Heavy quarkonia with Cornell potential on noncommutative space

The e?ect of noncommutative space, to the second order in ?, on heavy quarkonium spectra is studied within the framework of the nonrelativistic Schrodinger equation with the static Cornell potential. Due to this e?ect, a singular term 1?r^3 appears in the potential, which is remedied using a regularization scheme by introducing a cut-o? radius on the lower limit of the integrals needed for the perturbation computations. The results are applied to the 1S states of cc ?, and it is found that the energy shifts are quadratic in the noncommutative parameter ?. By comparing the results with those from experimental 1S-hyper?ne splitting of cc ?, we infer an upper limit on ?.