Application of current algebra to soft-pion production induced by the weak neutral current: Second-classV,Acase

We apply current-algebra techniques to study neutrino-proton elastic scattering and neutral-current-induced soft-pion production in the case of second-class vector and axial-vector currents. (Such currents are $\mathrm{CP}$-violating if the final and incident neutrinos are identical, but can be $\mathrm{CP}$-conserving if the final and incident neutrinos are different particles.) The second-class currents are constructed phenomenologically from meson fields and the usual first-class $V$, $A$ quark currents. The matrix elements of the second-class currents between one-nucleon states are estimated by inserting a complete set of intermediate states and saturating the sum with one-nucleon states. In this way the second-class matrix elements are expressed in terms of the experimentally measured renormalization constants of the first-class $V$, $A$ currents and the pion-nucleon coupling constant. Using standard soft-pion techniques, we analyze recently reported Brookhaven National Laboratory results for neutral-current-induced soft-pion production under the simplifying assumption of a purely isoscalar second-class $V$, $A$ neutral current. We find in this case that a second-class $V-A$ current is consistent with the reported results. Some qualitative features of second-class neutral currents are (i) equal cross sections for $\nu p$ and $\overline{\nu }p$ elastic scattering, with only the axial-vector current contributing, and (ii) very small $\nu p$ and $\overline{\nu }p$ elastic cross sections at energies of order 50 MeV, which are relevant for possible neutrino experiments of the Los Alamos Meson Physics Facility.