Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review (1610.06548v2)

Abstract: 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.

• The paper provides a comprehensive review of nuclear models used to calculate matrix elements for neutrinoless double-beta decay, highlighting challenges and advancements.
• It assesses methods such as the shell model, QRPA, EDF, and IBM, emphasizing their strengths, limitations, and treatment of nuclear correlations.
• The study outlines future directions including expanded configuration spaces, ab initio techniques, and rigorous uncertainty quantification to refine theoretical predictions.

An Overview of "Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review"

The paper "Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review" by Jonathan Engel and Javier Menéndez presents an extensive overview of the current theoretical efforts aimed at understanding nuclear matrix elements relevant to neutrinoless double-beta ($0\nu\beta\beta$) decay. This process is of paramount interest because it could establish whether neutrinos are Majorana particles and provide insights into the absolute neutrino mass scale.

Theoretical Framework and Nuclear Models

The paper critically evaluates a variety of nuclear models that are employed to compute matrix elements for $0\nu\beta\beta$ decay, such as the shell model, the quasiparticle random phase approximation (QRPA), energy density functional (EDF) theory, and the interacting boson model (IBM).

• Shell Model: Known for accurately capturing correlations among valence nucleons, the shell model is limited by its configuration space and demands computational resources that grow exponentially. Recent advancements enable calculations in two oscillator shells, although challenges persist in fully incorporating pairing correlations and capturing single-particle levels accurately.
• QRPA: This method can handle large configuration spaces, thus ensuring approximately correct behavior concerning particle-particle interactions. QRPA, however, often requires empirical adjustments, notably in the proton-neutron pairing interaction, to align theoretical predictions with experimental data.
• EDF and GCM: These methods provide a good description of collective correlations through configurational mixing and can include both deformation and pairing fluctuations. The primary limitation lies in missing non-collective correlations, leading often to larger matrix elements compared to the shell model.
• IBM: Focused on collective states, the interacting boson model offers another perspective on matrix element calculations. The authors highlight the need to incorporate generalized correlations to refine results derived from the IBM.

Addressing the $g_A$ Quenching Problem

A significant portion of the paper discusses the renormalization of the axial vector coupling constant $g_A$, often referred to as the $g_A$ problem. Empirical evidence has long suggested the need for quenching the Gamow-Teller transition operator $\bm{\sigma} \bm{\tau}$ to align theoretical predictions with experimental Gamow-Teller strengths in single-beta decay and two-neutrino double-beta decay. This discrepancy influences $0\nu\beta\beta$ decay predictions and necessitates a detailed understanding of its origins, whether due to missing many-body correlations or effects from two-nucleon currents (meson-exchange currents).

Future Directions and Improvements

The authors advocate several strategies for reducing uncertainties in matrix element calculations:

1. Extension of Configuration Spaces: Expanding configuration spaces in shell models using Monte Carlo methods or density-matrix renormalization group techniques can provide insight into correlations missing in smaller spaces.
2. Incorporating Collective Correlations: Enhancements of current models to systematically include correlations such as isoscalar pairing, known to potentially suppress matrix elements.
3. Ab Initio Methods: Application of methods like coupled-cluster theory and the in-medium similarity renormalization group (IMSRG) to perform more predictive calculations for heavy nuclei relevant to $0\nu\beta\beta$ decay. These approaches promise to describe nuclear structure directly from fundamental interactions.
4. Quantification of Theoretical Uncertainties: The development of rigorous error estimation procedures, possibly leveraging Bayesian methods, to provide uncertainties that reflect both parametric and systematic errors.

Conclusion

Engel and Menéndez's review carefully outlines the challenges and future prospects in computing nuclear matrix elements for $0\nu\beta\beta$ decay. The field is on the cusp of substantial progress, thanks largely to the convergence of improved computational techniques and a deeper theoretical understanding of nuclear interactions and correlations. The successful reduction of theoretical uncertainties is expected to significantly enhance experimental sensitivity to the rare $0\nu\beta\beta$ decay process, thereby offering insights into the fundamental nature of neutrinos and potentially, the larger framework of particle physics.