  A new method is developed to calculate multiloop Feynman diagrams in
non-relativistic field theories. A consistent scheme for regularizing and
renormalizing loop integrals is established and shown to reproduce the results
of dimensional regularization (DR) and modified minimal subtraction MS^bar or
DR and power divergence subtraction (PDS) up to next-to-leading order (NLO).
However, significantly less effort is required to evaluate the integrals and
the methods are easily generalized to higher order graphs. Thus, even the most
complicated multiloop graph can be expressed in terms of analytic functions.
These techniques are then used to calculate the quadrupole moment of the
deuteron to three loops in the Kaplan, Savage, and Wise effective field theory.
A new unfixed direct S->D wave counterterm occurs at this order and its value
is determined.
