The \mu - term in Effective Supergravity Theories

TL;DR

This paper derives a general expression for the Higgs mixing term in supergravity theories with string origins, highlighting conditions under which it vanishes or receives corrections, with implications for string compactifications.

Contribution

It provides a model-independent derivation of the effective bc-term in supergravity, including new contributions and conditions specific to string compactifications.

Findings

Derivative terms are zero in certain heterotic string models.

The bc-term vanishes when modular weights sum to two.

Discusses subleading bc-corrections with intermediate gauge symmetries.

Abstract

The Higgs mixing term coefficient $\mu_{eff}$ is calculated in the scalar potential in supergravity theories with string origin, in a model independent approach. A general low energy effective expression is derived, where new contributions are included which depend on the modular weights $q_{1,2}$ of the Higgs superfields, the moduli and derivative terms. We find that in a class of models obtained in the case of compactifications of the heterotic superstring, the derivative terms are identically zero. Further, the total $\mu_{eff}$-term vanishes identically if the sum of the two modular weights $q_1+q_2$ is equal to two. Subleading $\mu$- corrections, in the presence of intermediate gauge symmetries predicted in viable string scenarios, are also discussed.