Semirelativistic approximation to the ${\gamma }^{*}N\to N(1520)$ and ${\gamma }^{*}N\to N(1535)$ transition form factors

The representation of the wave functions of the nucleon resonances within a relativistic framework is a complex task. In a nonrelativistic framework the orthogonality between states can be imposed naturally. In a relativistic generalization, however, the derivation of the orthogonality condition between states can be problematic, particularly when the states have different masses. In this work we study the $N(1520)$ and $N(1535)$ states using a relativistic framework. We considered wave functions derived in previous works, but impose the orthogonality between the nucleon and resonance states using the properties of the nucleon, ignoring the difference of masses between the states (semirelativistic approximation). The $N(1520)$ and $N(1535)$ wave functions are then defined without any adjustable parameters and are used to make predictions for the valence quark contributions to the transition form factors. The predictions compare well with the data particularly for high momentum transfer, where the dominance of the quark degrees of freedom is expected.

Figure 1

Results of the ${\gamma }^{*}N\to N(1520)$ helicity amplitudes given by the semirelativistic approximation (thick solid line). The semirelativistic approximation includes only the effect of the valence quark core. Data are from PDG [11] (full squares) and CLAS [12, 13, 14] (full circles). The thin solid line represents the fit to the MAID data [16]. The extreme limit is represented by the dashed line.

Figure 2

Results of the ${\gamma }^{*}N\to N(1520)$ form factors given by the semirelativistic approximation (thick solid line). The semirelativistic approximation includes only the effect of the valence quark core. Data are from PDG [11] (full squares) and CLAS [12, 13, 14] (full circles). The thin solid line represents the fit to the MAID data [16]. The extreme limit is represented by the dashed line.

Figure 3

Results for the ${\gamma }^{*}N\to N(1535)$ transition form factors given by the semirelativistic approximation (thick solid line). The semirelativistic approximation includes only the effect of the valence quark core. Data are from CLAS [12] (full circles), MAID [15, 16] (full squares), and JLab/Hall C [17] (triangles). Out of the range is the PDG result $F_2^{*}(0)=0.83\pm 0.28$ [11].

Figure 4

Results for the ${\gamma }^{*}N\to N(1535)$ helicity amplitudes given by the model A (thick dashed line). Model A is based in the valence quark effects (see the description in the main text). The thin dashed line is the result of Eq. (5.4). Data are from PDG (empty square) [11], CLAS [12] (full circles), MAID [15, 16] (full squares), and JLab/Hall C [17] (triangles).

Figure 5

Results for the ${\gamma }^{*}N\to N(1535)$ helicity amplitudes given by the model B (thick solid line). Model B is valid for large $Q^2$ (see the description in the main text). The thin solid line is the result of Eq. (5.4). The dots represent the functions for $Q^2<1.5{\mathrm{GeV}}^2$. Data are from PDG (empty squares) [11], CLAS [12] (full circles), MAID [15, 16] (full squares), and Jlab/Hall C [17] (triangles).