Calculation Of Nuclear Matrix Elements Research Articles

New limit for the half-life of double beta decay of 94Zr to the first excited state of 94Mo

Neutrinoless Double Beta Decay is a phenomenon of fundamental interest in particle physics. The decay rates of double beta decay transitions to the excited states can provide input for Nuclear Transition Matrix Element calculations for the relevant two neutrino double beta decay process. It can be useful as supplementary information for the calculation of Nuclear Transition Matrix Element for the neutrinoless double beta decay process. In the present work, double beta decay of $^{94}$Zr to the $2^{+}_{1}$ excited state of $^{94}$Mo at 871.1 keV is studied using a low background $\sim$ 230 cm$^3$ HPGe detector. No evidence of this decay was found with a 232 g.y exposure of natural Zirconium. The lower half-life limit obtained for the double beta decay of $\rm^{94}Zr$ to the $2^{+}_{1}$ excited state of $\rm^{94}Mo$ is $T_{1/2} (0\nu + 2\nu)> 3.4 \times 10^{19}$ y at 90% C.L., an improvement by a factor of $\sim$ 4 over the existing experimental limit at 90\% C.L. The sensitivity is estimated to be $T_{1/2} (0\nu + 2\nu) > 2.0\times10^{19}$ y at 90% C.L. using the Feldman-Cousins method.

Search for two-neutrino double electron capture of Xe124 with XENON100

Two-neutrino double electron capture is a rare nuclear decay where two electrons are simultaneously captured from the atomic shell. For $^{124}$Xe this process has not yet been observed and its detection would provide a new reference for nuclear matrix element calculations. We have conducted a search for two-neutrino double electron capture from the K-shell of $^{124}$Xe using 7636 kg$\cdot$d of data from the XENON100 dark matter detector. Using a Bayesian analysis we observed no significant excess above background, leading to a lower 90 % credibility limit on the half-life $T_{1/2}>6.5\times10^{20}$ yr. We also evaluated the sensitivity of the XENON1T experiment, which is currently being commissioned, and find a sensitivity of $T_{1/2}>6.1\times10^{22}$ yr after an exposure of 2 t$\cdot$yr.

Search for Majorana Neutrinos Near the Inverted Mass Hierarchy Region with KamLAND-Zen.

We present an improved search for neutrinoless double-beta (0νββ) decay of ^{136}Xe in the KamLAND-Zen experiment. Owing to purification of the xenon-loaded liquid scintillator, we achieved a significant reduction of the ^{110m}Ag contaminant identified in previous searches. Combining the results from the first and second phase, we obtain a lower limit for the 0νββ decay half-life of T_{1/2}^{0ν}>1.07×10^{26} yr at 90%C.L., an almost sixfold improvement over previous limits. Using commonly adopted nuclear matrix element calculations, the corresponding upper limits on the effective Majorana neutrino mass are in the range 61-165meV. For the most optimistic nuclear matrix elements, this limit reaches the bottom of the quasidegenerate neutrino mass region.

Measurement of the double-beta decay half-life and search for the neutrinoless double-beta decay ofCa48with the NEMO-3 detector

The NEMO-3 experiment at the Modane Underground Laboratory has investigated the double-$\beta$ decay of $^{48}{\rm Ca}$. Using $5.25$ yr of data recorded with a $6.99\,{\rm g}$ sample of $^{48}{\rm Ca}$, approximately $150$ double-$\beta$ decay candidate events have been selected with a signal-to-background ratio greater than $3$. The half-life for the two-neutrino double-$\beta$ decay of $^{48}{\rm Ca}$ has been measured to be $T^{2\nu}_{1/2}\,=\,[6.4\, ^{+0.7}_{-0.6}{\rm (stat.)} \, ^{+1.2}_{-0.9}{\rm (syst.)}] \times 10^{19}\,{\rm yr}$. A search for neutrinoless double-$\beta$ decay of $^{48}{\rm Ca}$ yields a null result and a corresponding lower limit on the half-life is found to be $T^{0\nu}_{1/2} > 2.0 \times 10^{22}\,{\rm yr}$ at $90\%$ confidence level, translating into an upper limit on the effective Majorana neutrino mass of $< m_{\beta\beta} > < 6.0 - 26$ ${\rm eV}$, with the range reflecting different nuclear matrix element calculations. Limits are also set on models involving Majoron emission and right-handed currents.

