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
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.