Application of current-algebra techniques to soft-pion production by the weak neutral current:V,Acase

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 $v+n\to v+p+{\pi }^{-}$ would have implied a threshold cross section much larger than can be obtained with any neutral current formed solely from members of the usual $V$, $A$ nonets. We analyze recently reported Brookhaven National Laboratory results for neutral-current-induced soft-pion production under the simplifying assumption of a purely isoscalar $V$, $A$ 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 $\mathrm{}\left|g\right|=\left|\frac{2M_N{F}_2}{F_1}\right|$ or involves the ninth (${\mathrm{SU}}_3$ singlet) axial-vector current. A vector part with a large $\mathrm{}\left|g\right|\mathrm{}$ value leads to characteristic modifications in the pion-nucleon invariant-mass spectrum for $M\left(\pi N\right)\le 1.4$ GeV, an effect which should be testable in high-statistics experiments. Two other qualitative predictions of isoscalar $V$, $A$ structures are (i) except for a narrow range of values of $g$, constructive $V$, $A$ interference in $v+N\to v+N+\pi$ implies constructive interference in $v+p\to v+p$ and vice versa, and (ii) if $V$, $A$ interference is observed in neutral weak processes then (as is well-known) the neutral interaction may make a parity-violating contribution to the $\mathrm{pp}$, $\mathrm{ep}$, and $\mu p$ interactions. These features may help to distinguish $V$, $A$ neutral-current couplings from alternative coupling types, which will be discussed in detail in subsequent papers of this series.