[Paper Review] Neutrinoless Double $β$-Decay

S. M. Bilenky|ArXiv.org|Mar 23, 2004

Neutrino Physics Research4 citations

TL;DR

This paper reviews neutrinoless double beta decay (0νββ-decay) as the most sensitive probe for determining whether neutrinos are Majorana particles. It analyzes current experimental limits on the effective Majorana mass, predicts its possible values based on neutrino oscillation data, and proposes a model-independent test using multiple nuclei to validate nuclear matrix element calculations.

ABSTRACT

The neutrinoless double $β$-decay is reviewed. Model independent evidence in favor of neutrino masses and mixing is briefly summarized. The data of the recent experiments on the search for $0νββ$-decay are presented and some future experiments are discussed. The possible values of the effective Majorana mass, which can be predicted on the basis of the neutrino oscillation data under different assumptions on the pattern of the neutrino mass spectrum, are considered. A possible model independent test of the nuclear matrix element calculations is discussed.

Motivation & Objective

• To review the current experimental and theoretical status of neutrinoless double beta decay as a probe for the Majorana nature of neutrinos.
• To summarize model-independent evidence for neutrino masses and mixing from Super-Kamiokande, SNO, and KamLAND experiments.
• To estimate the range of possible values for the effective Majorana mass |mee| based on neutrino oscillation data and different mass spectrum patterns.
• To propose a model-independent test for nuclear matrix element calculations using the factorization property of 0νββ-decay matrix elements across multiple isotopes.
• To highlight the importance of observing 0νββ-decay in multiple isotopes (e.g., 76Ge, 130Te, 136Xe) for constraining theoretical models of nuclear matrix elements.

Proposed method

• Uses data from atmospheric (Super-Kamiokande), solar (SNO), and reactor (KamLAND) neutrino experiments to establish model-independent evidence for neutrino oscillations and mass differences.
• Applies two-neutrino oscillation parameters from SK, SNO, and KamLAND to constrain the effective Majorana mass |mee| in the context of the neutrino mass spectrum.
• Derives the factorization property of the 0νββ-decay matrix element, showing that the product |mee|² × |M⁰ν(A,Z)|² is independent of the nuclear model.
• Proposes a test using multiple isotopes: if |mee|² values derived from different nuclei are consistent across models, the model is viable; discrepancies can rule out models.
• Compares nuclear matrix elements from different theoretical models (e.g., QRPA and NSM) using the ratio η^{NSM;QRPA}(A,Z) to assess model dependence.
• Evaluates the sensitivity of future experiments (e.g., 130Te, 76Ge, 136Xe, 100Mo) to reach |mee| ≃ a few ×10⁻² eV, enabling discrimination between mass patterns.

Experimental results

Research questions

• RQ1 What are the current experimental bounds on the effective Majorana mass |mee| from 0νββ-decay searches?
• RQ2 How do neutrino oscillation data constrain the possible values of the effective Majorana mass for different neutrino mass spectra?
• RQ3 Can the factorization property of the 0νββ-decay matrix element be used to test the reliability of nuclear matrix element calculations?
• RQ4 How can the observation of 0νββ-decay in multiple isotopes help distinguish between competing theoretical models of nuclear matrix elements?
• RQ5 What is the expected sensitivity of next-generation 0νββ-decay experiments, and how will it impact the determination of the neutrino mass scale?

Key findings

• The current experimental bound on the effective Majorana mass is |mee| ≤ (0.3–1.2) eV, based on null results from existing 0νββ-decay experiments.
• Future experiments aim to reach a sensitivity of |mee| ≃ a few ×10⁻² eV, enabling the detection of the lightest neutrino mass state in the inverted hierarchy.
• Theoretical predictions for |mee| vary significantly depending on the assumed neutrino mass spectrum: normal hierarchy predicts |mee| ≈ 0.01–0.05 eV, while inverted hierarchy allows up to ~0.1 eV.
• Nuclear matrix elements (NMEs) calculated in different QRPA models differ by a factor of three or more, highlighting a major uncertainty in interpreting 0νββ-decay data.
• The ratio η^{NSM;QRPA}(A,Z) for 76Ge, 130Te, and 136Xe is 3.1, 2.1, and 2.5 respectively, indicating that NME models can be distinguished if multiple isotopes are observed.
• Observing 0νββ-decay in at least three isotopes would provide a powerful, model-independent test of nuclear matrix element calculations via the factorization property of the decay amplitude.