Anomaly Mediated Gaugino Mass and Path-Integral Measure

In recent years, there have been controversy concerning the anomaly mediated gaugino mass in the superspace formalism of supergravity. In this paper, we reexamine the gaugino mass term in this formalism by paying particular attention to symmetry which controls gaugino masses in supergravity. We first discuss super-Diffeomorphism invariance of path-integral measures of charged superfields. As we will show, the super-Diffeomorphism invariant measure is not invariant under a super-Weyl transformation, which is the origin of the anomaly mediated gaugino mass. We show how the anomaly mediated gaugino mass is expressed as a local operator in a Wilsonian effective action in a super-Diffeomorphism covariant way. We also obtain a gaugino mass term independent of the gauge choice of the fictitious super-Weyl symmetry in the super-Weyl compensator formalism, which reproduces the widely accepted result. Besides, we discuss how to reconcile the gaugino mass term in the local Wilsonian effective action and the gaugino mass term appearing in a non-local 1PI quantum effective action.