Search for two-neutrino double electron capture on 124Xe with the XMASS-I detector

Double electron capture is a rare nuclear decay process in which two orbital electrons are captured simultaneously in the same nucleus. Measurement of its two-neutrino mode would provide a new reference for the calculation of nuclear matrix elements whereas observation of its neutrinoless mode would demonstrate lepton number violation. A search for two-neutrino double electron capture on $^{124}$Xe is performed using 165.9 days of data collected with the XMASS-I liquid xenon detector. No significant excess above background was observed and we set a lower limit on the half-life as $4.7 \times 10^{21}$ years at 90% confidence level. The obtained limit has ruled out parts of some theoretical expectations. We obtain a lower limit on the $^{126}$Xe two-neutrino double electron capture half-life of $4.3 \times 10^{21}$ years at 90% confidence level as well.

QCD running in neutrinoless double beta decay: Short-range mechanisms

The decay rate of neutrinoless double beta ($0\nu\beta\beta$) 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 $0\nu\beta\beta$ amplitude and use RGE running to calculate 1-loop improved limits. Numerically, QCD running changes limits by factors of the order of or larger than typical uncertainties in nuclear matrix element calculations. For some specific cases, operator mixing in the running changes limits even by up to two orders of magnitude. Our results can be straightforwardly combined with new experimental limits or improved nuclear matrix element calculations to re-derive updated limits on all short-range contributions to $0\nu\beta\beta$ decay.

The nature of massive neutrinos and multiple mechanisms in neutrinoless double-beta decay

Determining the nature --Dirac or Majorana-- of massive neutrinos is one of the most pressing and challenging problems in the field of neutrino physics. We discuss how one can possibly extract information on the couplings, if any, which might be involved in $ (\beta\beta)_{0\nu}$ -decay using a multi-isotope approach. We investigate as well the potential of combining data on the half-lives of nuclides with largely different Nuclear Matrix Elements such as 136Xe and of one or more of the four nuclei 76Ge, 82Se, 100Mo and 130Te, for discriminating between different pairs of noninterfering or interfering mechanisms of $ (\beta\beta)_{0\nu}$ -decay. The case studies do not extend to the evaluation of the theoretical uncertainties of the results, due to the nuclear matrix elements calculations and other causes.

Search for two-neutrino double-βdecay ofZr96to excited states ofMo96

Background: Double-$\ensuremath{\beta}$ decay is a rare second-order nuclear decay. The importance of this decay stems from the possibility of neutrinoless double-$\ensuremath{\beta}$ decay and its applications to neutrino physics.Purpose: A search was conducted for the $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay of $^{96}\mathrm{Zr}$ to excited final states of the daughter nucleus, $^{96}\mathrm{Mo}$. Measurements of this decay are important to test nuclear matrix element calculations, which are necessary to extract the neutrino mass from a measurement of the neutrinoless double-$\ensuremath{\beta}$ decay half-life.Method: Two coaxial high-purity germanium detectors were used in coincidence to detect $\ensuremath{\gamma}$ rays produced by the daughter nucleus as it de-excited to the ground state. The experiment was carried out at the Kimballton Underground Research Facility and produced 685.7 d of data with a 17.91 g enriched sample.Results: No counts were seen above background. For the decay to the first excited ${0}^{+}$ state, a limit of ${T}_{1/2}g3.1\ifmmode\times\else\texttimes\fi{}{10}^{20}$ yr was produced. Limits to higher excited states are also reported.Conclusion: The new limits on double-$\ensuremath{\beta}$ decay are an improvement over previous experiments by a factor of 2 to 5 for the various excited states. The nuclear matrix element for the double-$\ensuremath{\beta}$ decay to the first excited ${0}^{+}$ state is found to be $l0.13$.

New physics effects on neutrinoless double beta decay from right-handed current

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 testable at next-generation experiments. It is very attractive, especially with recent cosmological constraint favoring the normal hierarchy under which the neutrinoless double beta decay is too small to be observed unless new physics appears as indicated by the recent diboson excess observed at ATLAS. The relative contributions from left- and right-handed currents can be reconstructed with the ratio between lifetimes of two different isotopes as well as the ratio of nuclear matrix elements. In this way, the theoretical uncertainties in the calculation of nuclear matrix elements can be essentially avoided. We also discuss the interplay of neutrinoless double beta decay measurements with cosmology, beta decay, and neutrino oscillation.

Neutrinoless double beta decay: Theoretical challenges

The recent progress in theoretical description of the neutrinoless double beta decay (0νββ-decay) is briefly reviewed. A possible effect of nuclear medium on exchange of three light neutrinos is addressed. It is shown that non-standard neutrino interaction generates in-medium Majorana neutrino masses, which influences the 0νββ-decay rate. A subject of interest is also a problem of reliable calculation of the 0νββ-decay nuclear matrix elements. An impact of the quenching of the axial-vector coupling constant on double beta decay processes is discussed. A connection between two-neutrino and neutrinoless double beta decay nuclear matrix elements is analyzed.

