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

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 $2\hat{I}½{\hat{I}}^2{\hat{I}}^2$ and $0\hat{I}½{\hat{I}}^2{\hat{I}}^2$ 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 $q\simeq 0.84$. Incorporating this quenching yields a $2\hat{I}½{\hat{I}}^2{\hat{I}}^2$ nuclear matrix element (NME) in excellent agreement with experiment. Applying the same framework to $0\hat{I}½{\hat{I}}^2{\hat{I}}^2$ decay, and including the contribution from short-range operators, we obtain a total NME of $M^{0\hat{I}½}=1.00\text{-}2.02$. Using 34 non-implausible chiral Hamiltonians, we establish from first principles strong linear correlations between the $0\hat{I}½{\hat{I}}^2{\hat{I}}^2$ NME and the NMEs governing $2\hat{I}½{\hat{I}}^2{\hat{I}}^2$ decay and double GT transitions. Combining these correlation relations within the 95% confidence level with the experimental $2\hat{I}½{\hat{I}}^2{\hat{I}}^2$-decay data yields a constrained prediction of $M^{0\hat{I}½}=1.30\text{-}1.65$. This work establishes IM-NCCI as a complementary ab initio framework for nuclear weak decays and opens a pathway toward constraining $0\hat{I}½{\hat{I}}^2{\hat{I}}^2$ NMEs in heavier candidate nuclei using experimentally accessible $2\hat{I}½{\hat{I}}^2{\hat{I}}^2$-decay data.

9 pages with 11 figures