Abstract
We give a brief account of the Dyson–Schwinger and Faddeev-equation approach and its application to nucleon resonances and their transition form factors. We compare the three-body with the quark–diquark approach and present a quark–diquark calculation for the low-lying nucleon resonances including scalar, axialvector, pseudoscalar and vector diquarks. We also discuss the timelike structure of transition form factors and highlight the advantages of form factors over helicity amplitudes.
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Klempt, E., Richard, J.-M.: Baryon spectroscopy. Rev. Mod. Phys. 82, 1095 (2010)
Tiator, L., et al.: Electromagnetic excitation of nucleon resonances. Eur. Phys. J. Spec. Topics 198, 141 (2011)
Aznauryan, I.G., et al.: Studies of nucleon resonance structure in exclusive meson electroproduction. Int. J. Mod. Phys. E22, 1330015 (2013)
Aznauryan, I., Burkert, V.: Electroexcitation of nucleon resonances. Prog. Part. Nucl. Phys. 67, 1 (2012)
Roberts, C.D., Williams, A.G.: Dyson-Schwinger equations and their application to hadronic physics. Prog. Part. Nucl. Phys. 33, 477 (1994)
Alkofer, R., von Smekal, L.: The Infrared behavior of QCD Green’s functions. Phys. Rep. 353, 281 (2001)
Fischer, C.S.: Infrared properties of QCD from Dyson–Schwinger equations. J. Phys. G32, R253 (2006)
Eichmann, G., Alkofer, R., Krassnigg, A., Nicmorus, D.: Nucleon mass from a covariant three-quark Faddeev equation. Phys. Rev. Lett. 104, 201601 (2010)
Sanchis-Alepuz, H., et al.: Delta and Omega masses in a three-quark covariant Faddeev approach. Phys. Rev. D84, 096003 (2011)
Eichmann, G.: Nucleon electromagnetic form factors from the covariant Faddeev equation. Phys. Rev. D84, 014014 (2011)
Sanchis-Alepuz, H., Williams, R.: Hadronic observables from Dyson–Schwinger and Bethe–Salpeter equations. J. Phys. Conf. Ser. 631(1), 012064 (2015)
Maris, P., Roberts, C.D., Tandy, P.C.: Pion mass and decay constant. Phys. Lett. B420, 267 (1998)
Maris, P., Tandy, P.C.: The Quark photon vertex and the pion charge radius. Phys. Rev. C61, 045202 (2000)
Maris, P., Tandy, P.C.: Bethe–Salpeter study of vector meson masses and decay constants. Phys. Rev. C60, 055214 (1999)
Sanchis-Alepuz, H., Fischer, C.S.: Octet and Decuplet masses: a covariant three-body Faddeev calculation. Phys. Rev. D90(9), 096001 (2014)
Alkofer, R., et al.: Electromagnetic baryon form factors in the Poincaré-covariant Faddeev approach. Hyperfine Interact. 234(1), 149 (2015)
Sanchis-Alepuz, H., Fischer, C.S.: Hyperon elastic electromagnetic form factors in the space-like momentum region. arXiv:1512.00833 [hep-ph]
Oettel, M., Pichowsky, M., von Smekal, L.: Current conservation in the covariant quark diquark model of the nucleon. Eur. Phys. J. A8, 251 (2000)
Maris, P.: Effective masses of diquarks. Few Body Syst. 32, 41 (2002)
Bender, A., Roberts, C.D., Von Smekal, L.: Goldstone theorem and diquark confinement beyond rainbow ladder approximation. Phys. Lett. B380, 7 (1996)
De Sanctis, M., Ferretti, J., Santopinto, E., Vassallo, A.: Electromagnetic form factors in the relativistic interacting quark-diquark model of baryons. Phys. Rev. C84, 055201 (2011)
Santopinto, E., Ferretti, J.: Strange and nonstrange baryon spectra in the relativistic interacting quark-diquark model with a Gürsey and Radicati-inspired exchange interaction. Phys. Rev. C92(2), 025202 (2015)
Eichmann, G., Fischer, C.S., Heupel, W.: The light scalar mesons as tetraquarks. Phys. Lett. B753, 282 (2016)
Roberts, H.L., et al.: Masses of ground and excited-state hadrons. Few Body Syst. 51, 1 (2011)
Chen, C., et al.: Spectrum of hadrons with strangeness. Few Body Syst. 53, 293 (2012)
Oettel, M., Hellstern, G., Alkofer, R., Reinhardt, H.: Octet and decuplet baryons in a covariant and confining diquark-quark model. Phys. Rev. C58, 2459 (1998)
Cloet, I.C., Eichmann, G., El-Bennich, B., Klahn, T., Roberts, C.D.: Survey of nucleon electromagnetic form factors. Few Body Syst. 46, 1 (2009)
Segovia, J., et al.: Completing the picture of the Roper resonance. Phys. Rev. Lett. 115(17), 171801 (2015)
Eichmann, G.: Hadron Properties from QCD Bound-State Equations. Ph.D. thesis, University of Graz (2009), arXiv:0909.0703 [hep-ph]
Eichmann, G., Cloet, I.C., Alkofer, R., Krassnigg, A., Roberts, C.D.: Toward unifying the description of meson and baryon properties. Phys. Rev. C79, 012202 (2009)
Eichmann, G., Nicmorus, D.: Nucleon to Delta electromagnetic transition in the Dyson–Schwinger approach. Phys. Rev. D85, 093004 (2012)
Nicmorus, D., Eichmann, G., Alkofer, R.: Delta and Omega electromagnetic form factors in a Dyson–Schwinger/Bethe–Salpeter approach. Phys. Rev. D82, 114017 (2010)
Mader, V., et al.: Hadronic decays of mesons and baryons in the Dyson–Schwinger approach. Phys. Rev. D84, 034012 (2011)
Krassnigg, A.: Survey of \(J=0,1\) mesons in a Bethe–Salpeter approach. Phys. Rev. D80, 114010 (2009)
Chang, L., Roberts, C.D.: Sketching the Bethe–Salpeter kernel. Phys. Rev. Lett. 103, 081601 (2009)
Williams, R., Fischer, C.S., Heupel, W.: Light mesons in QCD and unquenching effects from the 3PI effective action. arXiv:1512.00455 [hep-ph]
Olive, K.A., et al.: Review of particle physics. Chin. Phys. C38, 090001 (2014)
Eichmann, G., Ramalho, G.: (In preparation)
Ramalho, G., Tsushima, K.: A simple relation between the \(\gamma N\rightarrow N(1535)\) helicity amplitudes. Phys. Rev. D84, 051301 (2011)
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This article belongs to the special issue “Nucleon Resonances”.
This work is supported by the German Science Foundation DFG under project number DFG TR-16.
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Eichmann, G. Progress in the Calculation of Nucleon Transition form Factors. Few-Body Syst 57, 965–973 (2016). https://doi.org/10.1007/s00601-016-1134-9
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DOI: https://doi.org/10.1007/s00601-016-1134-9