A More-Effective Potential

Abstract

In theories with spontaneous symmetry breaking, the loop expansion of the effective potential is awkward. In such theories, the exact effective potential $V({\varphi }_c,T)$ is real and convex (as a function of the classical field ${\varphi }_c$), but its perturbative series can be complex with a real part that is concave. These flaws limit the utility of the effective potential, particularly in studies of the early universe. A generalization of the effective potential is available that is real, that has no obvious convexity problems, and that can be computed in perturbation theory. For the theory with classical potential $V(\varphi )=(\lambda /4)({\varphi }^2-{\sigma }^2{)}^2$, this more-effective potential closely tracks the usual effective potential where the latter is real $|{\varphi }_c|\ge \sigma /\sqrt{3}$ and naturally extends it to ${\varphi }_c=0$, revealing that the critical temperature at the one-loop level runs from $T_C\approx 1.81\sigma$ for $\lambda =0.1$ to $T_C\approx 1.74\sigma$ for $\lambda =1$.

32 pages and 3 figures (The present revision generalizes the original treatment to the case of an arbitrary quartic potential $V(\varphi )$.), LaTeX, postscript

Cited by in corpus (9)

• Manifestly scale-invariant regularization and quantum effective operators
• Electroweak Phase Transition, Higgs Diphoton Rate, and New Heavy Fermions
• The Equation of State of Dark Matter Superfluids
• Electrostatically defined Quantum Dots in a Si/SiGe Heterostructure
• An Effective Potential for Composite Operators
• Real effective potentials for phase transitions in models with extended scalar sectors
• Higgs potential near-criticality from a de Sitter swampland-like condition
• Symmetry allowed, but unobservable, phases in renormalizable Gauge Field Theory Models
• Finite temperature effective actions for double wells