Many-body correlations as the origin of Gamow-Teller quenching in nuclear $\beta$-decay

The longstanding quenching problem of Gamow-Teller (GT) strength in nuclear $\beta$-decay is attributed to missing contributions in the transition operator and/or incomplete nuclear correlations in the many-body wavefunction. Recent studies have predominantly emphasized operator renormalization, including chiral two-body currents, while the effects of many-body correlations–especially in heavy open-shell nuclei–remain underappreciated. We present a large-configuration shell-model calculation that incorporates chiral two-body weak current and treats both mechanisms on equal footing. Taking the neutrinoless double $\beta$-decay candidate ${}^{76}$Ge as an example, we demonstrate that strong nuclear correlations drive a substantial portion of GT strength to high excitation energies, leading to a pronounced suppression of low-energy strength responsible for the apparent quenching. We identify that the quenching originates mainly from deformation, cross-shell correlations, and mixing among densely-spaced highly excited states. In contrast, the chiral two-body current contributes only a modest $5-15\mathrm{\%}$ reduction, depending on the coupling constants employed. Our results thus suggest many-body correlations as the primary origin of GT quenching and provide a unified microscopic explanation for this phenomenon in nuclear $\beta$-decay.