The B-L/Electroweak Hierarchy in Heterotic String and M-Theory

TL;DR

This paper demonstrates how heterotic string and M-theory compactifications can naturally produce a B-L/electroweak hierarchy through right-handed sneutrino vacuum expectation values, aligning with phenomenological constraints.

Contribution

It provides a specific mechanism within heterotic models for spontaneous B-L breaking, establishing a viable hierarchy via renormalization group analysis and soft SUSY breaking.

Findings

B-L symmetry can be spontaneously broken at low scales.

The hierarchy is achievable with a right-handed sneutrino VEV.

The vacuum state is a stable local minimum.

Abstract

E8 x E8 heterotic string and M-theory, when compactified on a Calabi-Yau threefold admitting an SU(4) vector bundle with Wilson lines, can give rise to the exact MSSM spectrum with three right-handed neutrino chiral superields, one per family. Rank preserving Wilson lines require that the standard model group be augmented by a gauged U(1)_B-L. Since there are no fields in this theory for which 3(B-L) is an even, non-zero integer, the gauged B-L symmetry must be spontaneously broken at a low scale, not too far above the electroweak scale. It is shown that in these heterotic standard models, the B-L symmetry can be broken, with a phenomenologically viable B-L/electroweak hierarchy, by at least one right-handed sneutrino acquiring a vacuum expectation value. This is explicitly demonstrated, in a specific region of parameter space, using a renormalization group analysis and soft supersymmetry breaking operators. The vacuum state is shown to be a stable, local minimum of the potential and the resultant hierarchy is explicitly presented in terms of tan[beta].