Correlating Mu Parameter and Right-Handed Neutrino Masses in N=1 Supergravity

Abstract

The minimal supersymmetric standard model, when extended to embed the seesaw mechanism, obtains two dimensionful parameters in its superpotential: the mu parameter and the right-handed neutrino mass M_N. These mass parameters, belonging to the supersymmetric sector of the theory, pose serious naturalness problems as their scales are left completely undetermined. In fact, for correct phenomenology, mu must be stabilized at the electroweak scale while M_N lies at an intermediate scale. In this work we construct an explicit model of the hidden sector of N=1 supergravity for inducing both mu and M_N at their right scales. The model we build utilizes lepton number conservation and continuous R invariance as two fundamental global symmetries to forbid bare mu and M_N appearing in the superpotential, and induces them at phenomenologically desired scales via spontaneous breakdown of the global symmetries and the supergravity. We discuss briefly various phenomenological implications of the model.