A. Al-Jamel, Heavy Quarkonia with Cornell potential on Noncommutative space, Journal of Theoretical and Applied Physics, 5-1, 21-24 (2011).

We study the effects of noncommutative space, to the second order in ?, on heavy quarkonium spectra within the framework of the nonrelativisitc Cornell potential. Due to these effects, a singular term 1/r3 appears in the potential, which is remedied using a regularization scheme by introducing a cut-off radius on the lower limit of the integrals needed for the perturbation computations. The results are applied to the 1S states of c?c, and we find that the energy shifts are quadratic in the noncommutative parameter ?. By comparing the results with those from experimental 1S-hyperfine splitting of c?c, we infer an upper limit on ?.