The renormalization group improved effective potential in massless models

Abstract

The effective potential $V$ is considered in massless $\lambda {\varphi }_4^4$ theory. The expansion of $V$ in powers of the coupling $\lambda$ and of the logarithm of the background field $\varphi$ is reorganized in two ways; first as a series in $\lambda$ alone, then as a series in $\ln \varphi$ 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 $\varphi$) in conjunction with the expansion of $V$ in powers of $\ln \varphi$ fixes $V$ provided $v\ne 0$. In this case, the dependence of $V$ on $\varphi$ drops out and $V$ is not analytic in $\lambda$. Massless scalar electrodynamics is considered using the same approach.

9 pages, considerably expanded form. To be published in Mod. Phys. Lett. A

References in corpus (8)

• Improved Higgs Mass Stability Bound in the Standard Model and Implications for Supersymmetry
• Renormalization Group Improvement of the Effective Potential in Massive O(N) Symmetric ${\varphi }^4$ Theory
• Improving the Effective Potential
• Optimal Renormalization-Group Improvement of Two Radiatively-Broken Gauge Theories
• Renormalization-Group Improvement of Effective Actions Beyond Summation of Leading Logarithms
• Optimal Renormalization-Group Improvement of R(s) via the Method of Characteristics
• Vanishing of the Bare Coupling in Four Dimensions
• Summation of Higher Order Effects using the Renormalization Group Equation

Cited by in corpus (7)

• Renormalization Scheme Dependence with Renormalization Group Summation
• The Effective Potential in the Massive ${\varphi }_4^4$ Model
• Summing Radiative Corrections to the Effective Potential
• A Massive Non-Abelian Vector Model
• The Renormalization Group and the Effective Action
• The Effectve Potential in Massless Theories
• The Renormalization Group and the Effective Potential in the Wess-Zumino model