Effect of compactification of twisted toroidal extra-dimension on sterile neutrino

We consider a toroidal extra-dimensional space with shape moduli $\theta$ which is the angle between the two large extra dimensions $R_1$ and $R_2$ (twisted LED with $\delta=2$). The Kaluza-Klein (KK) compactification results in a tower of KK bulk neutrinos which are sterile in nature and couple to the active neutrinos in the brane. The active-sterile mixing probability strongly depends on the angle $\theta$ due to changing pattern of KK mass gaps which leads to level crossing. Considering only the first two lowest KK states in analogy with $(3+2)$ model, it is shown that $|U_{\alpha 4}| > |U_{\alpha 5}|$ when $\theta = \pi/2$ corresponding to the case of a normal torus. Since $\Delta_{14}^2 < \Delta_{15}^2$, this is expected in normal LED model as higher the sterile mass lower is the mixing probability. Contrary to this expectation, it is found that there exists a range in $\theta$ where $|U_{\alpha 5}| \ge |U_{\alpha 4}|$ even though $\Delta m_{14}^2 < \Delta m_{15}^2$ which has been demonstrated qantitatively using fourier transformation of reactor anti-neutrino spectrum. This is an important observation which can be linked to the oscillation parameters extracted by several $(3+2)$ global analyses of the neutrino and anti-neutrino data obtained from the short base line measurements.