GAUGE-SYMMETRICAL APPROACH TO EFFECTIVE LAGRANGIANS - THE ETA'-MESON FROM QCD

We present a general scheme for extracting effective degrees of freedo m from an underlying fundamental lagrangian, through a series of well- defined transformations in the functional integral of the cut-off theo ry. This is done by introducing collective fields in a gauge-symmetric manner. Through appropriate gauge fixings of this symmetry one can re move long-distance degrees of freedom from the underlying theory, repl acing them by the collective fields. Applying this technique to QCD, w e set out to extract the long-distance dynamics in the pseudoscalar fl avour singlet sector through a gauging (and subsequent gauge fixing) o f the U(1)A flavour symmetry which is broken by the anomaly. By this s eries of exact transformations of a cut-off generating functional for QCD, we arrive at a theory describing the long-distance physics of a p seudoscalar flavour singlet meson coupled to the residual quark-gluon degrees of freedom. As an example we show how to derive a Witten-Venez iano-like relation between the eta' mass and the topological susceptib ility. The resulting effective lagrangian contains an axial vector fie ld, which shares the relevant features with the Veneziano ghost. This field is responsible for removing the eta' degree of freedom from the fundamental QCD lagrangian.