The Dark Dimension and the Standard Model Landscape

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