The simplest minimal subtraction for massive scalar field theory

Abstract

The simplest minimal subtraction method for massive {\lambda}{\phi}4 scalar field theory is presented. We utilize the one-particle irreducible vertex parts framework to deal only with the primitive divergent ones that can be renormalized multiplicatively. We give a unified description for spacetime metric tensor with either Minkowski or Euclidean signature.The partial-p operation in the remaining diagrams of the two-point vertex part are used to get rid of its overlapping divergences. We show how the parametric dissociation transform effectively eliminates the external momentum dependence of the coefficient of the squared bare mass after performing the partial-p operation in the two-point vertex part diagrams. The resemblance of this method with a minimal subtraction scheme in the massless theory is pointed out. We derive the Callan-Symanzik equations using minimal subtraction arguments and discuss the scaling limit in the ultraviolet region. We apply the method to determine critical exponents for an O(N) internal symmetry at least up to two-loop order with a flat Euclidean metric and find perfect agreement with all previous results in the literature.