Abstract
The spectroscopy of light and strange baryons and elastic electromagnetic form factors of nucleon have been studied through a simple semi-relativistic quark model. For SU(6)-invariant part of spectrum, we treated the baryons as a spin-independent three-body bound system and presented the exact analytical solution of three-body Klein–Gordon equation. Considering the SU(6)-invariant interaction as a combination of scalar linear and vector Coulombic-like potentials, we obtained analytical formulas for energy levels and the hyperradial wave functions which have been employed in the calculations of the mass spectrum of baryons, electromagnetic elastic form factors, and charge radii of nucleon. The evaluated observables have been compared with experimental data, and it has been shown that the present model leads to a fairly good description of the observed resonances.
Similar content being viewed by others
References
R. Bijker, F. Iachello, A. Leviatan, Algebraic Models of Hadron Structure. I. Nonstrange Baryons. Ann. Phys. (N.Y.) 236, 69–116 (1994)
M. Ferraris, M. MGiannini, M. Pizzo, E. Santopinto, L. Tiator, A three-body force model for the baryon spectrum. Phys. Lett. B 364, 231–238 (1995)
L. YaGlozman, D.O. Riska, The spectrum of the nucleons and the strange hyperons and chiral dynamics. Phys. Rep. C 268, 263–303 (1996)
S. Capstick, W. Roberts, Quark models of baryon masses and decays. Prog. Part. Nucl. Phys. 45, S241–S331 (2000)
N. Isgur and G. Karl, Phys. Rev. D18,4187 (1978)
S. Bali et al., Static potentials and glueball masses from QCD simulations with Wilson sea quarks. Phys. Rev. D 62, 054503 (2000)
Y. Sumino, QCD potential as a “Coulomb-plus-linear” potential. Phys. Lett. B 571, 173–183 (2003)
E. Santopinto and J. Ferretti, Phys. Rev. C 92025202(2015)
C. Gutierrez, M. De Sanctis, A study of a relativistic quark-diquark model for the nucleon. Eur. Phys. J. A 50, 169 (2014)
M. Aslanzadeh, I.J.M. AARajabi, Phys. E. 1550032, 24 (2015)
M. Aslanzadeh, C. AARajabi, J. Phys. 100301, 53 (2015)
M. Aslanzadeh, AARajabi. Can. J. Phys. 94, 236–242 (2016)
D. Merten, U. Löring, K. Kretzschmar, B. Metsch, H.R. Petry, Electroweak form factors of non-strange baryons. Eur. Phys. J. A 14, 477–489 (2002)
M. De Sanctis, J. Ferretti, E. Santopinto, A. Vassallo, Phys. Rev. C 055201, 84 (2011)
M. Aslanzadeh, A.A.R.E. Phys, J. A, 50 (2014)
M. Aslanzadeh, AARajabi,Few-Body. Syst. 57, 145 (2016)
J. Ballot, M. Fabre de la Ripelle, Application of the hyperspherical formalism to the trinucleon bound state problems. Ann. of Phys. (N.Y.) 127, 62–125 (1980)
Y.A. Simonov, Sov. J. Nucl. Phys. 3, 461 (1966)
C.D. Lin, Hyperspherical coordinate approach to atomic and other Coulombic three-body systems. Phys. Rep. 257(1), 1–83 (1995)
V. Aqulanti, S. Tonzano, J. Chem. Phys. 126, 4066 (2004)
M.M. Giannini, E. Santopinto, A. Vassallo, An overview of the hypercentral constituent quark model. Prog. Part. Nucl. Phys. 50, 263–272 (2003)
F. Zernike, H.C. Brinkman, Proc. Kon. Ned. Acad. Wet. 33, 3 (1935)
