Abstract.
The Roper resonance, or (\( \gamma^{\ast}p \rightarrow p_{11} (1440)\)), is the lowest excited state of the nucleon. We study the scalar and transverse helicity amplitudes for the electroexcitation of the Roper resonance and obtain the \( Q^{2}\) dependence of the helicity amplitudes of the Roper resonance. The helicity amplitudes depend strongly on the quark wave function. In this paper, we consider the baryon as a simple, nonrelativistic three-body quark model and we also consider a hypercentral potential scheme for the internal baryon structure which makes three-body forces among three quarks. The hypercentral potential depends only on the hyperradius which itself is a function of Jacobi relative coordinates that are functions of particle positions (\( r_{1}\), \( r_{2}\), and \( r_{3}\)). For this purpose, the Cornell potential is regarded as a combination of the Coulombic-like term plus a linear confining term in our work. In solving the Schrödinger equation with the Cornell potential, the Nikiforov-Uvarov (NU) method is employed, and the analytic eigenenergies and eigenfunctions are obtained. By using the obtained eigenfunctions, the transition amplitudes are calculated. Presenting our results in the range \( 0\le Q^{2} (GeV^{2}) \le 5\) in comparison with the predictions obtained in other non-relativistic quark models, our results lead to an overall better agreement with the experimental data, especially in the medium \( Q^{2}\) range.
Similar content being viewed by others
References
V.D. Burkert, T.S.H. Lee, Int. J. Mod. Phys. E 13, 108 (2004)
L. Zhenping, D. Yubing, M. Weihsing, J. Phys. G 23, 151 (1997)
I.G. Aznauryan, V.D. Burkert, JLAB-PHY-11-1409
I.G. Aznauryan et al., Phys. Rev. C 78, 045209 (2008)
T. Kubota, K. Ohta, Phys. Lett. B 65, 374 (1976)
S. Capstick, Phys. Rev. D 46, 46 (1992)
S. Capstick, B.D. Keister, Phys. Rev. D 51, 3598 (1995)
E. Santopinto, M.M. Giannini, Phys. Rev. C 86, 065202 (2012) and references quoted therein
F. Cardarelli, E. Pace, G. Salm, S. Simula, Phys. Lett. B 397, 13 (1997) and references quoted therein
Z.P. Li, Phys. Rev. D 44, 2841 (1991)
F.E. Close, An Introduction to Quarks and Partons (Academic Press, New York, 1978)
Z.P. Li, V. Burkert, Zh. Li, Phys. Rev. D 46, 70 (1992)
S. Capstick, G. Karl, Phys. Rev. D 41, 2768 (1990)
J.J. Kelly et al., Phys. Rev. C 75, 025201 (2007)
M. Aiello, M. Ferraris, M.M. Giannini, M. Pizzo, E. Santopinto, Phys. Lett. B 387, 215 (1996)
I.G. Aznauryan, Phys. Rev. C 75, 025201 (2007) and references quoted therein
S.J. Brodsky, S.D. Drell, Phys. Rev. D 22, 2236 (1980)
S. Simula, Proceedings of the Workshop on the Physics of Excited Nucleons, NSTAR 2001, Mainz (Germany), March 7-10 (World Scientific, Singapore, 2001) p. 135
B. Julía-Díaz, D.O. Riska, F. Coester, Phys. Rev. C 69, 035212 (2004)
R. Bijker, F. Iachello, A. Leviatan, Ann. Phys. 236, 69 (1994)
S. Capstick, W. Roberts, Prog. Part. Nucl. Phys. 45, S241 (2000)
P. Stoler, Phys. Rep. 226, 103 (1993)
M.M. Giannini, E. Santopinto, A. Vassallo, Eur. Phys. J. A 25, 241 (2005)
M. Aiello, M.M. Giannini, E. Santopinto, J. Phys. G: Nucl. Part. Phys. 24, 753 (1998)
L.A. Copley, G. Karl, E. Obryk, Nucl. Phys. B 13, 303 (1969)
R.P. Feynman, M. Kislinger, F. Ravndal, Phys. Rev. D 3, 2706 (1971)
F.E. Close, Z. Li, Phys. Rev. D 42, 9 (1990)
Z. Dziembowski, M. Fabre de la Ripelle, G.A. Miller, Phys. Rev. C 53, R2038 (1996)
The CLAS Collaboration (I.G. Aznauryan, V.D. Burkert), Phys. Rev. C 80, 055203 (2009)
M.M. Giannini, Rep. Prog. Phys. 54, 453 (1991)
G.S. Bali et al., Phys. Rev. D 62, 054503 (2000)
G.S. Bali, Phys. Rep. 343, 1 (2001)
C. Alexandrou, P. de Forcrand, O. Jahn, Nucl. Phys. Proc. Suppl. 119, 667 (2003)
M. Fabre de la Ripelle, Proceedings of the International School on Nuclear Theoretical Physics (Predeal 1969), edited by A. Corciovei, (Inst. Atom. Phys., Bucarest, 1969) Rev. Roum. Phys. 14, 1215 (1969)
M. Fabre de la Ripelle, Few-Body Syst. 14, 1 (1993)
G. Morpurgo, Nuovo Cimento C 9, 461 (1952)
Yu.A. Simonov, Sov. J. Nucl. Phys. 3, 461 (1966)
J. Ballot, M. Fabre de la Ripelle, Ann. Phys. (N.Y.) 127, 62 (1980)
M. Fabre de la Ripelle, J. Navarro, Ann. Phys. (N.Y.) 123, 185 (1979)
A.M. Badalyan, Phys. Lett. B 199, 267 (1987)
E. Santopinto, F. Iachello, M.M. Giannini, Eur. Phys. J. A 1, 307 (1998)
M.M. Giannini, E. Santopinto, A. Vassallo, Nucl. Phys. A 699, 308 (2002)
A.A. Rajabi, Indian J. Pure Appl. Phys. 41, 89 (2003)
D. Griffits, Introduction to Elementary Particles (John Wiley&Sons, New York, 1987)
L.Ya. Glozman, D.O. Riska, Phys. Rep. C 268, 263 (1996)
A.F. Nikiforov, V.B. Uvarov, Special Functions of Mathematical Physics (Birkhauser, Bassel, 1988)
S.M. Ikhdair, Int. J. Mod. Phys. C 20, 1563 (2009)
C. Berkdemir, A. Berkdemir, R. Sever, Phys. Rev. C 74, 039902(E) (2006)
S.M. Ikhdair, R. Sever, Int. J. Theor. Phys. 46, 1643 (2007)
Particle Data Group (C. Amsler et al.), Phys. Lett. B 667, 1 (2008)
K.S. Krane, Introduction to Nuclear Physics (John Wiley&Sons, New York, 1995)
F. Halzen, A.D. Martin, Quarks and Leptons (John Wiley & Sons, New York, 1984)
F. Gürsey, L.A. Radicati, Phys. Rev. Lett. 13, 173 (1964)
R.M. Barnett et al., Phys. Rev. D 54, 174 (1996)
N. Salehi, A.A. Rajabi, Mod. Phys. Lett. A 24, 2631 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Parsaei, S., Akbar Rajabi, A. Electromagnetic transitions of the Roper resonance \(\gamma^{\ast} p \rightarrow p_{11}(1440)\) within the nonrelativistic quark model. Eur. Phys. J. Plus 132, 413 (2017). https://doi.org/10.1140/epjp/i2017-11676-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2017-11676-4