Change of nuclear configurations in the neutrinoless double-$β$ decay of $^{130}$Te $\rightarrow$ $^{130}$Xe and $^{136}$Xe $\rightarrow$ $^{136}$Ba
J. P. Entwisle, B. P. Kay, A. Tamii, S. Adachi, N. Aoi, J. A. Clark, S. J. Freeman, H. Fujita, Y. Fujita, T. Furuno, T. Hashimoto, C. R. Hoffman, E. Ideguchi, T… 展开作者
J. P. Entwisle, B. P. Kay, A. Tamii, S. Adachi, N. Aoi, J. A. Clark, S. J. Freeman, H. Fujita, Y. Fujita, T. Furuno, T. Hashimoto, C. R. Hoffman, E. Ideguchi, T. Ito, C. Iwamoto, T. Kawabata, B. Liu, M. Miura, H. J. Ong, J. P. Schiffer, D. K. Sharp, G. Süsoy, T. Suzuki, S. V. Szwec, M. Takaki, M. Tsumura, T. Yamamoto
The change in the configuration of valence protons between the initial and final states in the neutrinoless double-$β$ decay of $^{130}$Te $\rightarrow$ $^{130}$Xe and of $^{136}$Xe $\rightarrow$ $^{136}$Ba has been determined by measuring the cross sections of the ($d$,$^3$He) reaction with 101-MeV deuterons. Together with our recent determination of the relevant neutron configurations involved in the process, a quantitative comparison with the latest shell-model and interacting-boson-model calculations reveals significant discrepancies. These are the same calculations used to determine the nuclear matrix elements governing the rate of neutrinoless double-$β$ decay in these systems.
We analyze nuclear matrix elements (NME) of neutrinoless double beta decay calculated for the Cadmium isotopes. Energy density functional methods including beyond mean field effects such as symmetry restoration and shape mixing are used. Strong shell effects are found associated to the underlying nuclear structure of the initial and final nuclei. Furthermore, we show that NME for two-neutrino double beta decay evaluated in the closure approximation, $M^{2ν}_{\mathrm{cl}}$, display a constant proportionality with respect to the Gamow-Teller part of the neutrinoless NME, $M^{0ν}_{\mathrm{GT}}$. …
We compute nuclear matrix elements for neutrinoless double electron capture on $^{152}$Gd, $^{164}$Er and $^{180}$W nuclei. Recent precise mass measurements for these nuclei have shown a large resonance enhancement factor that makes them the most promising candidates for observing this decay mode. We use an advanced energy density functional method which includes beyond mean-field effects such as symmetry restoration and shape mixing. Our calculations reproduce experimental charge radii and $B(E2)$ values predicting a large deformation for all these nuclei. This fact reduces significantly the …
The detection of neutrinoless double-beta decay will establish the Majorana nature of neutrinos. In addition, if the nuclear matrix elements of this process are reliably known, the experimental lifetime will provide precious information about the absolute neutrino masses and hierarchy. I review the status of nuclear structure calculations for neutrinoless double-beta decay matrix elements, and discuss some key issues to be addressed in order to meet the demand for accurate nuclear matrix elements.
