Abstract
AbstractWe 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 ($${\text {c}}\bar{{\text {c}}}$$
c
c
¯
), bottomonium ($${\text {b}}\bar{{\text {b}}}$$
b
b
¯
) and bottom-charmed meson ($${\text {c}}\bar{{\text {b}}}$$
c
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 $$10^{-39}$$
10
-
39
, and taking into account the current experimental data, we obtain the upper bound at the order of $${10^{-18}\,{{\text {m}}}}$$
10
-
18
m
for the fundamental length scale of space.
Funder
Agentúra Ministerstva Školstva, Vedy, Výskumu a Športu SR
Comenius University in Bratislava
Publisher
Springer Science and Business Media LLC
Subject
General Physics and Astronomy,Fluid Flow and Transfer Processes
Reference39 articles.
1. D.J. Griffiths, Introduction to Quantum Mechanics (Prentice Hall, Hoboken, 1995)
2. S. Doplicher, K. Fredenhagen, J.E. Roberts, The quantum structure of spacetime at the Planck scale and quantum fields. Commun. Math. Phys. 172(1), 187–220 (1995)
3. A. Connes, Noncommutative Geometry (Academic Press, Cambridge, 1994)
4. J. Hoppe, Quantum Theory of a Massless Relativistic Surface and a Two-Dimensional Bound State Problem, Ph.D. thesis, Massachusetts Institute of Technology, 1982
5. J. Madore, The fuzzy sphere. Class. Quantum Gravity 9, 69 (1992)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献