Geodesic
Noncommutative correction to the Cornell potential in heavy-quarkonium atoms
Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 2, pp. 323-329 Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate the effect of space–time noncommutativity on the Cornell potential in heavy-quarkonium systems. It is known that the space–time noncommutativity can create bound states, and we therefore consider the noncommutative geometry of the space–time as a correction in quarkonium models. Furthermore, we take the experimental hyperfine measurements of the bottomium ground state as an upper limit on the noncommutative energy correction and derive the maximum possible value of the noncommutative parameter $\theta$, obtaining $\theta\le37.94\cdot10^{-34}$ m$^2$. Finally, we use our model to calculate the maximum value of the noncommutative energy correction for energy levels of charmonium and bottomium in $1\mathrm{S}$ and $2\mathrm{S}$ levels. The energy correction as a binding effect in quarkonium system is smaller for charmonium than for bottomium, as expected.
Keywords: noncommutative space–time, noncommutative parameter, Cornell potential, heavy quarkonium, hyperfine splitting. 
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     author = {A. Mirjalili and M. Taki},
     title = {Noncommutative correction to {the~Cornell} potential in heavy-quarkonium atoms},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2016_186_2_a9/}
}
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A. Mirjalili; M. Taki. Noncommutative correction to the Cornell potential in heavy-quarkonium atoms. Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 2, pp. 323-329. http://geodesic.mathdoc.fr/item/TMF_2016_186_2_a9/

[1] E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane, T. M. Yan, Phys. Rev. D, 17:11 (1978), 3090–3117 | DOI

[2] E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane, T. M. Yan, Phys. Rev. D, 21:1 (1980), 203–233 | DOI

[3] J. J. Aubert, U. Becker, P. J. Biggs et al., Phys. Rev. Lett., 33:23 (1974), 1404–1406 | DOI

[4] J.-E. Augustin, A. M. Boyarski, M. Breidenbach et al., Phys. Rev. Lett., 33:23 (1974), 1406–1408 | DOI

[5] C. Bacci, R. B. Celio, M. Berna-Rodini et al., Phys. Rev. Lett., 33:23 (1974), 1408–1410 | DOI

[6] G. S. Abrams, D. Briggs, W. Chinowsky et al., Phys. Rev. Lett., 33:24 (1974), 1453–1455 | DOI

[7] N. Rambilla, M. Krämer, R. Mussa et al., Heavy quarkonium physics, CERN Yellow Report, CERN, Geneva, 2005, arXiv: hep-ph/0412158

[8] E. Eichten, K. Gottfried, T. Kinoshita, J. Kogut, K. D. Lane, T.-M. Yan, Phys. Rev. Lett., 34:6 (1975), 369–372 | DOI

[9] H. J. Schnitzer, Phys. Rev. Lett., 35:22 (1975), 1540–1543 | DOI

[10] S. N. Gupta, S. F. Radford, W. W. Repko, Phys. Rev. D, 26:11 (1982), 3305–3308 | DOI

[11] S. N. Gupta, S. F. Radford, W. W. Repko, Phys. Rev. D, 31:1 (1985), 160–163 | DOI

[12] S. N. Gupta, S. F. Radford, W. W. Repko, Phys. Rev. D, 34:1 (1986), 201–206 | DOI

[13] S. F. Radford, W. W. Repko, Phys. Rev. D, 75:7 (2007), 074031 | DOI

[14] S. F. Radford, W. W. Repko, Nucl. Phys. A, 865:1 (2011), 69–75 | DOI

[15] T. J. Burns, Phys. Rev. D, 87:3 (2013), 034022, 8 pp. | DOI

[16] D. V. Vassilevich, A. Yurov, Phys. Rev. D, 69:10 (2004), 105006, 5 pp. | DOI | MR

[17] M. Chaichian, M. M. Sheikh-Jabbari, A. Tureanu, Phys. Rev. Lett., 86:13 (2001), 2716–2719 | DOI

[18] V. G. Kupriyanov, J. Phys. A: Math. Theor., 46:24 (2013), 245303, 7 pp., arXiv: 1209.6105 | DOI | MR | Zbl

[19] R. Wulkenhaar, JHEP, 03 (2002), 024, 35 pp., arXiv: hep-th/0112248 | DOI | MR

[20] J. Beringer, J.-F. Arguin, R. M. Barnett et al. [Particle Data Group], Phys. Rev. D, 86:1 (2012), 010001, 1528 pp. | DOI

[21] S. Slavyanov, V. Lai, Spetsialnye funktsii: edinaya teoriya, osnovannaya na analize osobennostei, Nevskii Dialekt, SPb., 2002 | MR | Zbl

[22] S. Yu. Slavyanov, TMF, 119:1 (1999), 3–19 | DOI | DOI | MR | Zbl

[23] M. Hortacsu, “Heun functions and their uses in physics”, Proceedings of the 13th Regional Conference on Mathematical Physics (Antalya, Turkey, October 27–31, 2010), eds. U. Camci, I. Semiz, World Sci., Singapore, 2013, 23–39, arXiv: 1101.0471 | MR | Zbl

[24] V. Lai, TMF, 101:3 (1994), 360–368 | DOI | MR | Zbl

[25] S. Yu. Slavyanov, TMF, 182:2 (2015), 223–230 | DOI | DOI | MR | Zbl