Revision 1

Accepted · first revision · record

Title: Neutrinoless double beta matrix elements to 30 percent uncertainty
Plain: Different nuclear models give matrix elements differing by factors of two to three for the same nucleus. Pinning them down for the isotopes used in experiments is the central task.
Precise: For light Majorana neutrino exchange, compute $M^{0\nu}$ for 76Ge, 82Se, 100Mo, 130Te and 136Xe including long-range, short-range contact and two-body-current terms, with quantified uncertainty below 30 percent. Shell model, QRPA (quasiparticle random-phase approximation), energy density functional and ab initio (in-medium similarity renormalization group, coupled cluster) results span roughly a factor of 3. Answer: $M^{0\nu}$ with uncertainties, validated on related observables (2nubb rates, double Gamow-Teller strengths, muon capture).
Settled by: Converged ab initio calculations with Bayesian uncertainty for 76Ge and 136Xe agreeing across at least two many-body methods.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: open
Status note: Ab initio calculations for 76Ge gave values at the low end of the model range (Belley et al., PRL 2021), and the first Bayesian uncertainty quantification for 76Ge gave $M^{0\nu} = 2.60 (+1.28, -1.36)$ (Belley et al., PRL 132, 182502, 2024); agreement across many-body methods for 136Xe was not established as of 2026.
Posed since: (empty)