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.

arXiv commentPublished at Phys. Rev. D. 11 pages, 2 figures, 1 table. Minor extension

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