Application of current-algebra techniques to soft-pion production by the weak neutral current:S,P,Tcase

We develop the cross-section formulas needed to correlate information on neutral currents obtained from deep-inelastic neutrino scattering, neutrino-proton elastic scattering, and neutral-current-induced soft-pion production, in the case of neutral currents with $S$, $P$, $T$ spatial structure. (The necessary $S$, $P$, $T$ current renormalization constants were estimated by us in a previous paper.) The pion-emission amplitude is obtained by current-algebra soft-pion techniques, with the effects of (3,3)-resonance excitation taken into account to leading nonvanishing order in the static approximation. We analyze recently reported Brookhaven National Laboratory results for neutral-current-induced soft-pion production under the simplifying assumption of a purely isoscalar $S$, $P$, $T$ neutral current, while simultaneously imposing existing bounds on neutrino-proton elastic scattering and fitting existing data on neutral-current-induced deep-inelastic scattering. If all $S$, $P$, $T$ renormalization constants are given their central quark-model values, the elastic-scattering and deep-inelastic restrictions constrain the pion-production cross section to be too low compared with experiment; if apparently reasonable deviations of the parameters from the quark-model values are permitted, satisfactory fits to all data are obtained with $S$, $T$, with $P$, $T$ or with $S$, $P$, $T$ mixtures. An isovector tensor or pseudoscalar neutral current is found to lead to a strong (3,3) peak in $\pi N$ invariant-mass plots, but an isovector scalar neutral current can be present without producing a visible (3,3) peak, even when ratios of the various $\pi N$ charge states produced by the neutral current are appreciably changed from the values which they have in the isoscalar-current case. Two other interesting qualitative features of $\mathrm{CP}$-conserving $S$, $P$, $T$ structures are the following: (1) constructive $T$ interference with $S$ (or $S$ and $P$) in $\nu +N\to \nu +N+\pi$ can accompany destructive interference in $\nu +p\to \nu +p$, and vice versa, and (ii) observation of unequal neutrino- and antineutrino-induced neutral-current cross sections would not be accompanied by neutral-current-induced parity-violating effects in the $\mathrm{pp}$, $\mathrm{ep}$, and $\mu p$ interactions.