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Register a new userTowards complete leading-order predictions for neutrinoless double $beta$ decay
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The amplitude for the neutrinoless double $beta$ ($0 ubetabeta$) decay of the two-neutron system, $nnto ppe^-e^-$, constitutes a key building block for nuclear-structure calculations of heavy nuclei employed in large-scale $0 ubetabeta$ searches. Assuming that the $0 ubetabeta$ 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 work, we develop a method to estimate the numerical value of its coefficient in analogy to the Cottingham formula and validate the result by reproducing the charge-independence-breaking contribution to the nucleon-nucleon scattering lengths. Our central result, while derived in the $overline{text{MS}}$ scheme, is given in terms of the renormalized amplitude $mathcal{A}_ u(|mathbf{p}|,|mathbf{p}^prime|)$, 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 $0 ubetabeta$ decay.
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We present a method to determine the leading-order (LO) contact term contributing to the $nn to pp e^-e^-$ amplitude through the exchange of light Majorana neutrinos. Our approach is based on the representation of the amplitude as the momentum integral of a known kernel (proportional to the neutrino propagator) times the generalized forward Compton scattering amplitude $n(p_1) n(p_2) W^+ (k) to p(p_1^prime) p(p_2^prime) W^- (k)$, in analogy to the Cottingham formula for the electromagnetic contribution to hadron masses. We construct model-independent representations of the integrand in the low- and high-momentum regions, through chiral EFT and the operator product expansion, respectively. We then construct a model for the full amplitude by interpolating between these two regions, using appropriate nucleon factors for the weak currents and information on nucleon-nucleon ($N! N$) scattering in the $^1S_0$ channel away from threshold. By matching the amplitude obtained in this way to the LO chiral EFT amplitude we obtain the relevant LO contact term and discuss various sources of uncertainty. We validate the approach by computing the analog $I = 2$ $N! N$ contact term and by reproducing, within uncertainties, the charge-independence-breaking contribution to the $^1S_0$ $N! N$ scattering lengths. While our analysis is performed in the $overline{rm MS}$ scheme, we express our final result in terms of the scheme-independent renormalized amplitude ${cal A}_ u(|{bf p}|,|{bf p}^prime|)$ at a set of kinematic points near threshold. We illustrate for two cutoff schemes how, using our synthetic data for ${cal A}_ u$, one can determine the contact-term contribution in any regularization scheme, in particular the ones employed in nuclear-structure calculations for isotopes of experimental interest.
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 goal is the computation of NMEs in many-body calculations with controllable approximations, using nuclear interactions and weak transition operators derived consistently from chiral EFT. We are expecting more progress towards this goal in the near future.
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.
We present the first ab initio calculations of neutrinoless double beta decay matrix elements in $A=6$-$12$ nuclei using Variational Monte Carlo wave functions obtained from the Argonne $v_{18}$ two-nucleon potential and Illinois-7 three-nucleon interaction. We study both light Majorana neutrino exchange and potentials arising from a large class of multi-TeV mechanisms of lepton number violation. Our results provide benchmarks to be used in testing many-body methods that can be extended to the heavy nuclei of experimental interest. In light nuclei we have also studied the impact of two-body short range correlations and the use of different forms for the transition operators, such as those corresponding to different orders in chiral effective theory.
We discuss a mechanism of neutrinoless double beta decay, where neutrinos of different flavours come into play. This is realized by effective flavour-violating scalar interactions. As one consequence, we find that within the normal mass ordering the neutrino effective mass may no longer vanish due to contributions from other flavours. We evaluate the necessary nuclear matrix elements, consider the interference between the standard diagram and the new scalar one, and analyze a UV-complete model that realizes the scalar interaction. Tests of the complete model are possible at colliders and future neutrino experiments. Our scenario represents an alternative mechanism for neutrinoless double beta decay, where nevertheless lepton number violation resides only in Majorana mass terms of light neutrinos.
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