  Building on an older method used to derive non-decoupling effects of a heavy
Higgs boson in the Standard Model, we describe a general procedure to integrate
out heavy fields in the path integral. The derivation of the corresponding
effective Lagrangian including the one-loop contributions of the heavy
particle(s) is particularly transparent, flexible, and algorithmic. The
background-field formalism allows for a clear separation of tree-level and
one-loop effects involving the heavy fields. Using expansion by regions the
one-loop effects are further split into contributions from large and small
momentum modes. The former are contained in Wilson coefficients of effective
operators, the latter are reproduced by one-loop diagrams involving effective
tree-level couplings. The method is illustrated by calculating potential
non-decoupling effects of a heavy Higgs boson in a singlet Higgs extension of
the Standard Model. In particular, we work in a field basis corresponding to
mass eigenstates and properly take into account non-vanishing mixing between
the two Higgs fields of the model. We also show that a proper choice of
renormalization scheme for the non-standard sector of the underlying full
theory is crucial for the construction of a consistent effective field theory.