We study neutrinoless double-beta decay in an effective field theory (EFT) for heavy nuclei, which are treated as a spherical core coupled to additional neutrons and/or protons. Since the low-energy constants of the EFT cannot be fitted to data for this unobserved decay, we follow an alternative strategy to constrain these through a correlation with double Gamow-Teller transitions. This correlation was recently found to hold for shell-model calculations, energy-density functionals, and other nuclear structure models. We therefore first calculate the nuclear matrix elements for double Gamow-Tel…
Nuclear matrix elements (NME) for the most promising candidates to detect neutrinoless double beta decay have been computed with energy density functional methods including deformation and pairing fluctuations explicitly on the same footing. The method preserves particle number and angular momentum symmetries and can be applied to any decay without additional fine tunings. The finite range density dependent Gogny force is used in the calculations. An increase of $10\%-40\%$ in the NME with respect to the ones found without the inclusion of pairing fluctuations is obtained, reducing the predict…
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 …
The discovery that neutrinos have finite rest mass has led to renewed interest in neutrinoless double beta decay. The development of large-scale experiments to search for neutrinoless double beta decay has increased the probability of a credible observation of the process in the near future. The reliability of calculations of the associated nuclear matrix elements is likely soon to become a critical issue. In this paper experimental techniques that access properties of the ground-state wave functions of double beta decay candidates, the occupancies of valence single- particle orbitals and pair…
Neutrinoless double beta decay searches are currently among the major foci of experimental physics. The observation of such a decay will have important implications in our understanding of the intrinsic nature of neutrinos and shed light on the limitations of the Standard Model. The rate of this process depends on both the unknown neutrino effective mass and the nuclear matrix element associated with the given neutrinoless double-beta decay transition. The latter can only be provided by theoretical calculations, hence the need of accurate theoretical predictions of the nuclear matrix element f…
We explore the influence of the deformation on the nuclear matrix elements of the neutrinoless double beta decay (NME), concluding that the difference in deformation -or more generally in the amount of quadrupole correlations- between parent and grand daughter nuclei quenches strongly the decay. We correlate these differences with the seniority structure of the nuclear wave functions. In this context, we examine the present discrepancies between the NME's obtained in the framework of the Interacting Shell Model and the Quasiparticle RPA. We surmise that part of the discrepancy can be due to th…
Neutrinoless double beta-decay(DBD) is of current interest in high-sensitivity frontiers of particle physics. The decay is very sensitive to Majorana neutrinos masses, neutrino CP phases, right-handed weak interactions and others, which are beyond the standard electro-weal model. DBDs are actually ultra-rare events, and thus DBD experiments with ultra-high sensitivity are required. Critical discussions are presented on nuclear and detector sensitivities for high-sensitivity DBD experiments to study the neutrino masses in the normal and inverted hierarchies.
We devise a framework based on the generalized contact formalism that combines the nuclear shell model and quantum Monte Carlo methods and compute the neutrinoless double-beta decay of experimentally relevant nuclei, including $^{76}$Ge, $^{130}$Te, and $^{136}$Xe. In light nuclei, we validate our nuclear matrix element calculations by comparing against accurate variational Monte Carlo results. Due to additional correlations captured by quantum Monte Carlo and introduced within the generalized contact formalism, in heavier systems, we obtain long-range nuclear matrix elements that are about 30…
We present a generator-coordinate calculation, based on a relativistic energy-density functional, of the low-lying spectra in the isotopes $^{150}$Nd and $^{150}$Sm and of the nuclear matrix element that governs the neutrinoless double-beta decay of the first isotope to the second. We carefully examine the impact of octupole correlations on both nuclear structure and the double-beta decay matrix element. Octupole correlations turn out to reduce quadrupole collectivity in both nuclei. Shape fluctuations, however, dilute the effects of octupole deformation on the double-beta decay matrix element…
