Effective Potential of $\lambda\phi^{4}_{1+3}$ at Zero and Finite Temperature

TL;DR

This paper evaluates the effective potential of the bb^4_{1+3} model at zero and finite temperature, estimating a critical temperature for symmetry restoration around 510 GeV using regularization, renormalization, and Green function methods.

Contribution

It introduces a simple regularization and renormalization method for the bb^4_{1+3} model and estimates the critical temperature for symmetry restoration in the standard model.

Findings

Critical temperature for symmetry restoration:  510 GeV

Effective potential evaluated at T=0 and T
e0

Method combines regularization, renormalization, and Green function approach

Abstract

The effective potential of $\lambda\phi^4_{1+3}$ model with both sign of parameter $m^2$ is evaluated at T=0 by means of a simple but effective method for regularization and renormalization. Then at $T\ne 0$, the effective potential is evaluated in imaginary time Green Function approach, using the Plana formula. A critical temperature for restoration of symmetry breaking in the standard model of particle physics is estimated to be $T_c\simeq 510$ GeV.