Tri-linear Couplings in an Heterotic Minimal Supersymmetric Standard Model

TL;DR

This paper computes the classical superpotential tri-linear couplings in a specific heterotic string-derived minimal supersymmetric Standard Model, revealing key features like Yukawa couplings, proton stability, and neutrino mass generation.

Contribution

It provides the first calculation of tri-linear couplings in this globally consistent heterotic MSSM, highlighting their role in Higgs and neutrino mass terms.

Findings

Non-zero Yukawa couplings for up-sector quarks

Vanishing R-parity violating terms, ensuring proton stability

Existence of couplings generating -mass and neutrino masses

Abstract

We calculate, at the classical level, the superpotential tri-linear couplings of the only known globally consistent heterotic minimal supersymmetric Standard Model [ hep-th/0512149 ]. This recently constructed model is based on a compactification of the E_8 x E_8 heterotic string theory on a Calabi-Yau threefold with Z_2 fundamental group, coupled with a slope-stable holomorphic SU(5) vector bundle. In the observable sector the massless particle content is that of the three-family supersymmetric Standard Model with n=0,1,2 massless Higgs pairs, depending on the location in the vector bundle moduli space, and no exotic particles. We obtain non-zero Yukawa couplings for the three up-sector quarks, and vanishing R-parity violating terms. In particular, the proton is stable. Another interesting feature is the existence of tri-linear couplings, on the loci with massless Higgs pairs, generating \mu-mass parameters for the Higgs pairs and neutrino mass terms, with specific vector bundle moduli playing the role of right-handed neutrinos.