Effect of heavy particles in low-energy light-particle processes

The "decoupling theorem" of Appelquist and Carazzone is found not always to be applicable to light-scalar-particle processes in spontaneously broken theories. If the Higgs scalar is considered to be light, then Higgs-scalar processes see the effect of heavy fermions and heavy vector gauge bosons at the one-loop level. If there is more than one scalar multiplet in a spontaneously broken gauge theory, the effect of a heavy Higgs particle in light-scalar-particle processes is significant at the tree level. In the latter case, such an effect can be absorbed completely into an effective ${\phi }^4$ coupling constant, ${\lambda }_{\mathrm{eff}}$, of the light particle provided that ${\lambda }_{\mathrm{eff}}$ is positive definite.