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Register a new userRelationship between Neutrinoless $betabeta$-Decay and Double Charge-Exchange Resonances
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C. De Conti
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To describe the double-charge-exchange (DCE) processes, we have designed recently the $(pn,2p2n)$-QTDA model which fully includes the pairing correlations and four quasiparticle excitations. It has been applied in $2 u$ double beta decays (DBDs), and the double charge-exchange resonances (DCERs). Here we extend it to $ 0 u $ DBD and discuss the relationship between the nuclear matrix elements (NMEs), and the DCE reaction matrix elements (RMEs) with the same spin-isospin structure. We do it for all final $0^+$ states, even in the region of DCERs, where the DBD is energetically forbidden. As an example, we evaluate the DBD $^{76}$Ge $rightarrow ^{76}$Se, both for $2 u$ and $0 u$ modes, as well as the associated DCE sum rules, excitation energies within the $Q$-value window for DBD, and the $Q$-value itself. We find that the $0 u$ NMEs are correlated with the RMEs, both at low energy, and in the DCER region where most of the transition strength is concentrated. These findings occur in other nuclei as well and suggest that measurements of $0^+$ DCERs could provide useful information regarding the $ 0 u $ DBD. An analogous comparison and conclusion cannot be made for the $2^+$ states, since the $0 u$ NMEs and RMEs transition operators are not similar to each other in this case.
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We study double gamma ($gammagamma$) decay nuclear matrix elements (NMEs) for a wide range of nuclei from titanium to xenon, and explore their relation to neutrinoless double-beta ($0 ubetabeta$) NMEs. To favor the comparison, we focus on double-magnetic dipole transitions in the final $betabeta$ nuclei, in particular the $gammagamma$ decay of the double isobaric analog of the initial $betabeta$ state into the ground state. For the most probable decay with equal-energy photons, our large-scale nuclear shell model results show a good linear correlation between the $gammagamma$ and $0 ubetabeta$ NMEs. Our analysis reveals that the correlation holds for $gammagamma$ transitions driven by the spin or orbital angular momentum due to the dominance of zero-coupled nucleon pairs, a feature common to $0 ubetabeta$ decay. Our findings point out the potential of future $gammagamma$ decay measurements to constrain $0 ubetabeta$ NMEs, which are key to answer fundamental physics questions based on $0 ubetabeta$ experiments.
The Gamow-Teller resonances are discussed in the context of a self-consistent RPA, based on the relativistic mean field theory. We inquire on the possibility of substituting the phenomenological Landau-Migdal force by a microscopic nucleon-nucleon interaction generated from the rho-nucleon tensor coupling. The effect of this coupling turns out to be very small when the short range correlations are not taken into account, but too large when these correlations are simulated by the simple extraction of the contact terms from the resulting nucleon-nucleon interaction.
A new generation of neutrinoless double beta decay experiments with improved sensitivity is currently under design and construction. They will probe inverted hierarchy region of the neutrino mass pattern. There is also a revived interest to the resonant neutrinoless double-electron capture, which has also a potential to probe lepton number conservation and to investigate the neutrino nature and mass scale. The primary concern are the nuclear matrix elements. Clearly, the accuracy of the determination of the effective Majorana neutrino mass from the measured 0 ubetabeta-decay half-life is mainly determined by our knowledge of the nuclear matrix elements. We review recent progress achieved in the calculation of 0 ubetabeta and 0 u ECEC nuclear matrix elements within the quasiparticle random phase approximation. A considered self-consistent approach allow 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. A possibility to evaluate 0 ubetabeta-decay matrix elements phenomenologically is discussed.
The interpretation of experiments that search for neutrinoless double beta decay relies on input from nuclear theory. Cirigliano et al. recently showed that, for the light Majorana exchange formalism, effective field theory calculations require a $nnto pp e^- e^-$ contact term at leading order. They estimated the size of this contribution by relating it to measured charge-independence-breaking (CIB) nucleon-nucleon interactions and making an assumption about the relative sizes of CIB operators. We show that the assumptions underlying this approximation are justified in the limit of the number of colors $N_c$ being large. We also obtain a large-$N_c$ hierarchy among CIB nucleon-nucleon interactions that is in agreement with phenomenological results.
The process at the heart of neutrinoless double-beta decay, $nn rightarrow p p, e^- e^-$ induced by a light Majorana neutrino, is investigated in pionless and chiral effective field theory. We show in various regularization schemes the need to introduce a short-range lepton-number-violating operator at leading order, confirming earlier findings. We demonstrate that such a short-range operator is only needed in spin-singlet $S$-wave transitions, while leading-order transitions involving higher partial waves depend solely on long-range currents. Calculations are extended to include next-to-leading corrections in perturbation theory, where to this order no additional undetermined parameters appear. We establish a connection based on chiral symmetry between neutrinoless double-beta decay and nuclear charge-independence breaking induced by electromagnetism. Data on the latter confirm the need for a leading-order short-range operator, but do not allow for a full determination of the corresponding lepton-number-violating coupling. Using a crude estimate of this coupling, we perform ab initio calculations of the matrix elements for neutrinoless double-beta decay for $^6$He and $^{12}$Be. We speculate on the phenomenological impact of the leading short-range operator on the basis of these results.
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