A Global Fit Determination of Effective \(\Delta m_{31}^2\) from Baseline Dependence of Reactor \(\bar{\nu}_e\) Disappearance

Abstract

Recently, three reactor neutrino experiments, Daya Bay, Double Chooz and RENO have directly measured the neutrino mixing angle \(\theta_{13}\). In this paper, another important oscillation parameter, effective \(\Delta m_{31}^2\) (= \(\Delta \tilde{m}_{31}^2\)) is measured using baseline dependence of the reactor neutrino disappearance. A global fit is applied to publicly available data and \(\Delta \tilde{m}_{31}^2 = 2.95^{+0.42}_{-0.61} \times 10^{-3}\) eV\(^2\), \(\sin^22\theta_{13} = 0.099^{+0.016}_{-0.012}\) are obtained by setting both parameters free. This result is complementary to \(\Delta tilde{m}_{31}^2\) to be measured by spectrum shape analysis. The measured \(\Delta \tilde{m}_{31}^2\) is consistent with \(\Delta \tilde{m}_{32}^2\) measured by \(\nu_{\mu}\) disappearance in MINOS, T2K and atmospheric neutrino experiments within errors. The minimum \(\chi^2\) is small, which means the results from the three reactor neutrino experiments are consistent with each other.