Extra dimensions with light and heavy neutral leptons: An application to CE$\nu$NS

We explore the possibility of relating extra dimensions with light and heavyDirac-type neutral leptons and develop a framework for testing them in variouslaboratory experiments. The Kaluza-Klein modes in the large extra dimensionmodels of the light neutral leptons could mix with the standard model neutrinosand produce observable effects in the oscillation experiments. We show that thechirality flipping up-scattering processes occurring through either neutrinomagnetic dipole moment or the weakly coupled scalar interactions can alsoproduce heavy Kaluza-Klein modes of the corresponding right-handed neutralleptons propagating in one or more extra dimensions. However, to conserve thefour-dimensional energy-momentum, their masses must be below the maximum energyof the neutrinos in the initial state. The appreciable size of extra dimensionsconnected with these heavy neutral leptons can thus affect the cross-sectionsof these processes. This framework applies to any up-scattering process. Ourwork here focuses only on its application to the coherent elasticneutrino-nucleus scattering process. We derive constraints on the size of extradimensions using the COHERENT data in oscillation and up-scattering processes.For model with one large extra dimension for the light neutral leptons, weobtain the limits, $R \sim 3 \ \mu$m (NH) and $R \sim 2.5 \ \mu$m (IH), on thesize of extra dimension corresponding to the absolute mass limit, $m_{0} \leq 3\times 10^{-3}$ eV at 90$\%$ C.L. from the short-baseline oscillations. Usingthe up-scattering process for heavy neutral leptons, we obtain new parameterspaces between the size of extra dimensions and parameters of the dipole orscalar interactions.