Proton Stability, Gauge Coupling Unification and a Light $Z^\prime$ in Heterotic-string Models

TL;DR

This paper investigates the feasibility of a light Z' gauge boson in heterotic-string models, focusing on proton stability and gauge coupling unification, and finds that viable models require E6 embedding of U(1)_Z' charges.

Contribution

It demonstrates that a light Z' in heterotic-string models can suppress proton decay but requires E6 embedding for compatibility with gauge coupling data.

Findings

Light Z' can prevent baryon number violation

Gauge coupling data restricts Z' viability

E6 embedding of charges is necessary for consistent models

Abstract

We explore the phenomenological viability of a light Z' in heterotic-string models, whose existence has been motivated by proton stability arguments. A class of quasi-realistic string models that produce such a viable Z' are the Left-Right Symmetric (LRS) heterotic-string models in the free fermionic formulation. A key feature of these models is that the matter charges under U(1)_Z' do not admit an E6 embedding. The light Z' in the LRS heterotic-string models forbids baryon number violating operators, while allowing lepton number violating operators, hence suppressing proton decay yet allowing for sufficiently small neutrino masses via a seesaw mechanism. We show that the constraints imposed by the gauge coupling data and heterotic-string coupling unification nullify the viability of a light Z' in these models. We further argue that agreement with the gauge coupling data necessitates that the U(1)_Z' charges admit an E6 embedding. We discuss how viable string models with this property may be constructed.