Relativistic oscillator model with spin for nucleon resonances

• Authors: Dmitry Kulikov , Ivan Uvarov , Arkadiy Yaroshenko
• Languages of publication: EN

Abstracts

EN

The relativistic three-body problem is approached via the extension of the SL(2, C) group to the Sp(4, C) one. In terms of Sp(4, C) spinors, a Dirac-like equation with three-body kinematics is composed. After introducing the linear in coordinates interaction, it describes the spin-1/2 oscillator. For this system, the exact energy spectrum is derived and then applied to fit the Regge trajectories of baryon N-resonances in the (E
2, J) plane. The model predicts linear trajectories at high total energy E with some form of nonlinearity at low E.

Keywords

EN

three-body problem; relativistic oscillator; nucleon resonances

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2013
• Volume: 11
• Issue: 8
• Pages: 1006-1015

Dates

published

1 - 8 - 2013

online

23 - 10 - 2013

Contributors

author

Dmitry Kulikov

• Dnipropetrovsk National University, 72 Gagarin avenue, 49010, Dnipropetrovsk, Ukraine

author

Ivan Uvarov

• Dnipropetrovsk National University, 72 Gagarin avenue, 49010, Dnipropetrovsk, Ukraine

author

Arkadiy Yaroshenko

• Dnipropetrovsk National University, 72 Gagarin avenue, 49010, Dnipropetrovsk, Ukraine

References

• [1] R. P. Feynman, M. Kislinger, F. Ravndal, Phys. Rev. D 3, 2706 (1971) http://dx.doi.org/10.1103/PhysRevD.3.2706[Crossref]
• [2] A. N. Mitra, Phys. Rev. D 11, 3270 (1975) http://dx.doi.org/10.1103/PhysRevD.11.3270[Crossref]
• [3] H. Toki, J. Dey, M. Dey, Phys. Lett. B 133, 20 (1983) http://dx.doi.org/10.1016/0370-2693(83)90096-5[Crossref]
• [4] A. Bohm, M. E. Loewe, P. Magnollay, Phys. Rev. D 32, 791 (1985) http://dx.doi.org/10.1103/PhysRevD.32.791[Crossref]
• [5] S. Ishida, K. Yamada, Progr. Theor. Phys. 91, 775 (1994) http://dx.doi.org/10.1143/ptp/91.4.775[Crossref]
• [6] F. Buisseret, C. Semay, Phys. Rev. D 73, 114011 (2006) http://dx.doi.org/10.1103/PhysRevD.73.114011[Crossref]
• [7] R. Bijker, F. Iachello, A. Leviatan, Annals of Phys. 284, 89 (2000) http://dx.doi.org/10.1006/aphy.2000.6064[Crossref]
• [8] M. Kirchbach, M. Moshinsky, Yu. F. Smirnov, Phys. Rev. D 64, 114005 (2001) http://dx.doi.org/10.1103/PhysRevD.64.114005[Crossref]
• [9] M. Moshinsky, A. Szczepaniak, J. Phys. A 22, L817 (1989) http://dx.doi.org/10.1088/0305-4470/22/17/002[Crossref]
• [10] D. A. Kulikov, R. S. Tutik, A. P. Yaroshenko, Phys. Lett. B 644, 311 (2007) http://dx.doi.org/10.1016/j.physletb.2006.11.068[Crossref]
• [11] E. M. Lifshitz, L. P. Pitaevskii, V. I. Berestetskii, Quantum Electrodynamics (Pergamon, Oxford, 1982)
• [12] Ph. Droz-Vincent, Phys. Rev. A 73, 042101 (2006) http://dx.doi.org/10.1103/PhysRevA.73.042101[Crossref]
• [13] J. P. Elliott, P. G. Dawber, Symmetry in Physics, Vol. 2 (Oxford University Press, New York, 1986)
• [14] A. Selem, F. Wilczek, arXiv: hep-ph/0602128 (2006)
• [15] M. Anselmino, E. Predazzi, S. Ekelin, S. Fredriksson, D.B. Lichtenberg, Rev. Mod. Phys. 65, 1199 (1993) http://dx.doi.org/10.1103/RevModPhys.65.1199[Crossref]
• [16] A. V. Anisovich, V. V. Anisovich, M. A. Matveev, V. A. Nikonov, A. V. Sarantsev, T. O. Vulfs, Int. J. Mod. Phys. A 25, 2965 (2010) http://dx.doi.org/10.1142/S0217751X10049050[Crossref]
• [17] J. Beringer et al. (Particle Data Group), Phys. Rev. D 86, 010001 (2012) http://dx.doi.org/10.1103/PhysRevD.86.010001[Crossref]
• [18] N. Isgur, G. Karl, Phys. Rev. D 19, 2653 (1979) http://dx.doi.org/10.1103/PhysRevD.19.2653[Crossref]
• [19] M. Nuñez V. S. Lerma H. P. O. Hess, S. Jesgarz, O. Civitarese, M. Reboiro, Phys. Rev. C 70, 025201 (2004) http://dx.doi.org/10.1103/PhysRevC.70.025201[Crossref]
• [20] M. Kirchbach, C. B. Compean, Phys. Rev. D 82, 034008 (2010) http://dx.doi.org/10.1103/PhysRevD.82.034008[Crossref]
• [21] K. Nagata, A. Hosaka, J. Phys. G 32, 777 (2006) http://dx.doi.org/10.1088/0954-3899/32/6/003[Crossref]
• [22] R. L. Jaffe, D. Pirjol, A. Scardicchio, Phys. Rept. 435, 157 (2006) http://dx.doi.org/10.1016/j.physrep.2006.09.004[Crossref]
• [23] S. S. Afonin, Int. J. Mod. Phys. A 22, 4537 (2007) http://dx.doi.org/10.1142/S0217751X07037238[Crossref]
• [24] T. D. Cohen, L. Y. Glozman, Phys. Rev. D 65, 016006 (2002) http://dx.doi.org/10.1103/PhysRevD.65.016006[Crossref]
• [25] H. Forkel, E. Klempt, Phys. Lett. B 679, 77 (2009) http://dx.doi.org/10.1016/j.physletb.2009.07.008[Crossref]
• [26] E. Klempt, Chinese Phys. C 34, 1241 (2010) http://dx.doi.org/10.1088/1674-1137/34/9/017[Crossref]
• [27] S. Capstick, N. Isgur, Phys. Rev. D 34, 2809 (1986) http://dx.doi.org/10.1103/PhysRevD.34.2809[Crossref]
• [28] E. Santopinto, Phys. Rev. C 72, 022201 (2005) http://dx.doi.org/10.1103/PhysRevC.72.022201[Crossref]
• [29] U. Löring, B. Ch. Metsch, H. R. Petry, Eur. Phys. J. A 10, 447 (2001) http://dx.doi.org/10.1007/s100500170106[Crossref]
• [30] M. Karliner, M. P. Mattis, Phys. Rev. D 34, 1991 (1986) http://dx.doi.org/10.1103/PhysRevD.34.1991[Crossref]

Identifiers

DOI

10.2478/s11534-013-0303-4