What triggers $θ_{13}$ discrepancy between Daya Bay and T2K?

Abstract

There seems to be a non-negligible discrepancy between Daya Bay and T2K experimental results of a neutrino mixing angle, $θ_{13}$ . We show the discrepancy can be simply passed away even in the standard three neutrinos framework by taking the same value of $Δm^2_{32}$ with a normal neutrino mass hierarchy and Dirac CP phase $δ= -π/ 2$, which is favorable in T2K experiment. For numerical analyses of neutrino oscillation probabilities, there are five independent parameters, $Δm_{21}^2$, $Δm_{32}^2$, $θ_{12}$, $θ_{23}$, and $δ$. We reevaluate $θ_{13}$ by scatter plots within $1 σ$ range of five-dimensional parameters space suggested by PDG, T2K, and Daya Bay. We project onto $δ$-$\sin^2 2 θ_{13}$ plane and find an overlap area of $θ_{13}$ suggested by T2K and Daya Bay. In the normal hierarchy case, the largest overlap area is given by parameters set suggested by T2K, and the overlap area becomes small in order of parameters sets suggested by PDG and Daya Bay. In the inverted hierarchy case, there is a tiny overlap area only in parameters set suggested by T2K. We also show several sample points of four parameters set, $Δm_{21}^2$, $Δm_{32}^2$, $θ_{12}$, and $θ_{23}$, where the dissonance of $θ_{13}$ is really disappeared with $δ= -π/2$.