Neutrinoless $ββ$ decay nuclear matrix elements calculated with the shell model and energy-density functional theory typically disagree by more than a factor of two in the standard scenario of light-neutrino exchange. In contrast, for a decay mediated by sterile heavy neutrinos the deviations are reduced to about 50\%, an uncertainty similar to the one due to short-range effects. We compare matrix elements in the light- and heavy-neutrino-exchange channels, exploring the radial, momentum transfer and angular momentum-parity matrix element distributions, and considering transitions that involve…
Accurate nuclear matrix elements (NMEs) for neutrinoless double beta decays of candidate nuclei are important for the design and interpretation of future experiments. Significant progress has been made in the modeling of these NMEs from first principles. The NME for 48Ca shows a good agreement among three different ab initio calculations starting from the same nuclear interaction constructed within the chiral EFT and the same decay operator. These studies open the door to ab initio calculations of the matrix elements for the decay of heavier nuclei such as 76Ge, 130Te, and 136Xe. The ultimate …
Searches of neutrinoless double-beta decay require information on the value of the nuclear matrix elements that rule the process to plan and interpret experiments. At present, however, even the matrix elements obtained with the most reliable many-body approaches do not agree to each other better than a factor two or three. A usual test of the many-body calculations is the comparison to several nuclear observables, but so far no nuclear structure property has been found to show a good correlation to neutrinoless double-beta decay. Here we propose that double charge-exchange experiments can offe…
Experiments using nuclei to probe new physics beyond the Standard Model, such as neutrinoless $ββ$ decay searches testing whether neutrinos are their own antiparticle, and direct detection experiments aiming to identify the nature of dark matter, require accurate nuclear physics input for optimizing their discovery potential and for a correct interpretation of their results. This demands a detailed knowledge of the nuclear structure relevant for these processes. For instance, neutrinoless $ββ$ decay nuclear matrix elements are very sensitive to the nuclear correlations in the initial and final…
The calculated nuclear matrix elements for the neutrinoless double-beta ($0νββ$) decay suffer from several limitations. Predicted matrix-element values depend on the many-body method used to calculate them and, in addition, they may need to be "quenched", albeit by an unknown amount due to the relatively high momentum transferred in the decay. These uncertainties are hard to figure out from theoretical calculations alone because of the unique character of $0νββ$ decay, not clearly related to other nuclear structure observables. We present recent progress in the determination of the nuclear mat…
We evaluate the leading-order short-range nuclear matrix element for the neutrinoless double-beta ($0νββ$) decay of the nuclei most relevant for experiments, including $^{76}$Ge, $^{100}$Mo, $^{130}$Te and $^{136}$Xe. In our calculations, performed with the nuclear shell model and proton-neutron quasiparticle random-phase approximation (pnQRPA) methods, we estimate the coupling of this term by the contact charge-independence-breaking coupling of various nuclear Hamiltonians. Our results suggest a significant impact of the short-range matrix element, which is about $15\%-50\%$ and $30\%-80\%$ o…
We calculate the nuclear matrix elements (NMEs) for neutrinoless double-beta decays ($0νββ$) of $pf$-shell nuclei using the shell model (SM) and energy density functional (EDF) methods. The systematic study of non-physical decays (except for $^{48}$Ca) of Ca$\rightarrow$Ti, Ti$\rightarrow$Cr and Cr$\rightarrow$Fe allows for a detailed comparison between the two nuclear structure approaches. We observe that while the dominant Gamow-Teller part of the NME differs roughly by a factor of two between SM and EDF, when we restrict the calculations to spherical EDF states and seniority-zero SM configu…
Half-life estimates for neutrinoless double beta decay depend on particle physics models for lepton flavor violation, as well as on nuclear physics models for the structure and transitions of candidate nuclei. Different models considered in the literature can be contrasted - via prospective data - with a "standard" scenario characterized by light Majorana neutrino exchange and by the quasiparticle random phase approximation, for which the theoretical covariance matrix has been recently estimated. We show that, assuming future half-life data in four promising nuclei (Ge-76, Se-82, Te-130, and X…
The physics potential of neutrinoless double beta decay is discussed. Furthermore, experimental considerations are presented as well as the current status of experiments. Finally an outlook towards the future, work on nuclear matrix elements and alternative processes is given.
