Renormalization Group Determination of the Five-Loop Effective Potential for Massless Scalar Field Theory

The five-loop effective potential and the associated summation of subleading logarithms for O(4) globally-symmetric massless $\lambda {\varphi }^4$ field theory in the Coleman-Weinberg renormalization scheme $\frac{d^4V}{d\phi^4}|_{\phi = \mu} = \lambda$(where$\mu$ is the renormalization scale) is calculated via renormalization-group methods. An important aspect of this analysis is conversion of the known five-loop renormalization-group functions in the minimal-subtraction (MS) scheme to the Coleman-Weinberg scheme.