Masslesslike minimal subtraction for massive scalar field theory

TL;DR

This paper presents a minimal subtraction method for massive scalar field theory that simplifies calculations by separating mass and momentum contributions, verified through two-loop critical exponent computations.

Contribution

The authors develop a minimal subtraction approach for massive $oxed{ ext{scalar}}$ field theory that adapts techniques from massless cases using a two-step process involving partial-$p$ operation and parametric dissociation transform.

Findings

Method successfully applied to compute critical exponents.

Approach simplifies loop integral calculations.

Results consistent with known two-loop critical exponents.

Abstract

We introduce the simplest minimal subtraction method for massive $\lambda \phi^{4}$ field theory with $O(N)$ internal symmetry, which resembles the same method applied to massless fields by using two steps. First, the utilization of the partial-$p$ operation in every diagram of the two-point vertex part in order to separate it into a sum of squared mass and external momentum, respectively, with different coefficients. Then, the loop integral which is the coefficient of the quadratic mass can be solved entirely in terms of the mass, no longer depending upon the external momentum, using the {\it parametric dissociation transform}. It consists in the choice of a certain set of fixed values of Feynman parameters replaced inside the remaining loop integral after solving the internal subdiagrams. We check the results in the diagrammatic computation of critical exponents at least up to two-loop order using a flat metric with Euclidean signature.