On quarkonium masses in 3D non-commutative space

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