πNNform factor, chiral-symmetry breaking, and three-pion resonances

The extraction of the $\pi \mathrm{NN}$ form factor $F_{\pi \mathrm{NN}}\mathrm{}\left(t\right)\mathrm{}$ from Reggeized one-pion-exchange (OPE) fits to hadronic cross sections is reexamined. The objective is to explain the Goldberger-Treiman discrepancy ${\Delta }_{\pi }$ which is determined from the extrapolation of $F_{\pi \mathrm{NN}}$ to $t=0\mathrm{}$. Until now Reggeized OPE analyses have led to values of ${\Delta }_{\pi }$ that disagree with experiment by a factor of 2. It is argued that this failure is likely due to an insensitivity of the OPE amplitudes to heavy-pion (three-pion-resonance) contributions, at small $t$, when $F_{\pi \mathrm{NN}}$ is parametrized by standard forms, e.g., the monopole or the dual model. A new functional form is proposed for $F_{\pi \mathrm{NN}}\mathrm{}\left(t\right)\mathrm{}$ which has the virtue of enhancing these contributions at small momentum transfers, thus leading to OPE amplitudes more sensitive to $3\pi$-resonance effects. This form factor is then used to reanalyze differential cross sections for $\mathrm{pp}\to n{\Delta }^{++}$, $\mathrm{pp}\to p{\Delta }^{+}$, $\mathrm{np}\to \mathrm{pn}$, $\overline{p}p\to \overline{n}n$, and $\gamma p\to {\pi }^{+}n$, as well as asymmetries for $\gamma p\to {\pi }^{+}n$, at high energies ($E_L\simeq 5-25$ GeV) and $\mathrm{}\left|t\right|\mathrm{}\lesssim 0.3$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$. The results show that a self-consistent fit to all these data, with the correct value of ${\Delta }_{\pi }$, is indeed possible.