Inverse beta decay (IBD), ${\overline{\nu }}_{e}p\to e^{+}n(\gamma )$, 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, ${\overline{\nu }}_{e}p\to e^{+}n\gamma$. 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 subpermille theoretical precision, supporting current and future experiments.

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• Beta decay
• Cabibbo–Kobayashi–Maskawa matrix
• Chiral perturbation theory
• Effective field theory
• Electroweak interactions in nuclear physics
• Electroweak radiative corrections
• Neutrino interactions
• Neutrino mixing
• Neutrino oscillations
• Neutron decay time
• Nuclear decay
• Nucleon distribution
• Nucleus-neutrino interactions
• Particle detection signatures
• Particle interactions
• Perturbation theory
• Photon, lepton & quark production
• Proton emission
• Quantum electrodynamics