Global Ab initio Neutrino Mass Limits from Neutrinoless Double-Beta Decay

Technical Summary: Global Ab Initio Neutrino Mass Limits from Neutrinoless Double-Beta Decay

Problem Statement
The primary objective of this work is to establish global upper limits on the effective Majorana neutrino mass ($m_{\beta\beta}$) by integrating the latest experimental results from neutrinoless double-beta ($0\nu\beta\beta$) decay searches with ab initio nuclear theory. While neutrino oscillation experiments have constrained the squared-mass differences and established the existence of neutrino mass, they have not determined the absolute mass scale or the mass ordering (normal vs. inverted). The observation of $0\nu\beta\beta$ decay would confirm the Majorana nature of neutrinos and provide a direct measurement of $m_{\beta\beta}$. However, extracting $m_{\beta\beta}$ from experimental half-life limits requires precise Nuclear Matrix Elements (NMEs). Traditionally, NMEs have been calculated using phenomenological models (e.g., QRPA, Shell Model, IBM), which often yield significant discrepancies. This study addresses the uncertainty in NMEs by utilizing ab initio calculations derived from chiral effective field theory (EFT) to provide more rigorous constraints on the neutrino mass regime.

Methodology
The authors employ a Bayesian framework to derive 90% credible interval (CI) limits on $m_{\beta\beta}$. The methodology involves three core components:

1. Theoretical Framework and NMEs:

   • The decay rate is calculated assuming the standard light-neutrino-exchange mechanism. The rate depends on the phase-space factor ($G^{0\nu}$) and the NME ($M^{0\nu}$).
   • The NME is decomposed into a long-range part ($M^{0\nu}_L$) and a short-range part ($M^{0\nu}_S$). The inclusion of the short-range contact term is critical, as it is required to renormalize the theory within an EFT analysis.
   • Ab Initio Approach: The study utilizes the Valence Space In-Medium Similarity Renormalization Group (VS-IMSRG) method. This approach calculates NMEs from first principles using nuclear and electroweak forces derived from chiral EFT. The calculations cover the four key isotopes for current and next-generation experiments: $^{76}\text{Ge}$, $^{100}\text{Mo}$, $^{130}\text{Te}$, and $^{136}\text{Xe}$.
   • Comparison: These ab initio results are compared against a suite of phenomenological NMEs (IBM, pnQRPA, NSM, MR-CDFT, and the hybrid GCF method) to assess the impact of theoretical model choice on the final mass limits.

2. Experimental Inputs:

   • Current Generation: Likelihood functions are constructed from results of GERDA, LEGEND-200, CUPID-Mo, CUORE, EXO-200, and KamLAND-Zen. Where available, posterior distributions from the collaborations are used; otherwise, Poisson counting models with background marginalization are employed.
   • Next-Generation: Projected sensitivities are derived for experiments including nEXO, LEGEND-1000, CUPID/CUPID-1T, SNO+, AMoRE-II, NEXT-HD, PandaX-xT, DARWIN, and XLZD.

3. Statistical Analysis:

   • The global likelihood is computed by multiplying the individual likelihood functions of the experiments ($L_{\text{Comb}} = \prod L_i$).
   • The posterior distribution for $m_{\beta\beta}$ is derived using Bayes' theorem. The authors test three uninformative priors: uniform in $m_{\beta\beta}$, uniform in the decay rate $\Gamma^{0\nu}$ (equivalent to $m_{\beta\beta}^2$), and uniform in $\log(m_{\beta\beta})$.
   • NME uncertainties are treated by assuming a uniform distribution within the range of values provided by the different theoretical models.

Key Contributions

• Global Combination: The paper presents the first global Bayesian combination of $0\nu\beta\beta$ limits using ab initio NMEs derived from the VS-IMSRG method.
• Rigorous Treatment of Short-Range Terms: The analysis explicitly incorporates the short-range contact term ($M^{0\nu}_S$) in the ab initio NMEs, which has been shown to significantly enhance NMEs compared to traditional operators.
• Prior Sensitivity: The study systematically compares how different prior choices (uniform in mass vs. rate vs. log-mass) affect the resulting limits, noting that while the choice of prior influences the strictness of the limit, the ab initio vs. phenomenological distinction remains the dominant factor in the interpretation of the data.

Results

• Current Experiments:
  • Using phenomenological NMEs, the combined limits suggest that current experiments (particularly xenon-based ones) have partially probed the inverted mass ordering region.
  • However, using ab initio VS-IMSRG NMEs, the combined global limits are significantly weaker ($m_{\beta\beta} \leq 77 - 132$ meV for a $\Gamma^{0\nu}$ uniform prior) compared to phenomenological results ($m_{\beta\beta} \leq 30 - 76$ meV).
  • The authors conclude that, based on ab initio results, the current generation of experiments has likely not yet reached the sensitivity required to probe the mass regime allowed by neutrino-oscillation data for the inverted ordering.
• Next-Generation Experiments:
  • With phenomenological NMEs, individual next-generation experiments (e.g., nEXO, CUPID) appear capable of fully covering the inverted mass ordering.
  • With ab initio NMEs, no single next-generation experiment is projected to fully cover the inverted mass ordering with confidence.
  • Combined Reach: The study demonstrates that a global combination of the four key isotopes ($^{76}\text{Ge}$, $^{100}\text{Mo}$, $^{130}\text{Te}$, and $^{136}\text{Xe}$) across multiple next-generation experiments is necessary to achieve the sensitivity required to fully probe the inverted mass ordering. The combined projected reach is $m_{\beta\beta} \leq 7.4 - 13.1$ meV (or $\leq 5.6 - 10.8$ meV if CUPID-1T is included).

Significance and Claims
The paper claims that the shift from phenomenological to ab initio nuclear theory fundamentally alters the interpretation of $0\nu\beta\beta$ decay sensitivity. While phenomenological models suggest the inverted ordering is within reach of individual next-generation experiments, ab initio calculations indicate that a coordinated, worldwide effort involving multiple isotopes is required to definitively test the inverted mass ordering.

The authors emphasize that their results highlight the necessity of:

1. Global Collaboration: No single experiment dominates the sensitivity; a combined effort across different isotopes is essential.
2. Theoretical Refinement: The need for rigorous ab initio uncertainty quantification across all relevant isotopes to reduce theoretical errors and enable direct comparisons of limit posteriors.
3. Future Directions: The development of machine-learning emulators (such as BANNANE) to facilitate the analysis of theoretical uncertainties arising from chiral interactions, operators, and many-body methods.

The study concludes that while the inverted mass ordering is not yet fully excluded or confirmed by current data under ab initio assumptions, the combined sensitivity of the next generation of experiments offers a viable path to achieving this goal.