Experimental test of the PCAC hypothesis in the reactionsv ? p? ?? p?+ and $$ \bar v_\mu p \to \mu ^ + p\pi ^ - $$ in the?(1232) region

Abstract

Data on the reactionsv μ p→ μ− pπ+ and\( \bar v_\mu p \to \mu ^ + p\pi ^ - \) in the Δ(1232) region are presented and a test of the PCAC hypothesis, using a modified version of the Adler model, is performed. The analysis is based on 1081 events in the neutrino and on 180 events in the antineutrino reaction, obtained in a bubble chamber experiment with BEBC at CERN. The experimental cross-sections for an invariant hadronic massW<1.4 GeV and an (anti-)neutrino energyE L v >10 GeV are determined to be (0.628±0.059)·10−38 cm2 for the neutrino and (0.168±0.023)·10−38 cm2 for the antineutrino reaction. TheQ 2 andW distributions, the density matrix elements of the Δ resonance, and moments of the pion angular distribution are discussed. The data are found to be in good agreement with the Adler model in theQ 2 region below 1 GeV2. A maximum likelihood fit for the axial massm A in the axial-vector form factor yields a value ofm A =1.31±0.12 GeV. At lowQ 2 the data confirm the PCAC hypothesis and the discrepancy, formerly observed between the experimental and theoretical cross-sections forv μ p→ μ− pπ+ at low momentum transfers (Q 2≲0.2 GeV2), is understood as being due to inadequate pion ‘off-mass-shell’ corrections.