nucl-th digest · Feb 12, 2016

[Submitted on 11 Feb 2016] (cross-list from hep-ph)

Improved empirical parametrizations of the $γ^{} N \to Δ (1232)$ and $γ^{} N \to N (1520)$ helicity amplitudes and the Siegert's theorem

In the nucleon electroexcitation reactions, $γ^{*} N \to R$ , where $R$ is a nucleon resonance ( $N^{*}$ ), the electric amplitude $E$ , and the longitudinal amplitude $S_{1/2}$ , are related by $E \propto \frac{ω}{∣ q ∣} S_{1/2}$ , at the pseudo-threshold limit ( $∣ q ∣ \to 0$ ), where $ω$ and $∣ q ∣$ are respectively the energy and the magnitude of three-momentum of the photon. The previous relation is usually refereed as the Siegert's theorem. The form of the electric amplitude, defined in terms of the transverse amplitudes $A_{1/2}$ and $A_{3/2}$ , and the explicit coefficients of the relation, depend on the angular momentum and parity ( $J^{P}$ ) of the resonance $R$ . The Siegert's theorem is the consequence of the structure of the electromagnetic transition current, which induces constraints between the electromagnetic form factors in the pseudo-threshold limit. In the present work, we study the implications of the Siegert's theorem for the $γ^{*} N \to Δ (1232)$ and $γ^{*} N \to N (1520)$ transitions. For the $γ^{*} N \to N (1520)$ transition, in addition to the relation between electric amplitude and longitudinal amplitude, we obtain also a relation between the two transverse amplitudes: $A_{1/2} = A_{3/2} / 3$ , at the pseudo-threshold. % The constraints at the pseudo-threshold are tested for the MAID2007 parametrizations of the reactions under discussion. New parametrizations for the amplitudes $A_{1/2}$ , $A_{3/2}$ and $S_{1/2}$ , for the $γ^{*} N \to Δ (1232)$ and $γ^{*} N \to N (1520)$ transitions, valid for small and large $Q^{2}$ , are proposed. The new parametrizations are consistent with both: the pseudo-threshold constraints (Siegert's theorem) and the empirical data.

Comments:: Published in Phys. Rev. D. 21 pages, 13 figures, 5 tables
Subjects:: High Energy Physics — Phenomenology (hep-ph); High Energy Physics — Experiment (hep-ex); Nuclear Experiment (nucl-ex); Nuclear Theory (nucl-th)
arXiv:: 1602.03832 [pdf]

PRD(2016)·30 citations

Friday·February 12, 2016

Existence of the critical endpoint in the vector meson extended linear sigma model

Improved empirical parametrizations of the $γ^{} N \to Δ (1232)$ and $γ^{} N \to N (1520)$ helicity amplitudes and the Siegert's theorem

Affiliations

Existence of the critical endpoint in the vector meson extended linear sigma model

Improved empirical parametrizations of the γ∗N→Δ(1232) and γ∗N→N(1520) helicity amplitudes and the Siegert's theorem

Affiliations

Improved empirical parametrizations of the $γ^{} N \to Δ (1232)$ and $γ^{} N \to N (1520)$ helicity amplitudes and the Siegert's theorem