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arXiv · 1512.00854

Testing R-parity with Geometry

Yang-Hui He·Vishnu Jejjala·Cyril Matti·Brent D. Nelson
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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 νH\bar{H}, generating vacuum moduli spaces equivalent to those with a fundamental bilinear.

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Yang-Hui He, Vishnu Jejjala, Cyril Matti, Brent D. Nelson. 2015-12-02. Testing R-parity with Geometry. https://doi.org/10.1007/jhep03(2016)079

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