Testing R-parity with Geometry

TL;DR

This paper classifies vacuum geometries in the MSSM's electroweak sector, revealing how R-parity assignments influence the geometric structure and neutrino mass mechanisms.

Contribution

It provides a complete geometric classification of MSSM superpotentials, highlighting the impact of R-parity on vacuum structure and neutrino mass models.

Findings

Traditional R-parity supports the neutrino see-saw mechanism with complex geometry.

No geometric preference for a fundamental Higgs bilinear in the superpotential.

Operators violating lepton number lead to similar vacuum moduli spaces as those with bilinear operators.

Abstract

We present a complete classification of the vacuum geometries of all renormalizable superpotentials built from the fields of the electroweak sector of the MSSM. In addition to the Severi and affine Calabi-Yau varieties previously found, new vacuum manifolds are identified; we thereby investigate the geometrical implication of theories which display a manifest matter parity (or R-parity) via the distinction between leptonic and Higgs doublets, and of the lepton number assignment of the right-handed neutrino fields. We find that the traditional R-parity assignments of the MSSM more readily accommodate the neutrino see-saw mechanism with non-trivial geometry than those superpotentials that violate R-parity. However there appears to be no geometrical preference for a fundamental Higgs bilinear in the superpotential, with operators that violate lepton number, such as \nu H\bar{H}, generating vacuum moduli spaces equivalent to those with a fundamental bilinear.