Ground state energy shift of charmonium on noncommutative space

Document Type : Full length research Paper

Author

Abstract

A nonrelativistic model was used to determine the energy shift of low lying states of meson charmonium with respect to the Cornell, Martin, logarithm and global potentials. It is shown that at the lowest order of perturbation, the ground state acquires an energy shift that is proportional to the inverse square of the noncommutative length scale. We estimated an upper bound on noncommutative scale of order 0.397_ 3.021GeV, by using the recent most accurate experimental data on ortho and paracharmonium meson spectra.

Keywords

Main Subjects


[1] M. Chaichian, M.M. Sheikh-jabbari, A. tureanu, Hydrogen atom spectrum and the lamb shift in noncommutative qed, Physical Review Letters 86 (2001) 2716-2719.
 
[2] K. Gnatenko, V. Thachuk, Hydrogen atom in rotationally invariant noncommutative space, Physics Letters A 378 (2014) 3509-3515.
 
 [3] A. Prakash, A. Mitra, P.k. Das, Scattering in the noncommutative standard
Model, Physical Review D 82 (2010) 055020-055033.
 
[4] N. Seiberg, E. Witten, String theory and noncommutative geometry, Journal of high Energy Physics 9909 (1999) 1299–1305.
 
[5] B. Mira, M. Dehghani, noncommutative geometry and classical orbits of particles in a central force potential, communications in Theoretical Physics 42 (2004)183-184.
 
[6] A. Parmeggiani, noncommutative harmonic oscillators and related problems, Milan Journal of Mathematics 82 (2014) 343-387.
 
[7] J. BenGeloun, F.G. Schultz, Coherent states in noncommutative quantum mechanics, Journal of Mathematical Physics 50 (2009) 343-387. 
 
[8] A.Al- Jamel, Heavy quarkonia with Cornell potential on noncommutative space, Journal of Theoretical and Appliedphysics 5 (2011) 21-24.
 
[9] G.R. Boroun, H. Abdolmalki, Variational and exact solutions of the wave function at origin (WFO) for heavy quark onium by using a global potential, Physica Scripta 80 (2009) 065003-065008.
[10] K. Olive, P. Data, Review of Particle Physics, Chinese Physics C 38 (2014) 090001-091677.
 
[11] M. Moumni et al, Lyman- alpha spectroscopy in non-commutative space- time, International Journal of Modern Physics: Conference Series 1 (2010) 1-5.
[12] A. Stern, Particle-like solutions to classical noncommutative gauge theory, Physical Review D 78 (2008) 065006-065027.