Measurement of Effective $\mathrm{\Delta }{m}_{31}^2$ using Baseline Differences of Daya Bay, RENO and Double Chooz Reactor Neutrino Experiments

In 2011 and 2012, three reactor neutrino experiments, Double Chooz, Daya Bay and RENO showed positive signals of reactor neutrino disappearance and measured a mixing parameter sin^2(2th13) at average baselines 1.05, 1.65 and 1.44km, respectively. It is possible to measure effective Dm31^2 from distortion of neutrino energy spectrum (E dependence of the oscillation) in those experiments. However, since it requires a precise energy calibration, such measurements have not been reported yet. Dm31^2 can also be measured from baseline (L) dependence of the neutrino oscillation. In this paper, Dm31^2 is measured from disappearance probabilities of the three reactor experiments which have different baselines, to be 2.99^{+1.13}{-1.58}(^{+0.86}{-0.88}) X 10^{-3}eV^2, where the errors are two (one) dimensional uncertainties. This is consistent with Dm32^2 measured by \nu_{\mu} disappearance in accelerator experiments. Importance of Dm31^2 measurement and future possibilities are also discussed.