Effective Lagrangian approach to the theory of η photoproduction in theN*(1535) region

Abstract

We investigate η photoproduction in the ${\mathit{N}}^{\mathrm{*}}$(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 nonresonant pieces. In addition, we consider five resonance contributions in the s and u channels; in addition to the dominant ${\mathit{N}}^{\mathrm{*}}$(1535), these are ${\mathit{N}}^{\mathrm{*}}$(1440), ${\mathit{N}}^{\mathrm{*}}$(1520), ${\mathit{N}}^{\mathrm{*}}$(1650), and ${\mathit{N}}^{\mathrm{*}}$(1710). The amplitudes for the ${\mathrm{\pi }}^0$ and the η 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 η photoproduction of the s-channel excitation of the ${\mathit{N}}^{\mathrm{*}}$(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 √χ${\mathrm{\Gamma }}_{\mathrm{\eta }}$ ${\mathit{A}}_{1/2}$/${\mathrm{\Gamma }}_{\mathit{T}}$, characteristic of the photoexcitation of the ${\mathit{N}}^{\mathrm{*}}$(1535) resonance and its decay into the η-nucleon channel, of interest to precise tests of hadron models.