We study double gamma ($γγ$) decay nuclear matrix elements (NMEs) for a wide range of nuclei from titanium to xenon, and explore their relation to neutrinoless double-beta ($0νββ$) NMEs. To favor the comparison, we focus on double-magnetic dipole transitions in the final $ββ$ nuclei, in particular the $γγ$ decay of the double isobaric analog of the initial $ββ$ state into the ground state. For the decay with equal-energy photons, our large-scale nuclear shell model results show a good linear correlation between the $γγ$ and $0νββ$ NMEs. Our analysis reveals that the correlation holds for $γγ$ …
A quantitative description of the change in ground-state neutron occupancies between $^{136}$Xe and $^{136}$Ba, the initial and final state in the neutrinoless double-$β$ decay of $^{136}$Xe, has been extracted from precision measurements of the cross sections of single-neutron adding and -removing reactions. Comparisons are made to recent theoretical calculations of the same properties using various nuclear-structure models. These are the same calculations used to determine the magnitude of the nuclear matrix elements for the process, which at present disagree with each other by factors of 2 …
Background: The discovery of neutrinoless double-beta ($0νββ$) decay would demonstrate the nature of neutrinos, have profound implications for our understanding of matter-antimatter mystery, and solve the mass hierarchy problem of neutrinos. The calculations for the nuclear matrix elements $M^{0ν}$ of $0νββ$ decay are crucial for the interpretation of this process. Purpose: We study the effects of relativity and nucleon-nucleon short-range correlations on the nuclear matrix elements $M^{0ν}$ by assuming the mechanism of exchanging light or heavy neutrinos for the $0νββ$ decay. Methods: The nuc…
The possibility of observing neutrinoless double beta decay offers the opportunity of determining the neutrino mass IF the nuclear matrix element were known. Theoretical calculations are uncertain and measurements of the occupations of valence orbits by nucleons active in the decay can be important. The occupation of valence neutron orbits in the ground states of 76Ge and 76Se were determined by precisely measuring cross sections for both neutron-adding and removing transfer reactions. Our results indicate that the Fermi surface is much more diffuse than in theoretical (QRPA) calculations. We …
We investigate neutrinoless double-beta decay ($0νββ$) in the minimal extension of the standard model of particle physics, the $ν$SM, where gauge-singlet right-handed neutrinos give rise to Dirac and Majorana neutrino mass terms. We focus on the associated sterile neutrinos and argue that the usual evaluation of their contributions to $0νββ$, based on mass-dependent nuclear matrix elements, is missing important contributions from neutrinos with ultrasoft and hard momenta. We identify the hadronic and nuclear matrix elements that enter the new contributions, and calculate all relevant nuclear m…
We report a systematic study of nuclear matrix elements (NMEs) in neutrinoless double-beta decays with a state-of-the-art beyond mean-field covariant density functional theory. The dynamic effects of particle-number and angular-momentum conservations as well as quadrupole shape fluctuations are taken into account with projections and generator coordinate method for both initial and final nuclei. The full relativistic transition operator is adopted to calculate the NMEs. The present systematic studies show that in most of the cases there is a much better agreement with the previous non-relativi…
The possibility of observing neutrinoless double beta decay offers the opportunity of determining the effective neutrino mass if the nuclear matrix element were known. Theoretical calculations are uncertain and the occupations of valence orbits by nucleons active in the decay are likely to be important. The occupation of valence proton orbits in the ground states of 76Ge, a candidate for such decay, and 76Se, the corresponding daughter nucleus, were determined by precisely measuring cross sections for proton-removing transfer reactions. As in previous work on neutron occupations, we find that …
We calculate basis-space converged neutrinoless $ββ$ decay nuclear matrix elements for the lightest candidates: 48Ca, 76Ge and 82Se. Starting from initial two- and three-nucleon forces, we apply the ab initio in-medium similarity renormalization group to construct valence-space Hamiltonians and consistently transformed $ββ$-decay operators. We find that the tensor component is non-negligible in 76Ge and 82Se, and resulting nuclear matrix elements are overall 25-45% smaller than those obtained from the phenomenological shell model. While a final matrix element with uncertainties still requires …
