Poles and Resonances in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>η</mml:mi></mml:math>Photoproduction

Abstract

Various combinations of poles and resonances have been tried to determine just which combinations yield reasonable fits to the total and differential cross-section data for the process $\ensuremath{\gamma}+p\ensuremath{\rightarrow}\ensuremath{\eta}+p$. In each case the best values of the parameters have been obtained by minimizing ${\ensuremath{\chi}}^{2}$. Excellent fits ($\frac{{\ensuremath{\chi}}^{2}}{N}\ensuremath{\approx}0.8$) are obtained for certain combinations of poles and resonances. All solutions with the ${S}_{11}(1570)$ resonance omitted have rather poor values of ${\ensuremath{\chi}}^{2}$, and the ${P}_{11}(1400)$ resonance cannot be used in lieu of the ${S}_{11}(1570)$ in this process. Evidence is obtained for classifying the ${F}_{15}(1688)$ as a member of an octet rather than a 27-plet. For all the models considered here, the value of the $\ensuremath{\eta}$-nucleon coupling constant ($\frac{{{g}_{\ensuremath{\eta}}}^{2}}{4\ensuremath{\pi}}$) is less than 2, indicating a $\frac{D}{F}$ ratio larger than $\frac{3}{2}$.