Current Algebra and the Pion Mass in a Gauge Model

Abstract

Current-algebraic techniques are used to reproduce and extend the results of a gauge model for the pion mass and the ${\rho }^{\prime }$ vector boson. A formula is obtained, giving ${m_{\pi }}^2$ as an integral over spectral functions of certain SU(2) × SU(2) currents, and valid to second order in the ${\rho }^{\prime }$ coupling constant and all orders in the strong coupling. The general mechanism for generating the pion mass seems to be extendable to a wide class of models.