Neutrinoless double-$β$ ($0νββ$) decay is related to many fundamental concepts in nuclear and particle physics beyond the standard model. Currently there are many experiments searching for this weak process. An accurate knowledge of the nuclear matrix element for the $0νββ$ decay is essential for determining the effective neutrino mass once this process is eventually measured. We report the first full relativistic description of the $0νββ$ decay matrix element based on a state-of-the-art nuclear structure model. We adopt the full relativistic transition operators which are derived with the cha…
Theoretical estimates for the half life of neutrinoless double beta decay in candidate nuclei are affected by both particle and nuclear physics uncertainties, which may complicate the interpretation of decay signals or limits. We study such uncertainties and their degeneracies in the following context: three nuclei of great interest for large-scale experiments (76-Ge, 130-Te, 136-Xe), two representative particle physics mechanisms (light and heavy Majorana neutrino exchange), and a large set of nuclear matrix elements (NME), computed within the quasiparticle random phase approximation (QRPA). …
The generator coordinate method (GCM) is an important tool of choice for modeling large-amplitude collective motion in atomic nuclei. The computational complexity of the GCM increases rapidly with the number of collective coordinates. It imposes a strong restriction on the applicability of the method. In this work, we propose a subspace-reduction algorithm that employs optimal statistical ML models as surrogates for exact quantum-number projection calculations for norm and Hamiltonian kernels. The model space of the original GCM is reduced to a subspace relevant for nuclear low energy spectra …
We present the nuclear matrix element for the neutrinoless double-beta decay of $^{48}$Ca based on large-scale shell-model calculations including two harmonic oscillator shells ($sd$ and $pf$ shells). The excitation spectra of $^{48}$Ca and $^{48}$Ti, and the two-neutrino double-beta decay of $^{48}$Ca are reproduced in good agreement to experiment. We find that the neutrinoless double-beta decay nuclear matrix element is enhanced by about 30\% compared to $pf$-shell calculations. This reduces the decay lifetime by almost a factor of two. The matrix-element increase is mostly due to pairing co…
Neutrinoless double-beta decay is a forbidden, lepton-number-violating nuclear transition whose observation would have fundamental implications for neutrino physics, theories beyond the Standard Model and cosmology. In this review, we summarize the theoretical progress to understand this process, the expectations and implications under various particle physics models, as well as the nuclear physics challenges that affect the precise predictions of the decay half-life. We will also provide a synopsis of the current and future large-scale experiments that aim at discovering this process in physi…
Nuclear weak decays provide important probes to fundamental symmetries in nature. A precise description of these processes in atomic nuclei requires comprehensive knowledge on both the strong and weak interactions in the nuclear medium and on the dynamics of quantum many-body systems. In particular, an observation of the hypothetical double beta decay without emission of neutrinos ($0νββ$) would unambiguously demonstrate the Majorana nature of neutrinos and the existence of the lepton-number-violation process. It would also provide unique information on the ordering and absolute scale of neutr…
Neutrinoless double beta decay, which is a very old and yet elusive process, is reviewed. Its observation will signal that lepton number is not conserved and the neutrinos are Majorana particles. More importantly it is our best hope for determining the absolute neutrino mass scale at the level of a few tens of meV. To achieve the last goal certain hurdles have to be overcome involving particle, nuclear and experimental physics. Nuclear physics is important for extracting the useful information from the data. One must accurately evaluate the relevant nuclear matrix elements, a formidable task. …
The mass difference of the nuclides 180W and 180Hf has been measured with the Penning-trap mass spectrometer SHIPTRAP to investigate 180W as a possible candidate for the search for neutrinoless doubleelectron capture. The Q-value was measured to 143.20(27)keV. This value in combination with the calculations of the atomic electron wave functions and other parameters results in a half-life of the 0+ \rightarrow 0+ ground-state to ground-state double-electron capture transition of approximately 5\cdot10E27 years/<m_ee[eV]>^2.
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 decay. We then calculate for the first time the neutrinoless double-beta 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.
