On small Dirac Neutrino Masses in String Theory

TL;DR

This paper explores how tiny Dirac neutrino masses can naturally arise in string theory compactifications, linking neutrino properties to string scale physics and extra dimensions, with implications for phenomenology and model building.

Contribution

It demonstrates a mechanism within type IIA Calabi-Yau orientifold compactifications where neutrino masses are suppressed by gauge couplings, connecting neutrino data to string theory parameters.

Findings

Neutrino masses of order g_ν⟨H⟩ with g_ν ≈ 10^{-14}-10^{-12}

Presence of a tower of ν_R-like states at 0.1-500 eV scale

Large hidden dimensions at the neutrino scale with string scale 10-700 TeV

Abstract

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 ${\cal N}=1$ 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 $m_\nu \simeq g_\nu\langle H\rangle$, with $g_{\nu}$ the gauge coupling of the massive $U(1)$ under which the right-handed neutrinos $\nu_R$ are charged, and which should be in the range $g_{\nu}\simeq 10^{-14}-10^{-12}$ to reproduce neutrino data. The neutrino mass suppression occurs because the right-handed neutrino kinetic term behaves as $K_{\nu\nu} \simeq 1 /g_{\nu}^2 $. At the same time a tower of $\nu_R$-like states appears with characteristic scale $m_0\simeq g_{\nu}^2M_{\rm P}\simeq 0.1-500$ eV, in agreement with Swampland expectations. Two large hidden dimensions only felt by the $\nu_R$ sector arise at the same scale, while the string scale is around $M_s\simeq g_\nu M_{\rm P}\simeq 10-700$ 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.