https://doi.org/10.1140/epjp/s13360-023-04049-3
Regular Article
On quarkonium masses in 3D non-commutative space
Department of Theoretical Physics, Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, KTF FMFI, Mlynská dolina, 842 48, Bratislava, Slovakia
Received:
21
February
2023
Accepted:
1
May
2023
Published online:
5
June
2023
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 (
), bottomonium (
) and bottom-charmed meson (
) 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 
, and taking into account the current experimental data, we obtain the upper bound at the order of 
for the fundamental length scale of space.
© The Author(s) 2023
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