E. Santopinto, M.M. Giannini, F. Iachello, in Symmetries in Science VII, ed. by B. Gruber. (Plenum Press, New York, 1995), p. 445
J. Ballot, M. Fabre de la Ripelle, Application of the hyperspherical formalism to the trinucleon bound state problems. Ann. of Phys. (N.Y.) 127, 62–125 (1980)
M.M. Giannini, E. Santopinto, A. Vassallo, A new application of the Gürsey and Radicati mass formula. Eur. Phys. J. A 25, 241–247 (2005)
F. Güersey, L.A. Radicati, Spin and Unitary Spin Independence of Strong Interactions. Phys. Rev. Lett. 13, 173–175 (1964)
K.A, Olive et al. (particle data group collaboration),Chin. Phys. C 090001, 38 (2014)
F.J. Ernst, R.G. Sachs, K.C. Wali, Electromagnetic Form Factors of the Nucleon. Phys. Rev. 119, 1105–1114 (1960)
A.F. Sill, R.G. Arnold, P.E. Bosted, C.C. Chang, J. Gomez, A.T. Katramatou, C.J. Martoff, G.G. Petratos, A.A. Rahbar, S.E. Rock, Z.M. Szalata, D.J. Sherden, J.M. Lambert, R.M. Lombard-Nelsen, Measurements of elastic electron-proton scattering at large momentum transfer. Phys. Rev. D 48, 29–55 (1993)
C.F. Perdrisat, V. Punjabi, M. Vanderhaeghen, Nucleon electromagnetic form factors. Prog. Part. Nucl. Phys. 59, 694–764 (2007)
K. Hagiwara et al., Physical ReviewD 010001, 66 (2002)
J. Arrington, W Melnitchouk. J A Tjon,Phys. Rev.C 035205, 76 (2007)
R.C. Walker, B.W. Filippone, J. Jourdan, R. Milner, R. McKeown, D. Potterveld, L. Andivahis, R. Arnold, D. Benton, P. Bosted, G. deChambrier, A. Lung, S.E. Rock, Z.M. Szalata, A. Para, F. Dietrich, K. van Bibber, J. Button-Shafer, B. Debebe, R.S. Hicks, S. Dasu, P. de Barbaro, A. Bodek, H. Harada, M.W. Krasny, K. Lang, E.M. Riordan, R. Gearhart, L.W. Whitlow, J. Alster, Measurements of the proton elastic form factors for1≤Q2≤3(GeV/c)2at SLAC. Phys. Rev.D 49, 5671–5689 (1994)
H. Anklinet, al. Physics LettersB 428, 248 (1998)
a. W Bartelet, Measurement of proton and neutron electromagnetic form factors at squared four-momentum transfers up to 3 (GeV/c)2. Nucl. Phys.B 58, 429–475 (1973)
A. Lung, L.M. Stuart, P.E. Bosted, L. Andivahis, J. Alster, R.G. Arnold, C.C. Chang, F.S. Dietrich, W.R. Dodge, R. Gearhart, J. Gomez, K.A. Griffioen, R.S. Hicks, C.E. Hyde-Wright, C. Keppel, S.E. Kuhn, J. Lichtenstadt, R.A. Miskimen, G.A. Peterson, G.G. Petratos, S.E. Rock, S.H. Rokni, W.K. Sakumoto, M. Spengos, K. Swartz, Z. Szalata, L.H. Tao, Measurements of the electric and magnetic form factors of the neutron fromQ2=1.75 to 4.00 (GeV/c)2. Phys. Rev. Lett. 70, 718–721 (1993)
a. G Kubonet, P. Lett, B 524, 26 (2002)
K. Melnikov, T. vanRitbergen, Three-loop slope of the Dirac form factor and the1SLamb shift in hydrogen. Phys. Rev. Lett. 84, 1673–1676 (2000)
S. Kopeckyet, New measurement of the charge radius of the neutron. al., Phys. Rev. Lett. 74, 2427–2430 (1995)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sattari, F., Aslanzadeh, M. Structure of Baryons in a Semi-Relativistic Quark Model. Braz J Phys 49, 402–411 (2019). https://doi.org/10.1007/s13538-019-00649-6
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13538-019-00649-6