0νββand2νββnuclear matrix elements in the interacting boson model with isospin restoration

We introduce a method for isospin restoration in the calculation of nuclear matrix elements (NME) for $0\nu\beta\beta$ and $2\nu\beta\beta$ decay within the framework of interacting boson model (IBM-2). With this method, we calculate NME for all processes of interest in $0\nu\beta^-\beta^-$, $2\nu\beta^-\beta^-$, and in $0\nu\beta^+\beta^+$, $0\nu\beta^+ EC^+$, $R0\nu ECEC$, $2\nu\beta^+\beta^+$, $2\nu\beta^+EC$, and $2\nu ECEC$. With this method, the Fermi (F) matrix elements for $2\nu\beta\beta$ vanish, and those for $0\nu\beta\beta$ are considerably reduced.

Shell model calculations for neutrinoless double beta decay

The study of the neutrinoless double beta (0νββ) decay is of great interest because of its potential to provide us with information about the lepton number conservation and neutrino properties as the neutrinos character (are they Dirac or Majorana particles?) and their absolute mass. Since the 0νββ decay has not yet been discovered experimentally, one can only extract limits of the absolute neutrino mass. For that, one needs accurate calculations of both nuclear matrix elements (NMEs) and phase space factors (PSFs) which appear in the theoretical lifetime expressions, corroborated with experimental lifetime limits. In this paper I first present recent shell model (ShM) calculations of the NMEs and PSFs for 0νββ decay performed by our group, in the hypothesis that the mechanism of its occurrence is the exchange of light Majorana neutrinos between two nucleons inside the nucleus. Also, the consensus on the use of different nuclear structure ingredients/parameters in the computation of the NMEs is discussed. Then, I present new limits of the Majorana neutrino mass parameter derived from the analysis of 0νββ decay of nine isotopes.

Neutrinoless double-electron capture

Direct determination of the neutrino mass is at the present time one of the most important aims of experimental and theoretical research in nuclear and particle physics. A possible way of detection is through neutrinoless double-electron capture, $0\ensuremath{\nu}\mathrm{ECEC}$. This process can only occur when the energy of the initial state matches precisely that of the final state. We present here a calculation of prefactors (PFs) and nuclear matrix elements (NMEs) within the framework of the microscopic interacting boson model (IBM-2) for $^{124}\mathrm{Xe}$, $^{152}\mathrm{Gd}$, $^{156}\mathrm{Dy}$, $^{164}\mathrm{Er}$, and $^{180}\mathrm{W}$. From the PF and NME we calculate the expected half-lives and obtain results that are of the same order as those of $0\ensuremath{\nu}{\ensuremath{\beta}}^{+}{\ensuremath{\beta}}^{+}$ decay, but considerably longer than those of $0\ensuremath{\nu}{\ensuremath{\beta}}^{\ensuremath{-}}{\ensuremath{\beta}}^{\ensuremath{-}}$ decay.

Constraining neutrino mass from neutrinoless double beta decay

We re-analyze the compatibility of the claimed observation of neutrinoless double beta decay ($0\nu\beta\beta$) in $^{76}$Ge with the new limits on the half-life of $^{136}$Xe from EXO-200 and KamLAND-Zen. Including recent calculations of the nuclear matrix elements (NMEs), we show that while the claim in $^{76}$Ge is still compatible with the individual limits from $^{136}$Xe, it is inconsistent with the KamLAND-Zen+EXO-200 combined limit for all but one NME calculations. After imposing the most stringent upper limit on the sum of light neutrino masses from Planck, we find that the canonical light neutrino contribution cannot satisfy the claimed $0\nu\beta\beta$ signature or saturate the current limit, irrespective of the NME uncertainties. However, inclusion of the heavy neutrino contributions, arising naturally in TeV-scale Left-Right symmetric models, can saturate the current limit of $0\nu\beta\beta$. In a type-II seesaw framework, this imposes a lower limit on the lightest neutrino mass. Depending on the mass hierarchy, we obtain this limit to be in the range of 0.07 - 4 meV for a typical choice of the right-handed (RH) gauge boson and RH neutrino masses relevant for their collider searches. Using the $0\nu\beta\beta$ bounds, we also derive correlated constraints in the RH sector, complimentary to those from the LHC.

Neutrinoless double-positron decay and positron-emitting electron capture in the interacting boson model

Neutrinoless double-$\ensuremath{\beta}$ decay is of fundamental importance for determining the neutrino mass. Although double electron decay is the most promising mode, in very recent years interest in double positron decay, positron emitting electron capture, and double electron capture has been renewed. We present here results of a calculation of nuclear matrix elements for neutrinoless double-${\ensuremath{\beta}}^{+}$ decay and positron emitting electron capture within the framework of the microscopic interacting boson model (IBM-2) for ${}^{58}$Ni, ${}^{64}$Zn, ${}^{78}$Kr, ${}^{96}$Ru, ${}^{106}$Cd, ${}^{124}$Xe, ${}^{130}$Ba, and ${}^{136}$Ce decay. By combining these with a calculation of phase space factors we calculate expected half-lives.

