Multiloop Diagrams in Non-Relativistic Field Theories and the Deuteron Quadrupole Moment

Abstract

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.