Inverse beta decay (IBD), $\overline{ \nu}_e p \to e^+ n \left( \gamma \right)$, 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, $\overline{ \nu}_e p \to e^+ n \gamma$. 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 sub-permille theoretical precision, supporting current and future experiments.
Categories: hep-ph hep-ex nucl-ex nucl-th