Theory of inverse beta decay for reactor antineutrinos

TL;DR

This work delivers a high-precision theory of inverse beta decay for reactor antineutrinos, incorporating recoil, weak magnetism, nucleon structure, and QED radiative corrections within heavy baryon chiral perturbation theory. It provides fully analytic radiative IBD cross sections, exact three-body phase-space treatment for real photon emission, and a comprehensive uncertainty budget, achieving sub-permille precision relevant for JUNO-like experiments. The authors construct detailed energy- and angle-dependent spectra for the positron, electromagnetic energy, and neutron, and extend the formalism to charged-current neutrino-nucleon scattering and neutron decay, updating radiative corrections to the neutron lifetime and beta asymmetry. They compare with prior literature, clarify collinear behavior, and provide public code for fast cross-section evaluation, enabling robust event-rate predictions and improved energy reconstruction in precision reactor analyses.

Abstract

Inverse beta decay (IBD), $\overlineν_e p \to e^+ n \left( γ\right)$, is the main detection channel for reactor antineutrinos in water- and hydrocarbon-based detectors. As reactor antineutrino experiments now target sub-percent-level sensitivity to oscillation parameters, a precise theoretical description of IBD, including recoil, weak magnetism, nucleon structure, and radiative corrections, becomes essential. In this work, we give a detailed and precise calculation of the total and differential cross sections for radiative IBD, $\overlineν_e p \to e^+ n γ$. We use a heavy baryon chiral perturbation theory framework, systematically incorporating electroweak, electromagnetic, and strong-interaction corrections. We derive new analytic cross-section expressions, clarify the collinear structure of radiative corrections, and provide a systematic uncertainty analysis. We also discuss phenomenological applications for reactor antineutrino experiments, e.g., JUNO, and neutron decay. Our results enable sub-permille theoretical precision, supporting current and future experiments.

Figures (9)

• Figure 1: Kinematics in inverse beta decay (IBD).
• Figure 2: One-loop virtual QED diagram contributing to the IBD process.
• Figure 3: One-photon bremsstrahlung diagrams for $\overline{\nu}_e + p \rightarrow e^+ + n + \gamma$.
• Figure 4: The difference in radiative correction to the total unpolarized cross section between results from this paper and the application of the multiplicative factor $\frac{\alpha}{\pi} \delta_1$ is shown as a function of the antineutrino beam energy $E_{\overline{\nu}_e}$. The width of the curve corresponds to the allowed range of the recoil position energy in the radiative-free IBD.
• Figure 5: Total IBD cross section is shown as a function of the antineutrino beam energy $E_{\overline{\nu}_e}$ in the left panel. Our result is compared to the cross-section parameterization in Ref. Strumia:2003zx, labeled as "Strumia 2003", the treatment of radiative corrections in Ref. Kurylov:2002vj, labeled as "Kurylov 2002", and radiative corrections from Refs. Fayans:1985uejVogel:1999zyFukugita:2004cqRaha:2011aa, described in Section \ref{['sec:static_limit']} and labeled as "Raha 2011". The relative uncertainty of the total cross section, dominated by $\lambda$ and $V_{ud}$, is illustrated in the right panel.