Wave Function Based Characteristics of Hybrid Mesons
  We propose some extensions of the quark potential model to hybrids, fit them to the lattice data and use them for the purpose of calculating the masses, root mean square radii and wave functions at the origin of the conventional and hybrid charmonium mesons. We treat the ground and excited gluonic field between a quark and an antiquark as in the Born-Oppenheimer expansion, and use the shooting method to numerically solve the required Schr$\ddot{\textrm{o}}$dinger equation for the radial wave functions; from these wave functions we calculate the mesonic properties. For masses we also check through a Crank Nichelson discretization. For hybrid charmonium mesons, we consider the exotic quantum number states with $ J^{PC} = 0^{+ -}, 1^{- +}$ and $2^{+ -}$. We also compare our results with the experimentally observed masses and theoretically predicted results of the other models. Our results have implications for scalar form factors, energy shifts, magnetic polarizabilities, decay constants, decay widths and differential cross sections of conventional and hybrid mesons. 
Nosheen Akbar, Bilal Masud, Saba Noor
hep-ph