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The Neutrino Mass Hierarchy at Reactor Experiments now that theta13 is Large

Now that theta13 is known to be large, a medium baseline reactor experiment can observe the fine structure of the electron antineutrino survival probability curve, approximately periodic oscillations in L/E with wavelength 4pi/Delta M^2_31. The periodicity with respect to L/E is broken by 2-3 oscillations which, in the case of the normal (inverted) hierarchy, shift the first 16 oscillations nearly 1% higher (lower) and move the next 16 lower (higher). The energy of each peak determines a particular combination of the mass differences, for example cos^2(theta12)Delta M^2_31 + sin^2(theta12)Delta M^2_32 for nearly all peaks visible at baselines under 40 km. Comparing these combinations with each other or with NOvA results one can in principle determine the mass hierarchy. Alternately, as the Fourier transforms of the 1-3 and 2-3 oscillation probabilities are out of phase by the 1-2 oscillation probability, near the maximum of the 1-2 oscillation the complex phase of the total survival probability can be used to determine the hierarchy. Two interference effects make this task difficult. First, kilometer distances between the reactors reduce the amplitudes of peaks below about 4 MeV. Second, even reactors 100 or more kilometers away significantly obscure the 1-2 oscillation maximum, which also complicates a measurement of the solar mixing angle with a single detector.