The effective potential in the presence of several mass scales

We consider the problem of improving the effective potential in mass indepe ndent schemes, as e.g. the <(MS)over bar> or <(DR)over bar> renormalization scheme, in the presence of an arbitrary number of fields with phi-dependen t masses M-i(phi(c)). We use the decoupling theorem at the scales mu(i) = M -i(phi(c)) such that the matching between the effective (low energy) and co mplete (high energy) one-loop theories contains no thresholds. We find that for any value of phi(c), there is a convenient scale mu* = min(i){M-i(phi( c))}, at which the loop expansion has the best behaviour and the effective potential has the least mu-dependence. Furthermore, at this scale the effec tive potential coincides with the (improved) tree-level one in the effectiv e field theory. The decoupling method is explicitly illustrated with a simp le Higgs-Yukawa model, along with its relationship with other decoupling pr escriptions and with proposed multi-scale renormalization approaches. The p rocedure leads to a nice suppression of potentially large logarithms and ca n be easily adapted to include higher-loop effects, which is explicitly sho wn at the two-loop level. (C) 1999 Published by Elsevier Science B.V. All r ights reserved.