Hard-pion current-algebra calculations of meson processes-N-point functions
Hard-pion techniques are presented for calculating T products of an arbitrary number of vector and axial-vector currents under the assumptions of single σ-.π-,ρ-, and A1 meson saturation of intermediate sums, chiral SU(2)×SU (2)-algebra commutation relations, conservation of vector current (CVC), and partial conservation of axial-vector current (PCAC). The single-meson dominance hypothesis is shown to imply that one calculates the T products keeping only certain generalized tree and seagull diagrams. Alternatively, the assumption can be replaced by requiring that one calculate with an `effective' interaction Lagrangian ℒI to lowest nonvanishing order. The conditions that the remaining hypotheses (current commutation relations, CVC, and PCAC) impose on ℒI are expressed in terms of functional differential equations to determine the form of ℒI. These equations are shown to be consistent with each other and may in fact be integrated order by order. The ℒI needed to calculate any four-point function is given explicitly
