Masses of Third Family Vector-like Quarks and Leptons in Yukawa-Unified $E_6$

TL;DR

This paper investigates the masses of third family vector-like quarks and leptons in a supersymmetric $E_6$ model, deriving lower bounds based on Yukawa unification and experimental constraints on the $Z'_\psi$ boson.

Contribution

It provides a novel estimation of lower bounds on vector-like particle masses in a Yukawa-unified $E_6$ framework considering experimental constraints.

Findings

Lower bound on $D$-quark mass is approximately 5.85 TeV.

Lower bound on $L$-lepton mass is approximately 2.9 TeV.

Yukawa unification constrains vector-like particle masses in supersymmetric $E_6$.

Abstract

In supersymmetric $E_6$ the masses of the third family quarks and charged lepton, $t-b-\tau$, as well as the masses of the vector-like quarks and leptons, $D-\bar{D}$ and $ L-\bar{L}$, may arise from the coupling $27_3$ x $27_3$ x $27_H$, where $27_3$ and $27_H$ denote the third family matter and Higgs multiplets respectively. We assume that the SO(10) singlet component in $27_H$ acquires a TeV scale VEV which spontaneously breaks U(1)$_\psi$ and provides masses to the vector-like particles in $27_3$, while the MSSM doublets in $27_H$ provide masses to $ t, b$ and $\tau$. Imposing Yukawa coupling unification $h_t=h_b=h_{\tau}=h_D=h_L$ at $M_{GUT}$ and employing the ATLAS and CMS constraints on the $Z'_\psi$ boson mass, we estimate the lower bounds on the third family vector-like particles $D-\bar{D}$ and $L-\bar{L}$ masses to be around 5.85 TeV and 2.9 TeV respectively. These bounds apply in the supersymmetric limit.