We present a search for signatures of neutrino mixing of electron anti-neutrinos with additional hypothetical sterile neutrino flavors using the Double Chooz experiment. The search is based on data from 5 years of operation of Double Chooz, including 2 years in the two-detector configuration. The analysis is based on a profile likelihood, i.e. comparing the data to the model prediction of disappearance in a data-to-data comparison of the two respective detectors. The analysis is optimized for a model of three active and one sterile neutrino. It is sensitive in the typical mass range $5 cdot 10^{-3} $ eV$^2 lesssim Delta m^2_{41} lesssim 3cdot 10^{-1} $ eV$^2$ for mixing angles down to $sin^2 2theta_{14} gtrsim 0.02$. No significant disappearance additionally to the conventional disappearance related to $theta_{13} $ is observed and correspondingly exclusion bounds on the sterile mixing parameter $theta_{14} $ as function of $ Delta m^2_{41} $ are obtained.
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