On quarkonium masses in 3D non-commutative space

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We modify the calculation of quarkonium masses using the radial WKB and Pekeris-type approximations for the case of three-dimensional, rotationally invariant non-commutative space. We obtain corrections to the charmonium ({text {c}}bar{{text {c}}}), bottomonium ({text {b}}bar{{text {b}}}) and bottom-charmed meson ({text {c}}bar{{text {b}}}) masses due to the discrete short distance structure of the space introduced by the space non-commutativity. For the fundamental length at the Planck scale we obtain relative correction at the order of 10^{-39}, and taking into account the current experimental data, we obtain the upper bound at the order of {10^{-18},{{text {m}}}} for the fundamental length scale of space.