The renormalization group improved effective potential in massless models

Abstract

The effective potential $V$ is considered in massless $λϕ^4_4$ theory. The expansion of $V$ in powers of the coupling $λ$ and of the logarithm of the background field $ϕ$ is reorganized in two ways; first as a series in $λ$ alone, then as a series in $\lnϕ$ alone. By applying the renormalization group (RG) equation to $V$, these expansions can be summed. Using the condition $V^\prime(v) = 0$ (where $v$ is the vacuum expectation value of $ϕ$) in conjunction with the expansion of $V$ in powers of $\lnϕ$ fixes $V$ provided $v\neq 0$. In this case, the dependence of $V$ on $ϕ$ drops out and $V$ is not analytic in $λ$. Massless scalar electrodynamics is considered using the same approach.