Noncommutative correction to the Cornell potential in heavy-quarkonium atoms

We investigate the effect of space–time noncommutativity on the Cornell potential in heavy-quarkonium systems. It is known that the space–time noncommutativity can create bound states, and we therefore consider the noncommutative geometry of the space–time as a correction in quarkonium models. Furthermore, we take the experimental hyperfine measurements of the bottomium ground state as an upper limit on the noncommutative energy correction and derive the maximum possible value of the noncommutative parameter $\theta$, obtaining $\theta\le37.94\cdot10^{-34}$ m$^2$. Finally, we use our model to calculate the maximum value of the noncommutative energy correction for energy levels of charmonium and bottomium in $1\mathrm{S}$ and $2\mathrm{S}$ levels. The energy correction as a binding effect in quarkonium system is smaller for charmonium than for bottomium, as expected.