An electron flies out of a tritium nucleus with an energy of 18.57 keV, leaving behind an invisible partner: a neutrino. If that neutrino has access to a fifth dimension, its mass splits into a whole tower of states, and each one takes its own bite out of the spectrum. The KATRIN spectrometer in Karlsruhe examines this spectrum with precision down to fractions of an electronvolt, and hidden in its data could be not just a new particle, but the dark dimension itself.

The dark dimension scenario posits that an extra dimension of order a micron is tied to the dark energy scale. In this picture, the right-handed neutrino need not sit on the brane like all Standard Model particles; it can roam freely through the bulk. This naturally explains the smallness of neutrino masses: you don't need to introduce tiny Yukawa couplings, just geometry. The authors built a five-dimensional model with three right-handed neutrinos living in the bulk and solved the mass equation for the Kaluza-Klein states. The result is a spectrum and mixing matrices that determine how these states manifest in tritium beta decay.

Next comes the physics of kinks. If the bulk neutrino mass is small compared to the inverse radius, the beta decay spectrum acquires a series of kinks, one for each Kaluza-Klein excitation. For a radius smaller than 0.4 microns, several such kinks could fall within KATRIN's sensitivity. If the bulk mass is large, all excitations merge into a single effective kink at an energy equal to the bulk mass, with an effective mixing angle that can be computed analytically. Then the dark dimension signal looks like a sterile neutrino signal, and existing KATRIN limits on sterile neutrinos can be directly translated into constraints on the model parameters. For example, for a radius of 10 microns and a bulk mass around 1 eV, a significant portion of the parameter space remains allowed, but future data could probe it.

Previously, it was unclear whether a right-handed neutrino from the dark dimension could be seen at KATRIN at all, and what signal to look for. Now we have a map: for a small bulk mass, a series of kinks; for a large bulk mass, a single effective kink. This is not just a theoretical exercise: the extra-dimensional model becomes testable at a running experiment. The next step is detailed numerical simulation of the full spectrum, including all Kaluza-Klein states, and comparison with real KATRIN data. The future TRISTAN detector with improved resolution will open up the kiloelectronvolt mass region and provide additional constraints.

The echo from the fifth dimension might turn out to be not a fantasy, but a kink on a plot. If KATRIN sees such a signature, neutrino physics and quantum gravity will converge at a single point: the tritium decay spectrum.