Self-Energy approximation for the running coupling constant in thermal ϕ4 theory using Imaginary Time Formalism

A bstract We investigate the temperature dependence of the mass scale, running coupling constant, and running mass in thermal ϕ 4 theory using the Imaginary Time Formalism (ITF). Employing dimensional regularization and the minimal subtraction scheme, we compute the self-energy up to two-loop order. We introduce a novel Self-Energy Approximation (SEA), which equates the thermal and non-thermal self-energies in the zero external momentum limit. This approximation, combined with the renormalization group equation, imposes constraints that naturally lead to a temperature-dependent mass scale, μ ( T ), ensuring consistent behavior of the running coupling constant and running mass at finite temperatures. Using these results, the free energy density is evaluated at two-loop order and compared with the quasiparticle model.