RG-Improved Three-Loop Effective Potential of the Massive ${\varphi }^4$ theory

Abstract

The renormalization group method is applied to the three-loop effective potential of the massive ${\varphi }^4$ theory in the $\overline{\mathrm{MS}}$ 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 ${\beta }_{\lambda }$, ${\gamma }_m$, ${\gamma }_{\varphi }$, and ${\beta }_{\Lambda }$, 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 $\lambda$, $m^2$, $\varphi$, and $\Lambda$ within the accuracy of the three-loop order.

In version 3, title was changed and a subsection (Sec. IIA) of version 1, which appears in the appendix in version 2, was removed