Abstract
We use the effective chiral-symmetry Lagrangian to compute the amplitude for $\ensuremath{\nu}(\overline{\ensuremath{\nu}})+N\ensuremath{\rightarrow}\ensuremath{\nu}(\overline{\ensuremath{\nu}})+N+\ensuremath{\pi}+\ensuremath{\pi}$ and the integral of the differential cross sections for these processes over the kinematic region for which the Lagrangian tree approximation should be dominant. We estimate the effects of final-state interactions by comparing experimental $\ensuremath{\pi}N\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}N$ results with effective-Lagrangian predictions. Sensitivities to the neutral-current parameters $\ensuremath{\alpha}$, $\ensuremath{\beta}$, and $\ensuremath{\gamma}$ and to the chiral-symmetry-breaking parameter $\ensuremath{\xi}$ are considered.
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