On small Dirac Neutrino Masses in String Theory

We study how tiny Dirac neutrino masses consistent with experimental constraints can arise in string theory SM-like vacua. We use as a laboratory 4d N=1 type IIA Calabi--Yau orientifold compactifications, and in particular recent results on Yukawa couplings at infinite field-space distance. In this regime we find Dirac neutrino masses of the form m_ g_ H, with g_ the gauge coupling of the massive U (1) under which the right-handed neutrinos R are charged, and which should be in the range g_ 10^-14-10^-12 to reproduce neutrino data. The neutrino mass suppression occurs because the right-handed neutrino kinetic term behaves as K_ 1 /g_². At the same time a tower of R-like states appears with characteristic scale m₀ g_²M ₏ 0. 1-500 eV, in agreement with Swampland expectations. Two large hidden dimensions only felt by the R sector arise at the same scale, while the string scale is around Mₛ g_ M ₏ 10-700 TeV. Some phenomenological implications and model building challenges are described. As a byproduct, independently of the neutrino issue, we argue that a single large dimension in the context of SM-like type IIA Calabi--Yau orientifolds leads to too small Yukawa couplings for quarks and charged leptons.