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

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 Schrodinger 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.