Two-loop RG functions of the massive $\phi^4$ field theory in general dimensions

TL;DR

This paper computes two-loop Feynman integrals for massive phi^4 theory across various dimensions, expressing RG functions with hypergeometric functions, and providing useful mathematical relations.

Contribution

It provides explicit two-loop integrals and RG functions for phi^4 theory in general dimensions, expressed via hypergeometric functions, with new relations for these integrals and functions.

Findings

Explicit two-loop integrals for generic dimensions

Compact RG functions in terms of hypergeometric functions

New relations among integrals and special functions

Abstract

Two-loop Feynman integrals of the massive $\phi^4_d$ field theory are explicitly obtained for generic space dimensions $d$. Corresponding renormalization-group functions are expressed in a compact form in terms of Gauss hypergeometric functions. A number of interesting and useful relations is given for these integrals as well as for several special mathematical functions and constants.