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

Abstract

Poles and resonances are used to find ${\ensuremath{\chi}}^{2}$ fits to the data up to several hundred MeV above threshold for the processes ${\ensuremath{\pi}}^{\ensuremath{-}}+p\ensuremath{\rightarrow}n+\ensuremath{\eta}$ and $\ensuremath{\gamma}+p\ensuremath{\rightarrow}p+\ensuremath{\eta}$. Below center-of-mass energy $W=1700$ MeV, a consistent picture of these reactions is achieved with the following ingredients: a nucleon pole and ${P}_{11}(1400)$, ${S}_{11}(1570)$, and ${D}_{13}(1512)$ resonances for production by pions; a nucleon pole, a vector meson pole, and ${S}_{11}(1570)$ and ${D}_{13}(1512)$ resonances for photoproduction. Some ${F}_{15}(1688)$ also improves the fits. The value of the $\ensuremath{\eta}$-nucleon coupling constant, $\frac{{{g}_{\ensuremath{\eta}}}^{2}}{4\ensuremath{\pi}}$ is $\ensuremath{\lesssim}0.002$ in both processes. Implications of these results for quark models and $\mathrm{SU}(3)$ symmetry are discussed. Above $W=1700$, possible additional resonances are considered in $\ensuremath{\eta}$ production by pions.