Transition form factors and helicity amplitudes for electroexcitation of negative and positive parity nucleon resonances in a light-front quark model

A workable basis of quark configurations $s^3$, $s^{2}p$ and $s{p}^2$ at light front has been constructed to describe the high-$Q^2$ behavior of transition form factors and helicity amplitudes in the electroproduction of the lightest nucleon resonances, $N_{1/2^{-}}(1535)$ and $N_{1/2^{+}}(1440)$. High-quality data of the CLAS Collaboration are described in the framework of a model which takes into account mixing of the quark configurations and the hadron-molecular states. The model allows for a rough estimate of the quark core weight in the wave function of the resonance in a comparison with high momentum transfer data on resonance electroproduction.

Figure 1

Helicity amplitudes and form factors of the ${\gamma }^{*}N\to N^{*}(1535)$ transition. CLAS data: circles (bold) [2], squares (bold) [5], triangle (bold) [6], circles (empty) [7], triangles (empty) [8], squares (empty) [9], diamonds [10]. Theoretical description in terms of a light front (LF) quark model: dashed curves—results of calculations on the basis of three-quark configurations, $s^{2}p$ for the $N^{*}$ and $s^3$ for $N$, using a polelike quark core wave function ${\mathrm{\Phi }}_0$ (denoted by LFQM(P) in the legends); solid curves—results for the model of Eq. (50) with the “strong” value of mixing parameter $\cos \theta =0.951$ ($\theta =0.1\pi$); dotted curves—results of the soft-wall AdS/QCD model [35].

Figure 2

Helicity amplitudes and form factors of the ${\gamma }^{*}N\to N^{*}(1440)$ transition. Theoretical description in terms of a light front quark model (LFQM): dashed curves—results on the basis of three-quark configurations, $s{p}^2$ for the $N^{*}(1440)$ and $s^3$ for $N(940)$, using a polelike quark core wave function ${\mathrm{\Phi }}_0$; short dashed curves—results of calculations using a superposition given in Eq. (28) of polelike function (P) and Gaussian (G) in the quark core wave function ${\mathrm{\Phi }}_0^R$ with $\alpha =0.245$ (denoted by $\mathrm{LFQM}(\mathrm{P}+\mathrm{G})$ in the legends); solid curves—results for the mixed-state model given in Eq. (50) with a “strong” value of the mixing angle, $\cos {\theta }_R=0.930$ (${\theta }_R=-0.12\pi$) (denoted by $\mathrm{LFQM}(\mathrm{P}+\mathrm{G})+N\sigma$ in the legends); dotted curves—results obtained in the soft-wall AdS/QCD approach [33]; dashed-dotted curves—results for the nonrelativistic quark model (NRQM) with contributions of virtual $\overline{q}q$ pairs in terms of the ${}^3{P}_0$ model [51]. The CLAS data (bold and empty circles) on one-pion [2, 17] and two-pion [3] electroproduction off the proton. The A1 data on ${\pi }^0$ (the empty square) electroproduction [11].