  We consider the most general loop integral that appears in non-relativistic
effective field theories with no light particles. The divergences of this
integral are in correspondence with simple poles in the space of complex
space-time dimensions. Integrals related to the original integral by
subtraction of one or more poles in dimensions other than D=4 lead to
nonminimal subtraction schemes. Subtraction of all poles in correspondence with
ultraviolet divergences of the loop integral leads naturally to a
regularization scheme which is precisely equivalent to cutoff regularization.
We therefore recover cutoff regularization from dimensional regularization with
a nonminimal subtraction scheme. We then discuss the power-counting for
non-relativistic effective field theories which arises in these alternative
schemes.
