Bottomonia Under Effect Three Inspired QCD Potentials in the Framework of Non-Relativistic Quark Model
Abstract
In this paper, we have studied the spectrum of bottomonium mesons behavior under the effect of three types of potentials inspired by Quantum Chromodynamics. In addition, other properties like Hyperfine splitting behavior, and Fine splitting behavior have been studied. We used these potential models within the non-relativistic quark model to present this study. We found that our expectations are consistent with experimental data and other theoretical works as well we presented new conclusions regarding the spectrum of unseen bottomonium states for S, P, and D-wave bottomonia. And we have expected other their characteristics.
Downloads
References
D. Griffiths, Introduction to Elementary Particles, (John Wiley & Sons, Weinheim, 2020).
A. Bettini, Introduction to Elementary Particle Physics, (Cambridge University Press, 2014).
F. Hanzel, and A.D. Martin, Quarks and Leptons: An Introductory Course in Modern Particle Physics (John Wiley & Sons, New York, 1984).
D.H. Perkins, and D.H. Perkins, Introduction to High Energy Physics, (Cambridge university press, 2000). https://doi.org/10.1017/CBO9780511809040
I. Bigi, Y. Dokshitzer, V. Khoze, J. Kühn, and P. Zerwas, “Production and decay properties of ultra-heavy quarks,” Physics Letters B, 181(1-2), 157-163 (1986). https://doi.org/10.1016/0370-2693(86)91275-X
S. Herb, D. Hom, L. Lederman, J. Sens, H. Snyder, J. Yoh, J. Appel, et al., “Observation of a Dimuon Resonance at 9.5 GeV in 400-GeV Proton-Nucleus Collisions, ”Physical Review Letters, 39(5), 252 (1977). https://doi.org/10.1103/PhysRevLett.39.252
W.R. Innes, J. Appel, B. Brown, C. Brown, K. Ueno, T. Yamanouchi, S. Herb, et al., “Observation of Structure in the Υ Region,” Physical Review Letters, 39(20), 1240 (1977). https://doi.org/10.1103/PhysRevLett.39.1240
D. Besson, J. Green, R. Namjoshi, F. Sannes, P. Skubic, A. Snyder, R. Stone, et al., “Observation of New Structure in the e+e− Cross Section above the Υ(4S),” Physical Review Letters, 54(5), 381 (1985). https://doi.org/10.1103/PhysRevLett.54.381
B. Aubert, M. Bona, Y. Karyotakis, J. Lees, V. Poireau, E. Prencipe, X. Prudent, et al., “Observation of the Bottomonium Ground State in the Decay Υ(3S)→γηb,” Physical Review Letters, 101(7), 071801 (2008). https://doi.org/10.1103/PhysRevLett.101.071801
R. Mizuk, D. Asner, A. Bondar, T. Pedlar, I. Adachi, H. Aihara, K. Arinstein, et al., “Evidence for the ηb(2S) and Observation of hb(1P)→ηb(1S)γ and hb(2P)→ηb(1S)γ,” Physical Review Letters, 109(23), 232002 (2012). https://doi.org/10.1103/PhysRevLett.109.232002
K. Han, T. Böhringer, P. Franzini, G. Mageras, D. Peterson, E. Rice, J. Yoh, et al., “Observation of P-Wave b¯b Bound States,” Physical Review Letters, 49(22), 1612 (1982). https://doi.org/10.1103/PhysRevLett.49.1612
G. Eigen, G. Blanar, and H. Dietl, “Evidence for χb′ Production in the Exclusive Reaction Υ''→γχb′→(γγΥ′ or γγΥ),” Physical Review Letters, 49(22), 1616 (1982). https://doi.org/10.1103/PhysRevLett.49.1616
C. Klopfenstein, J. Horstkotte, J. Lee-Franzini, R. Schamberger, M. Sivertz, L. Spencer, P. Tuts, et al., “Observation of the Lowest P-Wave b¯b Bound States,” Physical Review Letters, 51(3), 160 (1983). https://doi.org/10.1103/PhysRevLett.51.160
