Few-Body Systems

, 60:13 | Cite as

Constituent-Quark Model with Pionic Contributions: Electromagnetic \({\varvec{N\rightarrow \varDelta }}\) Transition

  • Ju-Hyun Jung
  • Wolfgang SchweigerEmail author
  • Elmar P. Biernat
Open Access
Part of the following topical collections:
  1. NSTAR 2017


We report on ongoing work to determine the pion-cloud contribution to the electromagnetic \(N\rightarrow \varDelta \) transition form factors. The starting point is an SU(6) spin-flavor symmetric constituent-quark model with instantaneous confinement that is augmented by dynamical pions which couple directly to the quarks. This system is treated in a relativistically invariant way within the framework of point-form quantum mechanics using a multichannel formulation. The first step is to determine the electromagnetic form factors of the bare particles that consist only of three quarks. These form factors are basic ingredients for calculating the pion-cloud contributions. Already without the pion cloud, electromagnetic nucleon and \(N\rightarrow \varDelta \) transition form factors compare reasonably well with the data. By inclusion of the pion-cloud contribution coming from the \(\pi -N\) intermediate state the reproduction of the data is further improved.



J.-H. Jung acknowledges the support of the Fonds zur Förderung der wissenschaftlichen Forschung in Österreich (Grant No. FWF DK W1203-N16). He furthermore wants to thank Prof. T. Peña for giving him the opportunity to stay at the Centro de Física Teórica de Partículas, IST Lisboa, where part of this work was done. E. P. Biernat acknowledges the support of the Fundação para a Ciência e a Tecnologia (FCT) under Grant No. SFRH/BPD/100578/2014.


  1. 1.
    I.G. Aznauryan et al., Electroexcitation of nucleon resonances from CLAS data on single pion electroproduction. Phys. Rev. C 80, 055203 (2009)ADSCrossRefGoogle Scholar
  2. 2.
    A. Blomberg et al., Electroexcitation of the \(\Delta ^{+}\)(1232) at low momentum transfer. Phys. Lett. B 760, 267 (2016)ADSCrossRefGoogle Scholar
  3. 3.
    G. Ramalho, M.T. Pena, F. Gross, D-state effects in the electromagnetic \(N\Delta \) transition. Phys. Rev. D 78, 114017 (2008)ADSCrossRefGoogle Scholar
  4. 4.
    G. Ramalho, M.T. Pena, Valence quark contribution for the \(\gamma N \rightarrow \Delta \) quadrupole transition extracted from lattice QCD. Phys. Rev. D 80, 013008 (2009)ADSCrossRefGoogle Scholar
  5. 5.
    C. Alexandrou et al., The N to \(\Delta \) electromagnetic transition form-factors from lattice QCD. Phys. Rev. Lett. 94, 021601 (2005)ADSCrossRefGoogle Scholar
  6. 6.
    T. Ledwig, A. Silva, M. Vanderhaeghen, Electromagnetic properties of the \(\Delta (1232)\) and decuplet baryons in the self-consistent SU(3) chiral quark-soliton model. Phys. Rev. D 79, 094025 (2009)ADSCrossRefGoogle Scholar
  7. 7.
    H. Sanchis-Alepuz, R. Alkofer, C.S. Fischer, Electromagnetic transition form factors of baryons in the space-like momentum region. Eur. Phys. J. A 54, 41 (2018)ADSCrossRefGoogle Scholar
  8. 8.
    V. Pascalutsa, M. Vanderhaeghen, S.-N. Yang, Electromagnetic excitation of the \(\Delta (1232)\)-resonance. Phys. Rep. 437, 125–232 (2007)ADSCrossRefGoogle Scholar
  9. 9.
    E.P. Biernat, W. Schweiger, K. Fuchsberger, W.H. Klink, Electromagnetic meson form factor from a relativistic coupled-channel approach. Phys. Rev. C 79, 055203 (2009)ADSCrossRefGoogle Scholar
  10. 10.
    M. Gomez-Rocha, W. Schweiger, Electroweak form factors of heavy-light mesons: a relativistic point-form approach. Phys. Rev. D 86, 053010 (2012)ADSCrossRefGoogle Scholar
  11. 11.
    E.P. Biernat, W. Schweiger, Electromagnetic rho-meson form factors in point-form relativistic quantum mechanics. Phys. Rev. C 89, 055205 (2014)ADSCrossRefGoogle Scholar
  12. 12.
    E.P. Biernat, W.H. Klink, W. Schweiger, Point-form Hamiltonian dynamics and applications. Few Body Syst. 49, 149 (2011)ADSCrossRefGoogle Scholar
  13. 13.
    B. Pasquini, S. Boffi, Electroweak structure of the nucleon, meson cloud and light-cone wavefunctions. Phys. Rev. D 76, 07401 (2007)Google Scholar
  14. 14.
    J.-H. Jung, W. Schweiger, On the microscopic structure of \(\pi NN\), \(\pi N\Delta \) and \(\pi \Delta \Delta \) vertices. Few Body Syst. 58, 73 (2017)ADSCrossRefGoogle Scholar
  15. 15.
    J. Carbonell, B. Desplanques, V.A. Karmanov, J.F. Mathiot, Explicitly covariant light front dynamics and relativistic few body systems. Phys. Rep. 300, 215 (1998)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    S.N. Sokolov, Relativistic addition of direct interactions in the point form of dynamics. Theor. Math. Phys. 36, 682 (1979)CrossRefGoogle Scholar
  17. 17.
    F. Cardarelli, E. Pace, G. Salme, S. Simula, Nucleon and pion electromagnetic form-factors in a light front constituent quark model. Phys. Lett. B 357, 267 (1995)ADSCrossRefGoogle Scholar
  18. 18.
    D. Kupelwieser, W. Schweiger, The pion-cloud contribution to the electromagnetic nucleon form factors. EPJ Web Conf. 113, 05006 (2016)CrossRefGoogle Scholar
  19. 19.
    H.F. Jones, M.D. Scadron, Multipole \(\gamma \text{- }N \Delta \) form-factors and resonant photoproduction and electroproduction. Ann. Phys. 81, 1 (1973)ADSCrossRefGoogle Scholar
  20. 20.
    L. Tiator, D. Drechsel, S. Kamalov, M.M. Giannini, E. Santopinto, A. Vassallo, Electroproduction of nucleon resonances. Eur. Phys. J. A 19, 55 (2004)ADSCrossRefGoogle Scholar
  21. 21.
    E. Santopinto, M.M. Giannini, Systematic study of longitudinal and transverse helicity amplitudes in the hypercentral constituent quark model. Phys. Rev. C 86, 065202 (2012)ADSCrossRefGoogle Scholar
  22. 22.
    I.G. Aznauryan et al., Studies of nucleon resonance structure in exclusive meson electroproduction. Int. J. Mod. Phys. E 22, 1330015 (2013)ADSCrossRefGoogle Scholar

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© The Author(s) 2018

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Authors and Affiliations

  1. 1.Institut für Physik, FB Theoretische PhysikUniversität GrazGrazAustria
  2. 2.CFTP, Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal

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