Two topics in elementary particle physics: 1) The reaction γ + N → π + N [photon + nucleon going to pion + nucleon] at high energies. 2) K leptonic decay and partially conserved currents

Abstract

1. γ + N → π + N The process γ + N → π + N is studied at high energies in both the forward and backward directions. The helicity formalism is used. Contributions from the ρ, ω, φ and π trajectories in the t channel and from the N*3+/2, N1+/2, and N*1-/2 trajectories in s‾ channel are included. Polarization formulae for the final state nucleon are given. If we may neglect cuts in the angular momentum plane, then at high energies for momentum transfers -t >> μ2π the ρ trajectory should dominate charged pion photoproduction in the forward direction. A curde estimate of the cross section yields dσ/dt ~ s2jρ(0)-2 ≈ 1/s. However, the pion trajectory is expected to be important for small momentum transfers up to very high energies. For forward neutral pion photoproduction both the ρ and ω trajectories should be important. The cross section is estimated to be dσ/dt ~ 1/s. For photoproduction in the backward direction, the situation is much more complex with at least three trajectories contributing to dσ/ds‾. However, since the same set of trajectories are to be used in πN scattering, backward πN scattering and backward photoproduction are expected to have the same energy dependence. Assuming that the N*3+/2 trajectory dominates with jN*3+/2(0) ≈ 0, we obtain dσ/ds‾ ~ s2jN*3+/2(0)-2 ≈ 1/s2. 2. K Leptonic Decay and Partially Conserved Currents An operational definition for the partial conservation of the strangeness changing vector current is given and applied to leptonic K+ and K°2 decay. The K* resonance is explicitly included in the calculation and quantitative agreement with experiment is obtained. A detailed comparison with the K+ data of Brown et. al. and Dobbs et al. is given. Because of rapid variations of a form factor, it is found that the data of these two groups are not in contradiction. From the K°2 experiment of Luers et. al., I = 1/2 and 3/2 currents are seen to exist. Λβ-decay is briefly considered. It is found that an explanation for the slowness of K leptonic decay and the vector part of Λβ-decay may be connected with the partial conservation of the strangeness changing vector current.