RG-Improved Three-Loop Effective Potential of the Massive $ϕ^4$ theory

Abstract

The renormalization group method is applied to the three-loop effective potential of the massive $ϕ^4$ theory in the $\bar{\rm MS}$ scheme in order to obtain the next-next-next-to-leading logarithm resummation. For this, we exploit four-loop parts of the renormalization group functions $β_λ$, $γ_m$, $γ_ϕ$, and $β_Λ$, which were already given to five-loop order via the renormalization of the zero-, two-, and four-point one-particle-irreducible Green's functions, to solve evolution equations for the parameters $λ$, $m^2$, $ϕ$, and $Λ$ within the accuracy of the three-loop order.