First \textit{ab initio} calculations of first-forbidden $β$ transitions in the reactor antineutrino anomaly

Abstract

Forbidden $β$ transitions are important for understanding the reactor antineutrino anomaly. Starting from chiral two- plus three-nucleon forces, we have derived the valence-space effective Hamiltonian and effective operators of first-forbidden transitions using the many-body perturbation theory. 20 dominant first-forbidden transitions have been investigated, which provide important contributors to the reactor antineutrino spectrum anomaly. Calculated $\log ft$ values are in reasonable agreement with experimental data. Obtained shape factors exhibit significant deviations from the values approximated with forbidden transitions treated as allowed transitions. The ``5 MeV bump'' observed in the experimental ${}^{235}$U-fission antineutrino spectrum was discussed with self-consistent shape factors obtained in the present \textit{ab initio} calculations. Unlike phenomenological models that require empirical quenching factors to reproduce $β$-decay data, the present \textit{ab initio} calculations do not need to introduce quenching factors for calculations of the first-forbidden transitions.