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Low--Energy Theorems for Weak Pion Production
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abstract
We derive novel low--energy theorems for single pion production off nucleons through the isovector axial current. We find that the $k^2$-dependence of the multipole $L_{0+}^{(+)}$ at threshold is given by the nucleon scalar form factor, namely $\sigma(k^2-M_\pi^2 ) /(3 \pi M_\pi F_\pi )$. The relation to PCAC results for soft pions including electroweak form factors is also clarified.
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Pion photoproduction off nucleons in covariant chiral perturbation theory
Including the Delta(1232) resonance in a third-order covariant chiral perturbation theory fit reproduces near-threshold pion photoproduction data across all charge channels far better than leaving it out.
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