A formula for the sensitivity to sin²{2theta₁3} in reactor experiments with a spectral analysis

Using an analytical approach, the sensitivity to sin^2{2theta_13} with infinite statistics in a spectral analysis is investigated in reactor neutrino oscillation experiments with one reactor and two identical detectors. We derive an useful formula for the sensitivity which depends only two parameters sigma_db/\sqrt{n} (the uncorrelated bin-to-bin systematic error over the square-root of the number of bins) and sigma_dB (the bin-to-bin correlated detector specific systematic error).