The Dark Dimension and the Standard Model Landscape

We study the landscape of lower-dimensional vacua of the SM coupled to gravity in the presence of the ``dark dimension'' of size $R_\perp$ in the micron range, focusing on the validity of the swampland conjecture forbidding the presence of non-SUSY AdS vacua in a consistent quantum gravity theory. We first adopt the working assumption that right-handed neutrinos propagate in the bulk, so that neutrino Yukawa couplings become tiny due to a volume suppression, leading to naturally light Dirac neutrinos. We show that the neutrino KK towers compensate for the graviton tower to maintain stable dS vacua found in the past, but neutrino oscillation data set restrictive bounds on $R_\perp$ and therefore the first KK neutrino mode is too heavy to alter the shape of the radon potential or the required maximum mass for the lightest neutrino to carry dS rather than AdS vacua found in the absence of the dark dimension, $m_{1,{\rm max}}\lesssim 7.63~{\rm meV}$. We also show that a very light gravitino (with mass in the meV range) could help relax the neutrino mass constraint $m_{1,{\rm max}} \lesssim 50~{\rm meV}$. The differences for the predicted total neutrino mass $\sum m_\nu$ among these two scenarios are within reach of next-generation cosmological probes that may measure the total neutrino mass with an uncertainty $\sigma (\sum m_\nu) = 0.014~{\rm eV}$. We also demonstrate that the KK tower of a very light gravitino can compensate for the graviton tower to sustain stable dS vacua and thus right-handed neutrinos can (in principle) be locked on the brane. For this scenario, Majorana neutrinos could develop dS vacua, which is not possible in the SM coupled to gravity. Finally, we investigate the effects of bulk neutrino masses in suppressing oscillations of the 0-modes into the first KK modes to relax the oscillation bound on $R_\perp$.