F. Pauss, H. Dietl, G. Eigen, E. Lorenz, G. Mageras, H. Vogel, P. Franzini, et al. “Observation of χb production in the exclusive reaction ϒ′→γγχb→γγϒ→γγ(e+e−orμ+μ−),” Physics Letters B, 130(6), 439 (1983). https://doi.org/10.1016/0370-2693(83)91539-3
J. Lees, V. Poireau, E. Prencipe, V. Tisserand, J.G. Tico, E. Grauges, M. Martinelli, et al. (BABAR Collaboration), “Evidence for the hb(1P) meson in the decay Υ(3S)→π0hb(1P),” Physical Review D, 84(9), 091101 (2011). https://doi.org/10.1103/PhysRevD.84.091101
I. Adachi, H. Aihara, K. Arinstein, D.M. Asner, T. Aushev, T. Aziz, A. Bakich, et al. (Belle Collaboration), “First Observation of the P-Wave Spin-Singlet Bottomonium States hb(1P) and hb(2P),” Physical Review Letters, 108(3), 032001 (2012). https://doi.org/10.1103/PhysRevLett.108.032001
P. del Amo Sanchez, J. Lees, V. Poireau, E. Prencipe, V. Tisserand, J.G. Tico, E. Grauges, et al. (BABAR Collaboration), “Observation of the Υ(13DJ) bottomonium state through decays to π+π−Υ(1S),” Physical Review D, 82(11), 111102 (2010). https://doi.org/10.1103/PhysRevD.82.111102
T. Kuhr, C. Pulvermacher, M. Ritter, T. Hauth, and N. Braun, “The Belle II Core Software,” Computing and Software for Big Science, 3, 1 (2019). https://doi.org/10.1007/s41781-018-0017-9
Z.-G. Wang, “The radiative decays B∗±c→B±cγ→ with QCD sum rules,” The European Physical Journal C, 73, 1 (2013). https://doi.org/10.1140/epjc/s10052-013-2559-7
K. Azizi, and J. Süngü, “On the mass and decay constant of the P-wave ground and radially excited hc and hb axial-vector mesons,” Journal of Physics G: Nuclear and Particle Physics, 46(3), 035001 (2019). https://doi.org/10.1088/1361-6471/aaee21
C.S. Fischer, S. Kubrak, and R. Williams, “Spectra of heavy mesons in the Bethe-Salpeter approach,” The European Physical Journal A, 51(1), 10 (2015). https://doi.org/10.1140/epja/i2015-15010-7
D.-M. Li, B. Ma, Y.-X. Li, Q.-K. Yao, and H. Yu, “Meson spectrum in Regge phenomenology,” The European Physical Journal C-Particles and Fields, 37, 323 (2004). https://doi.org/10.1140/epjc/s2004-02002-5
S. Gershtein, A. Likhoded, and A. Luchinsky, “Systematics of heavy quarkonia from Regge trajectories on (n,M2) and (M2,J) planes,” Physical Review D, 74(1), 016002 (2006). https://doi.org/10.1103/PhysRevD.74.016002
K.-W. Wei, and X.-H. Guo, et al. “Mass spectra of doubly heavy mesons in Regge phenomenology,” Physical Review D, 81(7), 076005, (2010). https://doi.org/10.1103/PhysRevD.81.076005
A. Badalian, and B. Bakker, “Radial and orbital Regge trajectories in heavy quarkonia,” Physical Review D, 100(5), 054036 (2019). https://doi.org/10.1103/PhysRevD.100.054036
Y. Kiyo, and Y. Sumino, “Perturbative heavy quarkonium spectrum at next-to-next-to-next-to-leading order,” Physics Letters B, 730, 76 (2014). https://doi.org/10.1016/j.physletb.2014.01.030
J. Daldrop, C. Davies, R. Dowdall, H. Collaboration, et al. “Prediction of the Bottomonium D-Wave Spectrum from Full Lattice QCD,” Physical Review Letters, 108(10), 102003 (2012). https://doi.org/10.1103/PhysRevLett.108.102003
R. Lewis, and R. Woloshyn, “Higher angular momentum states of bottomonium in lattice nonrelativistic QCD,” Physical Review D, 85(11), 114509 (2012). https://doi.org/10.1103/PhysRevD.85.114509
M. Wurtz, R. Lewis, and R. Woloshyn, “Free-form smearing for bottomonium and B meson spectroscopy,” Physical Review D, 92(5), 054504 (2015). https://doi.org/10.1103/PhysRevD.92.054504
