Possible effects of quark and gluon condensates in quarkonium spectra

The Cornell potential with the best fitted parameters $\alpha_{s}$ and $\kappa$ are modified by adding terms derived from non-perturbative QCD, which are characterized by a series of non-vanishing vacuum condensates of quarks and gluons. In terms of this potential, we study the system of heavy quarkonia. The results show that the correction caused by the additional terms reduces the deviation between the data and the values calculated with the pure Cornell potential and improves the splittings of energy levels. The achievements indicate that the non-perturbative effects induced by vacuum condensates play an important role for the correction to $1/q^2$, which in general was phenomenologically put in by hand. This result would be helpful for understanding non-perturbative QCD along a parallel direction to the QCD sum rules.