Hidden-charm and hidden-beauty hybrid mesons

Abstract

The mass spectra of $\Pi_u$, $\Sigma_u^-$, $\Pi_g$, $\Delta_g$, $\Sigma_g^-$, $\Delta_u$, and $\Sigma_u^+$ hybrid charmonium and hybrid bottomonium states are computed using a non-relativistic potential model. The hybrid potential is modelled as a linear combination of quarkonium potential and gluonic excited potential. The gluonic excited potential is computed by fitting the potential difference between hybrid potential and quarkonium potential obtained from the lattice quantum chromodynamics. Experimental masses and $J^{PC}$ values of $\Psi(4230)$, $\Psi(4500)$, $X(4500)$, and $\Psi(4660)$ are compatible with hybrid charmonium states, and $\Upsilon(10753)$ and $\Upsilon(11050)$ are compatible with hybrid bottomonium states obtained from our model, respectively.