Dressing a Scalar Mass up to Two-Loop Order at Finite Temperature

TL;DR

This paper demonstrates that the Modified Self-Consistent Resummation method can reliably compute finite-temperature scalar masses up to two-loop order, ensuring finiteness in renormalizable theories unlike other methods.

Contribution

It introduces and applies MSCR to calculate finite-temperature scalar masses at two-loop order, showing its advantage in maintaining finiteness in renormalizable models.

Findings

MSCR yields finite corrected masses at finite temperature.

The method is effective up to two-loop order.

It outperforms other approximation techniques in ensuring finiteness.

Abstract

In this paper we use Modified Self-Consistent Resummation (MSCR) in order to obtain the scalar dressed mass by evaluating the self-energy up to two loops in the neutral scalar $\lambda \phi^4$ model at finite temperature. With this laboratory model we show that, if a theory is renormalizable at zero temperature, using the MSCR it is always possible to obtain a finite corrected mass at finite temperature. This feature of the MSCR is not observed in some other approximation techniques usually found in the literature.