Hadronic probes of nonstandard neutrino interactions

In this work, we study leptonic decays of hadrons as probes of light neutrinophilic scalars that mediate enhanced neutrino self-interactions. Such scalars can be emitted in processes involving neutrinos, turning two-body decays into three-body final states and producing characteristic spectral distortions. We compute these effects for charged pion decay and nuclear electron capture decay, including both on-shell and off-shell scalar emission, as well as the loop-induced renormalization required to cancel divergences. Using these results, we derive the projected sensitivity of PIONEER and assess the current and future reach of BeEST. The resulting low-energy spectral tails provide a characteristic signal for light neutrinophilic scalars, making upcoming hadron decay experiments powerful probes of light mediators of nonstandard neutrino self-interactions.