Scheme invariants in phi^4 theory in four dimensions

TL;DR

This paper analyzes the structure of renormalization scheme invariants in four-dimensional phi^4 theory, revealing more invariants than expected and discussing the omission of certain contributions in specific schemes.

Contribution

It provides a comprehensive analysis of scheme invariants up to four loops and partial results at five loops, highlighting the complexity of invariants in phi^4 theory.

Findings

More invariants than expected in four-loop analysis

Omission of one-vertex reducible contributions in certain schemes

Partial five-loop results indicating increased invariants

Abstract

We provide an analysis of the structure of renormalisation scheme invariants for the case of $\phi^4$ theory, relevant in four dimensions. We give a complete discussion of the invariants up to four loops and include some partial results at five loops, showing that there are considerably more invariants than one might naively have expected. We also show that one-vertex reducible contributions may consistently be omitted in a well-defined class of schemes which of course includes MSbar.