Electromagnetic transitions of the Roper resonance \(\gamma^{\ast} p \rightarrow p_{11}(1440)\) within the nonrelativistic quark model

Regular Article

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.

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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Faculty of PhysicsShahrood University of TechnologyShahroodIran
  2. 2.Shams Institute of Higher EducationGolestan ProvinceGonbadIran

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