Potential Model for ${\Sigma }_u^{-}$ Hybrid Meson State

Abstract

In this paper, lattice simulations are used to propose a potential model for gluonic excited ${\Sigma }_u^{-}$ states of bottomonium meson . This proposed model is used to calculate radial wave functions, masses and radii of ${\Sigma }_u^{-}$ bottomonium hybrid mesons. Here, gluonic field between a quark and an antiquark is treated as in the Born-Oppenheimer expansion, and Schr$\ddot{o}$dinger equation is numerically solved employing shooting method. Results of calculated masses for ${\Sigma }_u^{-}$ state are in quite good agreement with the lattice simulations.

8 pages, 3 figures