We apply current-algebra techniques to study the constraints imposed on neutral-current-induced soft-pion production, using as input existing bounds on neutrino-proton elastic scattering and existing data on neutral-current-induced deep-inelastic scattering. In the case of a purely isoscalar weak neutral current, a simple soft-pion argument relates the cross section for threshold (in pion-nucleon invariant mass) weak pion production directly to the cross section for neutrino-proton elastic scattering. Hence, a bound on the latter cross section implies a bound on the former. To apply the method away from threshold and to nonisoscalar neutral currents, we extend a model which we had developed earlier for weak pion production in the (3,3) resonance region so as to include the low-energy-theorem constraints. Numerical work using the extended model shows that a threshold peak (now attributed to background) in preliminary Argonne data on

v + n \to v + p + π^{-}

would have implied a threshold cross section much larger than can be obtained with any neutral current formed solely from members of the usual

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nonets. We analyze recently reported Brookhaven National Laboratory results for neutral-current-induced soft-pion production under the simplifying assumption of a purely isoscalar

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neutral current. We find in this case that the magnitude of the Brookhaven observations exceeds the theoretical maximum by more than a factor of 2 unless the assumed isoscalar current either contains a vector part with an anomalously large gyromagnetic ratio

| g | = | \frac{2 M_{N} F_{2}}{F_{1}} |

or involves the ninth (

{SU}_{3}

singlet) axial-vector current. A vector part with a large

| g |

value leads to characteristic modifications in the pion-nucleon invariant-mass spectrum for

M (π N) \leq 1.4

GeV, an effect which should be testable in high-statistics experiments. Two other qualitative predictions of isoscalar

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structures are (i) except for a narrow range of values of

g

, constructive

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interference in

v + N \to v + N + π

implies constructive interference in

v + p \to v + p

and vice versa, and (ii) if

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interference is observed in neutral weak processes then (as is well-known) the neutral interaction may make a parity-violating contribution to the

pp

ep

, and

μ p

interactions. These features may help to distinguish

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neutral-current couplings from alternative coupling types, which will be discussed in detail in subsequent papers of this series.

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