Addendum to: Quasiparticle random phase approximation uncertainties and their correlations in the analysis of0νββdecay

In a previous article [A. Faessler et al., Phys. Rev. D 79, 053001 (2009)], we estimated the correlated uncertainties associated to the nuclear matrix elements of neutrinoless double beta decay ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) within the quasiparticle random phase approximation. Such estimates encompass recent independent calculations of nuclear matrix elements and can thus still provide a fair representation of the nuclear model uncertainties. In this context, we compare the claim of $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay in $^{76}\mathrm{Ge}$ with recent negative results in $^{136}\mathrm{Xe}$ and in other nuclei, and we infer the lifetime ranges allowed or excluded at 90% C.L. We also highlight some issues that should be addressed in order to properly compare and combine results coming from different $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ candidate nuclei.

Nuclear matrix elements for neutrinoless double-beta decay and double-electron capture

A new generation of neutrinoless double-beta decay (0νββ-decay) experiments with improved sensitivity is currently being designed and under construction. They will probe the inverted hierarchy region of the neutrino mass pattern. There is also a revived interest in the resonant neutrinoless double-electron capture (0νECEC), which also has the potential to probe lepton number conservation and to investigate the neutrino nature and mass scale. The primary concerns are the nuclear matrix elements. Clearly, the accuracy of the determination of the effective Majorana neutrino mass from the measured 0νββ-decay half-life is mainly determined by our knowledge of the nuclear matrix elements. We review recent progress achieved in the calculation of 0νββ and 0νECEC nuclear matrix elements within the quasiparticle random phase approximation. A considered self-consistent approach allows us to derive the pairing, residual interactions and the two-nucleon short-range correlations from the same modern realistic nucleon–nucleon potentials. The effect of nuclear deformation is taken into account. The possibility of evaluating 0νββ-decay matrix elements phenomenologically is discussed.

Neutron pair correlations inA=100nuclei involved in neutrinoless double-βdecay

The pairing properties of the neutrinoless double beta decay $(0\nu2\beta)$ candidate $^{100}$Mo have been studied, along with its daughter $^{100}$Ru, to provide input for nuclear matrix element calculations relevant to the decay. The $(p,t)$ two-neutron transfer reaction was measured on nuclei of $^{102,100}$Ru and $^{100,98}$Mo. The experiment was designed to have particular sensitivity to $0^{+}$ states up to excitation energies of $\sim 3$ MeV with high energy resolution. Measurements were made at two angles and L=0 transitions identified by the ratio of yields between the two angles. For the reactions leading to and from $^{100}$Ru, greater than 95% of the L=0 $(p,t)$ strength was in the ground state, but in $^{100}$Mo about 20% was in excited $0^{+}$ states. The measured $(p,t)$ data, together with existing $(t,p)$ data, suggest that $^{100}$Mo is a shape-transitional nucleus while $^{100}$Ru is closer to the spherical side of that transition. Theoretical calculations of the $0\nu2\beta$ nuclear matrix element may be complicated by this difference in shape.

Constraining neutrinoless double β decay matrix elements in 130Te

If a reliable measurement of a neutrinoless double beta decay (0v2β) rate is made, the effective neutrino masses can be determined from the nuclear matrix element. Theoretical calculations of nuclear matrix elements, however, show some disagreement. To test the suitability of various theoretical models, they should be benchmarked against experimentally measured nuclear properties, such as the ground-state distribution of nucleons in the parent-daughter nuclei, and how they change as a result of the decay process. Single neutron-adding reactions have been performed on the 0v2β candidate nucleus, 130Te. The Macfarlane-French sum rules have then been used to determine the single-particle vacancies. Some quasi-random phase approximations (QRPA) can greatly simplify theoretical calculations by describing the ground state of even-even nuclei using a BCS wavefunction. This assumption has been tested using two-neutron removal, (p,t) reactions. The BCS wavefunction appeared to be a valid approximation for valence neutrons.

Limits on Neutrino Masses from Neutrinoless Double-βDecay

Neutrinoless double-β decay is of fundamental importance for the determining neutrino mass. By combining a calculation of nuclear matrix elements within the framework of the microscopic interacting boson model with an improved calculation of phase space factors, we set limits on the average light neutrino mass and on the average inverse heavy neutrino mass (flavor-violating parameter).