CURRENT ALGEBRAS AND POLE DOMINANCE - A CONSISTENT TREATMENT OF ARHOPI SYSTEM

A new technique for obtaining consistent solutions to the current-algebra equations for vertex functions in the pole-dominance approximation is developed and applied to the Aπρ system. We consider matrix elements of the retarded commutator of two currents (or of one current and DAaaμAμ) taken between single-particle states (the π, A, and ρ mesons) and the vacuum. The absorptive parts of such amplitudes contain terms proportional to δ(q2-mπ2) and δ(Δ2-mρ2), for example; we demonstrate that erroneous results are obtained if unsubtracted dispersion relations (UDR) at either fixed q2 or Δ2 are assumed for these matrix elements. We therefore write UDR at fixed μaαq2+(1-α)Δ2, where α is an arbitrary number (unequal to zero or one). We are then able to derive consistent solutions to the current-algebra equations. Several sum rules involving the ρ→ππ and A→ρπ couplings are derived, as well as the first Weinberg sum rule. Our method, and the difficulties of earlier calculations based upon fixed-q2 UDR, are discussed in detail. A careful discussion of the relevant experimental quantities is given. These include the ρ and A widths, the pion form factor, and the structure-dependent radiative pion decay. There is good order-of-magnitude agreement between theory and experiment. © 1968 The American Physical Society.