First principles calculations of weak decays in atomic nuclei

This talk reports on recent progress in first principles computations of neutrinoless and two-neutrino double-beta decay in~$^{\mathrm{48}}$Ca, with interactions and currents from chiral effective field theory. Predictions from coupled-cluster and in-medium similarity-renormalization-group calculations agree, and they yield a nuclear matrix element for the neutrinoless double beta decay that is smaller than expected. Calculations of Gamow-Teller decays from~$p$-shell nuclei to tin isotopes reveal that the long-standing problem of the quenching of the axial coupling constant~$g_{\mathrm{A}}~$can be resolved by meson exchange currents and a proper treatment for many-body~correlations. In particular,~meson-exchange currents play a crucial role in the~super-allowed Gamow-Teller decay of~$^{\mathrm{100}}$Sn.