Ab initio correlations between neutrinoless and two-neutrino double-beta decays in $^{48}$Ca

TL;DR

This paper introduces a new ab initio framework combining in-medium similarity renormalization group and chiral Hamiltonians to accurately predict neutrinoless and two-neutrino double-beta decay NMEs in calcium-48, establishing correlations with experimental data.

Contribution

The novel IM-NCCI framework enables first-principles calculations of double-beta decay NMEs and reveals strong correlations with experimental observables, aiding future predictions in heavier nuclei.

Findings

Reproduces main resonance peaks in Gamow-Teller strength distribution.

Achieves excellent agreement with experimental $2 uetaeta$ NME after including quenching.

Predicts $0 uetaeta$ NME in the range 1.00-2.02, constrained to 1.30-1.65 using correlations.

Abstract

We develop a novel ab initio in-medium no-core configuration-interaction (IM-NCCI) framework for nuclear charge-exchange processes by combining the in-medium similarity renormalization group with chiral nuclear Hamiltonians, and apply it to the $2\nu\beta\beta$ and $0\nu\beta\beta$ decays of $^{48}$Ca. This framework reproduces the locations of several main resonance peaks in the Gamow-Teller (GT) strength distribution for the $^{48}\mathrm{Ca}\to{}^{48}\mathrm{Sc}$ transition. The cumulative GT strength indicates missing contributions from two-body weak currents, corresponding to an effective quenching factor of $q\simeq0.84$. Incorporating this quenching yields a $2\nu\beta\beta$ nuclear matrix element (NME) in excellent agreement with experiment. Applying the same framework to $0\nu\beta\beta$ decay, and including the contribution from short-range operators, we obtain a total NME of $M^{0\nu}=1.00\text{-}2.02$. Using 34 non-implausible chiral Hamiltonians, we establish from first principles strong linear correlations between the $0\nu\beta\beta$ NME and the NMEs governing $2\nu\beta\beta$ decay and double GT transitions. Combining these correlation relations within the 95% confidence level with the experimental $2\nu\beta\beta$-decay data yields a constrained prediction of $M^{0\nu}=1.30\text{-}1.65$. This work establishes IM-NCCI as a complementary ab initio framework for nuclear weak decays and opens a pathway toward constraining $0\nu\beta\beta$ NMEs in heavier candidate nuclei using experimentally accessible $2\nu\beta\beta$-decay data.