Scheming in dimensional regularization

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 non-minimal 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 cut-off regularization. We therefore recover cut-off regularization from dimensional regularization with a non-minimal subtraction scheme. We then discuss the power counting for non-relativistic effective field theories which arises in these alternative schemes.