The role of spin-isospin symmetries in nuclear $β$-decays
Simone Salvatore Li Muli, Tor R. Djärv, Christian Forssén, Daniel R. Phillips
TL;DR
The study shows that Wigner’s SU(4) spin-isospin symmetry strongly organizes light-nucleus structure and beta decay. Using ab initio NCSM calculations with χEFT interactions up to N2LO and a Lanczos-based decomposition of the SU(4) Casimir $C_2$, it finds that $A=3-8$ states are overwhelmingly dominated by a single SU(4) irrep, yielding robust, symmetry-driven predictions for Gamow-Teller amplitudes. The axial current in χEFT comprises a one-body piece that largely preserves SU(4) structure and a two-body component that couples different irreps, explaining both observed suppression patterns (e.g., in $A=8$ decays) and the unexpectedly large two-body corrections. These results provide a symmetry-based lens for interpreting beta-decay data, improving uncertainty quantification in beyond-Standard-Model searches, and suggest SU(4) structure as a guiding principle for light-nucleus electroweak transitions, with implications for heavier systems as admixtures of irreps grow.
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 ($χ$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 $χ$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.