Effective Lagrangian Approach to the Theory of Eta Photoproduction in the $N^{*}(1535)$ Region

TL;DR

This paper uses an effective Lagrangian approach to analyze eta photoproduction near the $N^{*}(1535)$ resonance, fitting data to extract resonance properties and compare with pion photoproduction results.

Contribution

It introduces a comprehensive effective Lagrangian model including multiple resonances and background terms, providing new precise estimates of the $N^{*}(1535)$ resonance's photoexcitation and decay parameters.

Findings

Determined the $ ext{A}_{1/2}$ helicity amplitude for $N^{*}(1535) ightarrow ext{γ} p$ as approximately $97 imes 10^{-3} ext{GeV}^{-1/2}$.

Extracted the resonance decay parameter $ ext{√χΓ}_η ext{A}_{1/2}/ ext{Γ}_T$ as about $0.22 ext{GeV}^{-1}$.

Found significant differences in the amplitudes for $ ext{η}$ and $ ext{π}^0$ photoproduction near threshold.

Abstract

We investigate eta photoproduction in the $N^{*}(1535)$ resonance region within the effective Lagrangian approach (ELA), wherein leading contributions to the amplitude at the tree level are taken into account. These include the nucleon Born terms and the leading $t$-channel vector meson exchanges as the non-resonant pieces. In addition, we consider five resonance contributions in the $s$- and $u$- channel; besides the dominant $N^{*}(1535)$, these are: $N^{*}(1440),N^{*}(1520),N^{*}(1650)$ and $N^{*}(1710)$. The amplitudes for the $\pi^\circ$ and the $\eta$ photoproduction near threshold have significant differences, even as they share common contributions, such as those of the nucleon Born terms. Among these differences, the contribution to the $\eta$ photoproduction of the $s$-channel excitation of the $N^{*}(1535)$ is the most significant. We find the off-shell properties of the spin-3/2 resonances to be important in determining the background contributions. Fitting our effective amplitude to the available data base allows us to extract the quantity $\sqrt{\chi \Gamma_\eta} A_{1/2}/\Gamma_T$, characteristic of the photoexcitation of the $N^{*}(1535)$ resonance and its decay into the $\eta$-nucleon channel, of interest to precise tests of hadron models. At the photon point, we determine it to be $(2.2\pm 0.2)\times 10^{-1} GeV^{-1}$ from the old data base, and $(2.2\pm 0.1) \times 10^{-1} GeV^{-1}$ from a combination of old data base and new Bates data. We obtain the helicity amplitude for $N^{*}(1535)\rightarrow \gamma p$ to be $A_{1/2}=(97\pm 7)\times 10^{-3} GeV^{-1/2}$ from the old data base, and $A_{1/2}=(97\pm 6)\times 10^{-3} GeV^{-1/2}$ from the combination of the old data base and new Bates data, compared with the results of the analysis of pion photoproduction yielding $74\pm 11$, in the same units.