General Quartic ${\hat{I}}^2$-Function at Three Loops

Abstract

We determine the three-loop $\overline{\text{MS}}$ quartic ${\hat{I}}^2$-function for the most general renormalisable four-dimensional theories. A general parametrization of the ${\hat{I}}^2$-function is compared to known ${\hat{I}}^2$-functions for specific theories to fix all coefficients. Three-loop ${\hat{I}}^2$-functions for the cubic coupling and scalar mass terms also follow from the result, which is made available in software packages.

30 pages