Searching for a Dark Dimension Right-handed Neutrino in KATRIN

TL;DR

This work investigates a right-handed neutrino propagating in a micron-scale dark dimension, producing a KK tower that modifies the KATRIN beta-decay spectrum. By solving the mass spectrum via the transcendental condition $h_i(Rm_{i(n)})=0$ and classifying cot and coth regimes, the authors connect neutrino oscillation data and cosmology to bounds on the compactification radius $R$ and bulk masses $c_i$, $\mu_i$. They identify two experimentally distinct signatures: a cascade of kinks from KK excitations when the bulk mass is small, and an effective single kink near the bulk mass when the bulk mass is large, which can resemble a 3+1 sterile neutrino; these signatures can be confronted with KATRIN and its TRISTAN upgrade. Overall, the results indicate substantial regions of the dark-dimension parameter space are accessible to current or near-future tritium beta-decay measurements, offering a concrete pathway to test micron-scale extra dimensions and the dark dimension proposal.

Abstract

We study the possibility that the Right-handed neutrino is a five-dimensional state propagating along a micron size extra dimension, as required in the dark dimension proposal. We work out the signatures of R-neutrino production in KATRIN experiment and compare them with those of a sterile neutrino which manifests by a kink in the electron energy spectrum of the beta-decay at a value corresponding to the sterile neutrino mass. We explore the allowed parameter space of the compactification scale and the R-neutrino bulk mass versus the Yukawa coupling, and show that a large part of it is within KATRIN's sensitivity. When the bulk mass is much smaller than the compactification scale, several kinks could be observed corresponding to the positions of the R-neutrino Kaluza-Klein excitations, while for large bulk mass there will be effectively one kink at the position of the bulk mass.

Figures (5)

• Figure 1: The two panels illustrate the roots of the mass equation \ref{['transcendental']} as the intersections of $x^2+\pi\bar{\mu}_i^2\bar{c}_i$ (black curve) with the third term in \ref{['hi-def']} as the red and blue curves for the $x<|\bar{c}_i|$ (coth) and $x>|\bar{c}_i|$ (cot) parts, respectively. The left panel shows the case $h(|\bar{c}_i|)<0$ where the coth part $x<|\bar{c}_i|$ has no solution, while the right panel shows the case $h(|\bar{c}_i|)>0$ where the coth part $x<|\bar{c}_i|$ has one solution.
• Figure 2: For an extra dimension with radius $R=0.2~\mu\text{m}$, the region near the endpoint of the spectrum is distorted due to the KK modes. In this case, KK modes with $n=1,2$ contribute. We can see the two characteristic "kink" signatures on the spectrum.
• Figure 3: The left panel depicts a general structure of the mass spectrum. The right panel illustrates a behaviour in the large $|\bar{c}$ limit, where a mass gap between neighbouring KK modes becomes much smaller than the gap for the lightest two modes $n=0,1$. The density of the colour in each continuous KK mass spectrum depicts the magnitude of the mixing ${\mathcal{L}}^i_{0n}$; the thicker the colour is, the larger the mixing is.
• Figure 4: Sterile neutrino exclusion contour and the simulated sensitivity contour from KATRIN measurement campaigns KNM1--5 are shown in the black and red dashed line respectively KATRIN:2025lph. The blue line represent the $\sin^2\theta_{\rm eff}^{{\mathrm{max}}} = 0.050$ boundary. Below this upper bound, we can make the identification: $m_4^2 \rightarrow c^2$ and $\sin^2\theta_{ee} \rightarrow \sin^2\theta_{\rm eff}$.
• Figure 5: Exclusion contours for $R=1.0$ and $10.0~{\mu m}$ in the $(\bar{c},\bar{\mu}_1)$-plane are shown as the black dashed and solid curves respectively. The blue curve represents the $\sin^2(\theta_{\rm eff}^{{\mathrm{max}}}) = 0.050$ boundary.