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

Abstract

The $\gamma^\ast N \to N(1520)$ 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 $\gamma^\ast N \to N(1520)$ 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 $Q^2 = 1$ 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 $Q^2=0$...0.5 GeV$^2$,a region with almost non existent 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.