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

Abstract

We present the first \textit{ab initio} calculations of first-forbidden $β$ transitions which are important for understanding the reactor antineutrino anomaly. Starting from chiral two- plus three-nucleon forces, we derive both valence-space effective Hamiltonians and forbidden transition operators self-consistently. Focusing on the dominant first-forbidden transitions relevant to reactor antineutrino spectra, we compute 20 key transitions and obtain $\log ft$ values that show reasonable agreement with experimental data. Obtained shape factors exhibit significant deviations from the values approximated with forbidden transitions treated as allowed transitions, indicating the importance of explicit treatments of forbidden transitions in reactor antineutrino studies. By incorporating these microscopic shape factors into the calculation of the ${}^{235}$U antineutrino spectrum, we observe a pronounced spectrum enhancement around 5 MeV of the antineutrion energy, which may partially explain the well-known ``5 MeV bump'' observed in reactor experiments.

Figures (4)

• Figure 1: Calculated normalized shape factor for $\Delta J=0$ forbidden transitions as a function of electron kinetic energy. For allowed transitions, the normalized shape factor is identically one and marked as black dotted line.
• Figure 2: Calculated normalized shape factor for $\Delta J=1$ forbidden transitions as a function of electron kinetic energy.
• Figure 3: Calculated normalized shape factor for $\Delta J=2$ forbidden transitions as a function of electron kinetic energy.
• Figure 4: Change in the predicted antineutrino spectrum relative to the allowed approximation from the fission of ${ }^{235}$U as a function of antineutrino energy. The shaded band represents the theoretical uncertainty arising from the many-body calculations.