Particle physics and cosmology of the string derived no-scale flipped $SU(5)$

TL;DR

This paper explores a string-derived flipped SU(5) model that achieves Starobinsky inflation and realistic particle phenomenology, including stable protons and hierarchical Yukawa couplings, with high-scale supersymmetry breaking.

Contribution

It provides a detailed analysis of the vacuum structure and phenomenology of a string-derived flipped SU(5) model post-inflation, including explicit superpotential calculations and vacuum solutions.

Findings

Successful realization of Starobinsky inflation within the model

Extra color triplets become superheavy, ensuring proton stability

Higgs doublet mass matrix has a massless eigenstate with realistic Yukawa couplings

Abstract

In a recent paper, we identified a cosmological sector of a flipped $SU(5)$ model derived in the free fermionic formulation of the heterotic superstring, containing the inflaton and the goldstino superfields with a superpotential leading to Starobinsky type inflation, while $SU(5){\times}U(1)$ is still unbroken. Here, we study the properties and phenomenology of the vacuum after the end of inflation, where the gauge group is broken to the Standard Model. We identify a set of vacuum expectation values, triggered by the breaking of an anomalous $U(1)_A$ gauge symmetry at roughly an order of magnitude below the string scale, that solve the F and D-flatness supersymmetric conditions up to 6th order in the superpotential which is explicitly computed, leading to a successful particle phenomenology. In particular, all extra colour triplets become superheavy guaranteeing observable proton stability, while the Higgs doublet mass matrix has a massless pair eigenstate with realistic hierarchical Yukawa couplings to quarks and leptons. The supersymmetry breaking scale is constrained to be high, consistent with the non observation of supersymmetric signals at the LHC.