<i>Ab Initio</i> Neutrinoless Double-Beta Decay Matrix Elements for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>Ca</mml:mi></mml:mrow><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>48</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>Ge</mml:mi></mml:mrow><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>76</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow></mml:math>, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>Se</mml:mi></mml:mrow><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>82</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow></mml:math>
A. Belley, Charlie Payne, S. R. Stroberg, T. Miyagi, J. D. Holt
Abstract
We calculate basis-space converged neutrinoless $\ensuremath{\beta}\ensuremath{\beta}$-decay nuclear matrix elements for the lightest candidates: $^{48}\mathrm{Ca}$, $^{76}\mathrm{Ge}$, and $^{82}\mathrm{Se}$. Starting from initial two- and three-nucleon forces, we apply the ab initio in-medium similarity renormalization group to construct valence-space Hamiltonians and consistently transformed $\ensuremath{\beta}\ensuremath{\beta}$-decay operators. We find that the tensor component is non-negligible in $^{76}\mathrm{Ge}$ and $^{82}\mathrm{Se}$, and the resulting nuclear matrix elements are overall 25%--45% smaller than those obtained from the phenomenological shell model. While a final matrix element with uncertainties still requires substantial developments, this work nevertheless opens a path toward a true first-principles calculation of neutrinoless $\ensuremath{\beta}\ensuremath{\beta}$ decay in all nuclei relevant for ongoing large-scale searches.