The role of spin-isospin symmetries in nuclear $\beta$-decays

Abstract

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 $\geq 90$\% probability of being in a single SU(4) irreducible representation. Meanwhile, our analysis of axial current operators in chiral effective field theory ($\chi$EFT) 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 $\chi$EFT expansion and explain key phenomenological observations, e.g., the unnaturally large two-body corrections to the axial-current matrix elements in eight-body nuclei.