Test of an Equivalence Theorem at One-Loop
  We show that the equivalence theorem approximating one-loop gauge sector diagrams by including only Goldstone bosons in the loop gives a remarkably poor approximation to the amplitude for the decay $H\rightarrow \gamma \gamma $ and for the process $\gamma \gamma \rightarrow HH$. At one loop, large logarithms can arise that evade power counting arguments. 
M. S. Berger