E. Van Beveren, G. Rupp, T. Rijken, and C. Dullemond, “Radial spectra and hadronic decay widths of light and heavy mesons,” Physical Review D, 27(7), 1527 (1983). https://doi.org/10.1103/PhysRevD.27.1527
N. Tornqvist, Physical Review Letters, 53(9), 878 (1984). https://doi.org/10.1103/PhysRevLett.53.878
J.-F. Liu, and G.-J. Ding, The European Physical Journal C, 7253(1), 18 (2012). https://doi.org/10.1140/epjc/s10052-011-1853-5
Y. Lu, M.N. Anwar, and B.-S. Zou, Physical Review D, 94(3), 034021 (2016). https://doi.org/10.1103/PhysRevD.94.034021
D. Ebert, R.N. Faustov, and V.O. Galkin, The European Physical Journal C, 71, 1825 (2011). https://doi.org/10.1140/epjc/s10052-011-1825-9
M. Bhat, A.P. Monteiro, and K. Kumar, (2017). https://doi.org/10.48550/arXiv.1702.06774
S. Godfrey, and N. Isgur, Physical Review D, 32(1), 189 (1985). https://doi.org/10.1103/PhysRevD.32.189
S. Godfrey, and K. Moats, Physical Review D, 92(5), 054034 (2015). https://doi.org/10.1103/PhysRevD.92.054034
J.-Z. Wang, Z.-F. Sun, X. Liu, and T. Matsuki, The European Physical Journal C, 78, 915 (2018). https://doi.org/10.1140/epjc/s10052-018-6372-1
S.N. Gupta, S.F. Radford, and W.W. Repko, Physical Review D, 34(1), 201 (1986). https://doi.org/10.1103/PhysRevD.34.201
A. Badalian, A. Veselov, and B. Bakker, Physical Review D, 70(1), 016007 (2004). https://doi.org/10.1103/PhysRevD.70.016007
M. Shah, A. Parmar, and P. Vinodkumar, Physical Review D, 86(3), 034015 (2012). https://doi.org/10.1103/PhysRevD.86.034015
C. Semay, and B. Silvestre-Brac, Nuclear Physics A, 618(4), 455 (1997). https://doi.org/10.1016/S0375-9474(97)00060-2
R.L. Workman, et al., “Review of Particle Physics,” PTEP, 2022, 083C01 (2022). https://doi.org/10.1093/ptep/ptac097
J.-E. Augustin, A. Boyarski, M. Breidenbach, F. Bulos, J. Dakin, G. Feldman, G. Fischer, et al., Physical Review Letters, 34(4), 233 (1975). https://doi.org/10.1103/PhysRevLett.34.233
T. Appelquist, A. De Rujula, S.L. Glashow, and H. Plitzer, tech. rep., SIS-75-0111, 1974.
A. De Rujula, and S.L. Glashow, Physical Review Letters, 34(1), 46 (1975). https://doi.org/10.1103/PhysRevLett.34.46
A.A. Bykov, I.M. Dremin, and A.V. Leonidov, Soviet Physics Uspekhi, 27(5), 321 (1984).
T. Barnes, S. Godfrey, and E. Swanson, Physical Review D, 72(5), 054026 (2005). https://doi.org/10.1103/PhysRevD.72.054026
B.L. Ioffe, V.S. Fadin, and L.N. Lipatov, Quantum chromodynamics: Perturbative and nonperturbative aspects. No. 30, (Cambridge University Press, 2010).
O. Lakhina, PhD thesis, University of Pittsburgh, 2007.
A. Yasser, T. Nahool, and G. Hassan, (2014). https://doi.org/10.48550/arXiv.1410.5005
L. Bai-Qing and C. Kuang-Ta, Communications in Theoretical Physics, 52(4), 653 (2009). https://doi.org/10.1088/0253-6102/52/4/20
I. Asghar, F. Akram, B. Masud, and M.A. Sultan, Physical Review D, 100(9), 096002 (2019). https://doi.org/10.1103/PhysRevD.100.096002
V. Kher, R. Chaturvedi, N. Devlani, and A. Rai, The European Physical Journal Plus, 137(3), 357 (2022). https://doi.org/10.1140/epjp/s13360-022-02538-5
B. Chen, A. Zhang, and J. He, Physical Review D, 101(1), 014020 (2020). https://doi.org/10.1103/PhysRevD.101.014020
W.-J. Deng, H. Liu, L.-C. Gui, and X.-H. Zhong, Physical Review D, 95(7), 074002 (2017). https://doi.org/10.1103/PhysRevD.95.074002.
Copyright (c) 2023 Moustafa Ismail Hapareer, M. Allosh, G.S. Hassan, A.M. Yasser
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
