Several observed anomalies in neutrino oscillation data could be explained by a hypothetical fourth neutrino separated from the three standard neutrinos by a squared mass difference of a few 0.1 eV$^2$ or more. This hypothesis can be tested with MCi
neutrino electron capture sources ($^{51}$Cr) or kCi antineutrino $beta$-source ($^{144}$Ce) deployed inside or next to a large low background neutrino detector. In particular, the compact size of this source coupled with the localization of the interaction vertex lead to an oscillating pattern in event spatial (and possibly energy) distributions that would unambiguously determine neutrino mass differences and mixing angles.
Recently new reactor antineutrino spectra have been provided for 235U, 239Pu, 241Pu and 238U, increasing the mean flux by about 3 percent. To good approximation, this reevaluation applies to all reactor neutrino experiments. The synthesis of publishe
d experiments at reactor-detector distances <100 m leads to a ratio of observed event rate to predicted rate of 0.976(0.024). With our new flux evaluation, this ratio shifts to 0.943(0.023), leading to a deviation from unity at 98.6% C.L. which we call the reactor antineutrino anomaly. The compatibility of our results with the existence of a fourth non-standard neutrino state driving neutrino oscillations at short distances is discussed. The combined analysis of reactor data, gallium solar neutrino calibration experiments, and MiniBooNE-neutrino data disfavors the no-oscillation hypothesis at 99.8% C.L. The oscillation parameters are such that |Delta m_{new}^2|>1.5 eV^2 (95%) and sin^2(2theta_{new})=0.14(0.08) (95%). Constraints on the theta13 neutrino mixing angle are revised.
