A simple relation between the gamma N -> N(1535) helicity amplitudes

TL;DR

This paper derives a simple relation between helicity amplitudes in gamma N to N(1535) reactions at high Q^2, tests it with data, and discusses its implications for quark models.

Contribution

It introduces a new, simple relation between helicity amplitudes A_1/2 and S_1/2 at high Q^2, supported by experimental data and quark model interpretation.

Findings

The relation S_1/2 = - (sqrt(1+τ)/sqrt(2)) * ((M_S^2 - M^2)/(2 M_S Q)) * A_1/2 holds for Q^2 > 2 GeV^2.

Both amplitudes A_1/2 and S_1/2 share the same Q^2 dependence at high Q^2.

The assumption |A_1/2| >> |S_1/2| is invalid at high Q^2.

Abstract

It is shown that the helicity amplitudes A_1/2 and S_1/2 in the gamma N -> N(1535) reaction, can be well related by S_1/2 = -\frac{\sqrt{1+\tau}}{\sqrt{2}} \frac{M_S^2-M^2}{2 M_S Q} A_1/2 in the region Q^2 > 2 GeV^2, where M and M_S are the nucleon and N(1535) masses, q^2=-Q^2 the four-momentum transfer squared, and tau=\sfrac{Q^2}{(M_S+M)^2}. The observed relation is tested by the experimental data and the MAID parametrization. A direct consequence of the relation is that the assumption,|A_1/2| >> |S_1/2|, is not valid for high Q^2. Instead, both amplitudes A_1/2 and S_1/2 have the same Q^2 dependence in the high Q^2 region, aside from that S_{1/2} has an extra factor,-\sfrac{1}{\sqrt{2}}\sfrac{M_S-M}{2M_S}. The origin of this relation is interpreted in a perspective of a quark model.