Operator Coefficients for Composite Operators in the $(\phi^4)_4$ Theory

TL;DR

This paper investigates the relationship between operator product coefficients and anomalous dimensions in the four-dimensional  theory, computing coefficient functions and beta functions to first order in  coupling.

Contribution

It provides the first explicit calculation of operator coefficient functions in  theory, linking them to anomalous dimensions and beta functions.

Findings

Derived first-order coefficient functions for  operators

Computed two-loop beta functions in  theory

Confirmed the relation between operator coefficients and anomalous dimensions

Abstract

In a previous paper we derived a relation between the operator product coefficients and anomalous dimensions. We explore this relation in the $(\phi^4)_4$ theory and compute the coefficient functions in the products of $\phi^2$ and $\phi^4$ to first order in the parameter $\lambda$. The calculation results in two-loop beta functions.