Bound Energy Masses of Mesons Containing the Fourth Generation and Iso-singlet Quarks

The fourth Standard Model (SM) family quarks and weak iso-singlet quarks The fourth Standard Model (SM) family quarks and weak iso-singlet quarks predicted by ${\rm E}_{6\text{}}$ GUT are considered. The spin-average of the pseudoscalar $\eta_{4}(n^{1}S_{0})$ and vector $\psi_{4}(n^{3}S_{1})$ quarkonium binding masses of the new mesons formed by the fourth Standard Model (SM) family and iso-singlet ${\rm E}_{6\text{}}$ with their mixings to ordinary quarks are investigated. Further, the fine and hyperfine mass splittings of the these states are also calculated. We solved the Schr\"{o}dinger equation with logarithmic and Martin potentials using the Shifted large-${\rm N}$ expansion technique. Our results are compared with other models to gauge the reliability of the predictions and point out differences.