Gamow-Teller Transitions and its Relation to Neutrinoless ββ Decay

We study the double Gamow-Teller (DGT) strength distribution of ^{48}Ca with state-of-the-art large-scale nuclear shell model calculations. Our analysis shows that the centroid energy of the DGT giant resonance depends mostly on the isovector pairing interaction, while the resonance width is more sensitive to isoscalar pairing. Pairing correlations are also key in neutrinoless ββ (0νββ) decay. We find a simple relation between the centroid energy of the ^{48}Ca DGT giant resonance and the 0νββ decay nuclear matrix element. More generally, we observe a very good linear correlation between the DGT transition to the ground state of the final nucleus and the 0νββ decay matrix element. The correlation, which originates on the dominant short-range character of both transitions, extends to heavier systems including several ββ emitters and also holds in energy-density functional results. Our findings suggest that DGT experiments can be a very valuable tool to obtain information on the value of 0νββ decay nuclear matrix elements.

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).

Improved Limit on Neutrinoless Double-β Decay of ^{76}Ge from GERDA Phase II

The GERDA experiment searches for the lepton-number-violating neutrinoless double-β decay of ^{76}Ge (^{76}Ge→^{76}Se+2e^{-}) operating bare Ge diodes with an enriched ^{76}Ge fraction in liquid argon. The exposure for broad-energy germanium type (BEGe) detectors is increased threefold with respect to our previous data release. The BEGe detectors feature an excellent background suppression from the analysis of the time profile of the detector signals. In the analysis window a background level of 1.0_{-0.4}^{+0.6}×10^{-3}  counts/(keV kg yr) has been achieved; if normalized to the energy resolution this is the lowest ever achieved in any 0νββ experiment. No signal is observed and a new 90% C.L. lower limit for the half-life of 8.0×10^{25}  yr is placed when combining with our previous data. The expected median sensitivity assuming no signal is 5.8×10^{25}  yr.

First Results from CUORE: A Search for Lepton Number Violation via 0νββ Decay of ^{130}Te

The CUORE experiment, a ton-scale cryogenic bolometer array, recently began operation at the Laboratori Nazionali del Gran Sasso in Italy. The array represents a significant advancement in this technology, and in this work we apply it for the first time to a high-sensitivity search for a lepton-number-violating process: ^{130}Te neutrinoless double-beta decay. Examining a total TeO_{2} exposure of 86.3 kg yr, characterized by an effective energy resolution of (7.7±0.5)  keV FWHM and a background in the region of interest of (0.014±0.002)  counts/(keV kg yr), we find no evidence for neutrinoless double-beta decay. Including systematic uncertainties, we place a lower limit on the decay half-life of T_{1/2}^{0ν}(^{130}Te)>1.3×10^{25}  yr (90% C.L.); the median statistical sensitivity of this search is 7.0×10^{24}  yr. Combining this result with those of two earlier experiments, Cuoricino and CUORE-0, we find T_{1/2}^{0ν}(^{130}Te)>1.5×10^{25}  yr (90% C.L.), which is the most stringent limit to date on this decay. Interpreting this result as a limit on the effective Majorana neutrino mass, we find m_{ββ}<(110-520)  meV, where the range reflects the nuclear matrix element estimates employed.

Studying collective nuclear excitations with fast neutrons: a comparison of 76Ge and 76Se

The low-lying, low-spin level structures of 76Ge and 76Se were studied with the (n,n'γ) reaction. Gamma-ray excitation function and angular distribution measurements were performed, and level spins, level lifetimes, γ-ray intensities, and multipole mixing ratios were determined. Large observed B(E2) values support the identification of low-lying band structures.

Study of the double Gamow-Teller transitions using the shell model approach

The double Gamow-Teller strength distributions in the lightest double beta-decay candidate 48Ca and its isotope 46Ca were calculated using the nuclear shell model by applying the single Gamow-Teller operator two times sequentially on the ground state of parent nucleus. The nuclear matrix element of the double Gamow- Teller transition from the ground state to the ground state that goes into the double beta decay calculation was shown as a small fraction of the total transition.

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.

Nuclear structure of 82Kr and 82Se relevant for neutrinoless double-beta decay

Nuclear Resonance Fluorescence (NRF) experiments on the nuclei 82Kr and 82Se were performed, that are a candidates for a mother-daughter pair for the hypothetical neutrinoless double-beta (0νββ) decay. The experiment aimed at providing high-precision data to benchmark theoretical calculations of the nuclear matrix elements involved in this exotic decay mode. We have investigated the excitation energy range from 2.3MeV to 4.2MeV, where the nuclear scissors mode is expected to be located in nuclei of this mass region. Our experiment was able to constrain decay branches of the scissors mode down to a level of a few percents, comparable to previous experiments on heavy deformed 0νββ decay candidates. Reduced transition strengths of the magnetic dipole-excited states have been determined by a method that exploits the non-resonant background in the NRF spectra. They are compared to a calculation within the nuclear shell model for 82Se, which reveals their mixed orbital and spin character, hinting at a more complex microscopic structure of low-lying 1+ states.

Nuclear Matrix Elements for Tests of Local Lorentz Invariance Violation

The nuclear matrix elements for the spin operator and the momentum quadrupole operator are important for the interpretation of precision atomic physics experiments that search for violations of local Lorentz and CPT symmetry and for new spin-dependent forces. We use the configuration-interaction nuclear shell model and self-consistent mean-field theory to calculate the momentum matrix elements for ^{21}Ne, ^{23}Na, ^{133}Cs, ^{173}Yb, and ^{201}Hg. We show that these momentum matrix are strongly suppressed by the many-body correlations, in contrast to the well-known enhancement of the spatial quadrupole nuclear matrix elements.

Isotensor Axial Polarizability and Lattice QCD Input for Nuclear Double-β Decay Phenomenology

The potential importance of short-distance nuclear effects in double-β decay is assessed using a lattice QCD calculation of the nn→pp transition and effective field theory methods. At the unphysical quark masses used in the numerical computation, these effects, encoded in the isotensor axial polarizability, are found to be of similar magnitude to the nuclear modification of the single axial current, which phenomenologically is the quenching of the axial charge used in nuclear many-body calculations. This finding suggests that nuclear models for neutrinoful and neutrinoless double-β decays should incorporate this previously neglected contribution if they are to provide reliable guidance for next-generation neutrinoless double-β decay searches. The prospects of constraining the isotensor axial polarizabilities of nuclei using lattice QCD input into nuclear many-body calculations are discussed.