[Paper Review] What do we know about neutrinoless double-beta decay nuclear matrix elements?

J. Menéndez|arXiv (Cornell University)|May 17, 2016

Neutrino Physics Research3 citations

TL;DR

This paper reviews the current status of nuclear matrix element (NME) calculations for neutrinoless double-beta decay (0νββ), emphasizing that discrepancies of up to a factor of three in NMEs across different theoretical frameworks hinder precise extraction of neutrino masses. It highlights that improved NMEs require larger shell-model configuration spaces, inclusion of isoscalar pairing correlations, and the critical addition of two-body currents from chiral effective field theory, which reduce NMEs by ~35% and are essential for accuracy.

ABSTRACT

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.

Motivation & Objective

• To assess the current state of nuclear structure calculations for 0νββ decay matrix elements.
• To identify key theoretical uncertainties limiting the accuracy of NME predictions.
• To evaluate the impact of two-body currents in chiral effective field theory on NME calculations.
• To emphasize the importance of including isoscalar pairing and extended configuration spaces for reliable NMEs.
• To guide future theoretical efforts toward reducing uncertainties for precise neutrino mass determination.

Proposed method

• Uses shell model calculations with extended configuration spaces (e.g., two major harmonic-oscillator shells) to assess the impact on 48Ca NMEs.
• Applies the quasiparticle random-phase approximation (QRPA) and interacting boson model (IBM-2) to compare NMEs across frameworks.
• Evaluates two-body currents in chiral effective field theory (EFT) via normal-ordering approximation over a Fermi gas reference state.
• Incorporates leading-order (Q⁰), next-to-leading-order (Q²), and next-to-next-to-leading-order (Q³) contributions from chiral EFT currents.
• Compares results from phenomenological one-body currents with those from chiral EFT one- and two-body currents.
• Analyzes momentum-dependent modifications of axial and vector currents, particularly the Gamow-Teller quenching effect from Δ-isobar excitation.

Experimental results

Research questions

• RQ1 How do different nuclear structure frameworks (e.g., shell model, QRPA, EDF) compare in predicting 0νββ decay matrix elements?
• RQ2 To what extent do configuration space size and pairing correlations affect the calculated NMEs?
• RQ3 What is the quantitative impact of two-body currents in chiral effective field theory on 0νββ NMEs?
• RQ4 Why do existing NME calculations differ by a factor of two to three despite similar input models?
• RQ5 Can two-body current corrections resolve discrepancies between NME calculations and experimental lifetime constraints?

Key findings

• The inclusion of two major harmonic-oscillator shells in the shell model increases the 48Ca NME by approximately 30% compared to one-shell calculations, due to enhanced cross-shell pairing correlations.
• Two-body currents in chiral EFT reduce the NME by about 35% compared to one-body current calculations, primarily through quenching of the Gamow-Teller matrix element.
• The dominant two-body contribution arises from the axial current correction due to low-lying Δ-isobar excitation, which mimics the Gamow-Teller quenching observed in other nuclear transitions.
• The uncertainty in two-body current contributions is large (~35% error band) due to imprecise knowledge of low-energy chiral EFT couplings.
• Discrepancies between NME calculations are not fully explained by configuration space size alone, indicating that correlations and many-body currents remain key open issues.
• Future accurate NMEs must include both larger configuration spaces and two-body currents from chiral EFT to reduce theoretical uncertainty for neutrino mass extraction.