Massive Neutrinos and (Heterotic) String Theory

TL;DR

This paper investigates how small neutrino masses could be explained within heterotic string theory, specifically in Z_3 orbifold models, and finds that a simple see-saw mechanism does not naturally emerge in this context.

Contribution

It analyzes neutrino mass generation mechanisms in heterotic orbifold models and provides evidence of only 20 inequivalent models in this class, impacting string vacua counting.

Findings

Simple see-saw mechanism does not arise in the studied models.

Extended see-saw mechanisms may be possible, but require further analysis.

There are only 20 inequivalent models in the examined class.

Abstract

String theories in principle address the origin and values of the quark and lepton masses. Perhaps the small values of neutrino masses could be explained generically in string theory even if it is more difficult to calculate individual values, or perhaps some string constructions could be favored by generating small neutrino masses. We examine this issue in the context of the well-known three-family standard-like Z_3 heterotic orbifolds, where the theory is well enough known to construct the corresponding operators allowed by string selection rules, and analyze the D- and F-flatness conditions. Surprisingly, we find that a simple see-saw mechanism does not arise. It is not clear whether this is a property of this construction, or of orbifolds more generally, or of string theory itself. Extended see-saw mechanisms may be allowed; more analysis will be needed to settle that issue. We briefly speculate on their form if allowed and on the possibility of alternatives, such as small Dirac masses and triplet see-saws. The smallness of neutrino masses may be a powerful probe of string constructions in general. We also find further evidence that there are only 20 inequivalent models in this class, which affects the counting of string vacua.