About the magnitude of the ${\gamma }^{*}N\to N(1520)$ transverse amplitudes near $Q^2=0$

The ${\gamma }^{*}N\to N(1520)$ transition has a property that differs from the other low-lying nucleon resonance amplitudes: the magnitude of the transverse helicity amplitudes. The transition helicity amplitudes are defined in terms of square-transfer momentum $q^2$, or $Q^2=-q^2$. Near the photon point ($Q^2=0$) there is a significant difference in the magnitude of the transverse amplitudes: $A_{3/2}$ is very large and $A_{1/2}$ is very small. This atypical behavior contrasts with the relation between the amplitudes at the pseudothreshold [the limit where the nucleon and the $N(1520)$ are both at rest and $Q^2<0$], where $A_{3/2}=A_{1/2}/\sqrt{3}$, and also in the large-$Q^2$ region, where theory and data suggest that $A_{3/2}$ is suppressed relative to $A_{1/2}$. In the present work, we look for the source of the suppression of the $A_{1/2}$ amplitude at $Q^2=0$. The result is easy to understand in first approximation, when we look into the relation between the transverse amplitudes and the elementary form factors, defined by a gauge-invariant parametrization of the ${\gamma }^{*}N\to N(1520)$ transition current, near $Q^2=0$. There is a partial cancellation between contributions of two elementary form factors near $Q^2=0$. We conclude, however, that the correlation between the two elementary form factors at $Q^2=0$ is not sufficient to explain the transverse amplitude data below $Q^2=1{\mathrm{GeV}}^2$. The description of the dependence of the transverse amplitudes on $Q^2$ requires the determination of the scale of variation of the elementary form factors in the range $Q^2=0\dots 0.5{\mathrm{GeV}}^2$, a region with almost nonexistent data. We conclude at the end that the low-$Q^2$ data for the transverse amplitudes can be well described when we relate the scale of variation of the elementary form factors with the nucleon dipole form factor.

Figure 1

Transverse amplitudes $A_{1/2}$ and $A_{3/2}$ in terms of $Q^2$. The data are from JLab/CLAS single-pion production (solid bullets) [35], JLab/CLAS double-pion production (empty bullets) [20, 36], and PDG (square) [9]. The labels correspond to the parameters from Table 1.

Figure 2

Multipole form factors $G_E$ and $G_M$ in terms of $Q^2$. Data description as in Fig. 1. The labels correspond to the parameters from Table 1.