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 and width of the $^{48}$Ca DGT giant resonance and %the value of the $0νββ$ decay nuclear matrix element. More generally, we observe a very goo…
In a previous article [Phys. Rev. D 79, 053001 (2009)] we estimated the correlated uncertainties associated to the nuclear matrix elements (NME) of neutrinoless double beta decay (0 nu beta beta) within the quasiparticle random phase approximation (QRPA). Such estimates encompass recent independent calculations of NMEs, and can thus still provide a fair representation of the nuclear model uncertainties. In this context, we compare the claim of 0 nu beta beta decay in Ge-76 with recent negative results in Xe-136 and in other nuclei, and we infer the lifetime ranges allowed or excluded at 90% C.…
We study the impact of new physics contributions to neutrinoless double beta decay arising from right-handed current in comparison with the standard mechanism. If the light neutrinos obtain their masses from Type-II seesaw within left-right symmetric model, where the Type-I contribution is suppressed to negligible extent, the right-handed PMNS matrix is the same as its left-handed counterpart, making it highly predictable and can be tested at next-generation experiments. It is very attractive, especially with recent cosmological constraint favoring the normal hierarchy under which the neutrino…
Neutrinoless double beta decay has been the subject of intensive theoretical work as it represents the only practical approach to discovering whether neutrinos are Majorana particles or not, and whether lepton number is a conserved quantum number. Available calculations of matrix elements and phase-space factors are reviewed from the perspective of a future large-scale experimental search for neutrinoless double beta decay. Somewhat unexpectedly, a uniform inverse correlation between phase space and the square of the nuclear matrix element emerges. As a consequence, no isotope is either favore…
We perform a global fit of the most relevant neutrinoless double beta decay experiments within the standard model with massive Majorana neutrinos. Using Bayesian inference makes it possible to take into account the theoretical uncertainties on the nuclear matrix elements in a fully consistent way. First, we analyze the data used to claim the observation of neutrinoless double beta decay in Ge-76, and find strong evidence (according to Jeffrey's scale) for a peak in the spectrum and moderate evidence for that the peak is actually close to the energy expected for the neutrinoless decay. We also …
The variances and covariances associated to the nuclear matrix elements (NME) of neutrinoless double beta decay are estimated within the quasiparticle random phase approximation (QRPA). It is shown that correlated NME uncertainties play an important role in the comparison of neutrinoless double beta decay rates for different nuclei, and that they are degenerate with the uncertainty in the reconstructed Majorana neutrino mass.
The study of neutrinoless double beta decay is of outmost importance for neutrino physics. It is considered to be the gold plated channel to probe the fundamental character of neutrinos and to determine the neutrino mass. From the experimental point about nine different isotopes are explored for the search. After a general introduction follows a short discussion on nuclear matrix element calculations and supportive measurements. The current experimental status of double beta searches is presented followed by a short discussion of the ideas and proposals for large scale experiments.
The decay rate of neutrinoless double beta ($0νββ$) decay contains terms from heavy particle exchange, which lead to dimension-9 (d=9) six fermion operators at low energies. Limits on the coefficients of these operators have been derived previously neglecting the running of the operators between the high-scale, where they are generated, and the energy scale of double beta decay, where they are measured. Here we calculate the leading order QCD corrections to all possible d=9 operators contributing to the $0νββ$ amplitude and use RGE running to calculate 1-loop improved limits. Numerically, QCD …
We present a necessary condition on the solar oscillation amplitude for CP violation to be detectable through neutrinoless double beta (0νββ) decay. It depends only on the fractional uncertainty in the ν_e-ν_e element of the neutrino mass matrix. We demonstrate that even under very optimistic assumptions about the sensitivity of future experiments to the absolute neutrino mass scale, and on the precision with which nuclear matrix elements that contribute to 0νββdecay are calculable, it will be impossible to detect neutrino CP violation arising from Majorana phases.
