Role of spin-isospin symmetries in nuclear <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>β</mml:mi> </mml:math> -decays

A century ago, Wigner's SU(4) symmetry was introduced to explain the properties of atomic nuclei. Despite recent revived interest, its impact on nuclear structure, transitions, and reactions has not been fully explored. Here, we show that a variety of high-fidelity nuclear interactions predict nuclear states that have ≥90% probability of being in a single SU(4) irreducible representation. Meanwhile, our analysis of axial current operators in chiral effective field theory (χEFT) reveals that one-body currents at low momentum transfer act only within SU(4) irreducible representations, while two-body currents connect different representations. These selection rules interfere with the expected convergence pattern of the χEFT expansion and explain key phenomenological observations, e.g., the unnaturally large two-body corrections to the axial-current matrix elements in eight-body nuclei.