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

TL;DR

This paper investigates how the shape of a twisted extra-dimensional space affects sterile neutrino mixing, revealing non-intuitive relationships between sterile neutrino masses and mixing probabilities through Fourier analysis of reactor neutrino data.

Contribution

It demonstrates that the geometry of twisted extra dimensions can alter sterile neutrino mixing patterns, challenging previous expectations based on mass hierarchy.

Findings

Existence of a parameter range where higher mass sterile neutrinos have larger mixing.

Fourier analysis links extra-dimensional geometry to observable neutrino oscillation parameters.

Results relate to global neutrino oscillation data analyses.

Abstract

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.