The mu term and neutrino masses

TL;DR

This paper explores anomaly-free discrete symmetries compatible with SU(5) unification that forbid the superpotential mu term, explain neutrino mass suppression, and ensure proton stability, with the mu term generated non-perturbatively.

Contribution

It identifies specific Z_M^R symmetries that forbid the mu term in the superpotential while allowing necessary terms, and explains neutrino mass suppression within a unified framework.

Findings

Z_M^R symmetries are anomaly-free due to Green-Schwarz mechanism.

A unique symmetry allows the Weinberg operator for neutrino masses.

Certain Z_M^R symmetries explain suppressed Dirac neutrino masses.

Abstract

The well-known Giudice-Masiero mechanism explains the presence of a mu term of the order of the gravitino mass, but does not explain why the holomorphic mass term is absent in the superpotential. We discuss anomaly-free discrete symmetries which are both compatible with SU(5) unification of matter and the Giudice-Masiero mechanism, i.e. forbid the mu term in the superpotential while allowing the necessary Kaehler potential term. We find that these are Z_M^R symmetries with the following properties: (i) M is a multiple of four; (ii) the Higgs bilinear H_u H_d transforms trivially; (iii) the superspace coordinate theta has charge M/4 and, accordingly, the superpotential has charge M/2; (iv) dimension five proton decay operators are automatically absent. All Z_M^R symmetries are anomaly-free due to a non-trivial transformation of a Green-Schwarz axion, and, as a consequence, a holomorphic mu term appears at the non-perturbative level. There is a unique symmetry that is consistent with the Weinberg operator while there is a class of Z_M^R symmetries which explain suppressed Dirac neutrino masses.