A potential sterile neutrino search utilizing spectral distortion in a two-reactor/one-detector configuration

There is an observed deficit of about 6\% in the expected rate of anti-neutrino interactions when averaging over many different reactor experiments. While the significance of the deficit is low (98.6 \% CL), there is speculation that a non-interacting "sterile" neutrino could be the cause. In this paper we explore the possibility of a two-reactor/one-detector experiment at intermediate distances (100-500 meters) to look for a sterile neutrino in the mass range implied by this deficit. A method for probing $\Delta m^2$ phase space is developed using interference patterns between two oscillated spectra at different baselines. This method is used to investigate the potential sensitivity of the Double Chooz experiment, which has a single Near Detector at distances of 351 m and 465 m from two reactors of identical design. We conclude that Double Chooz could investigate sterile neutrino in the $\Delta m^{2}$ range of 0.002 to 0.5 eV$^2$ over 5 years of near detector running.