Renormalization Group Analysis of the Heavy Field Decoupling in a Scalar Theory

The problem of two coupled scalar fields, one with mass much lighter than the other is analysed by means of Wilson's renormalization group approach. Coupled equations for the potential and the wave function renormalization are obtained by means of the gradient expansion. The Appelquist-Carazzone theorem is checked at energies comparable with the light mass; the physics of the light field is also studied at energies comparable and greater than the heavy mass.