Thermodynamics from the S-matrix reloaded: emergent thermal mass

TL;DR

This paper revisits the DMB formalism relating the thermal partition function to the S-matrix, exploring how the Debye mass emerges at higher orders in QFT, thereby enabling advanced thermal calculations.

Contribution

It demonstrates how the Debye mass appears within the S-matrix formalism, facilitating higher-order thermal free energy computations in relativistic quantum field theories.

Findings

Debye mass arises naturally in the S-matrix formalism

Higher-order IR divergences are resolved through this approach

Enables advanced thermal free energy calculations in QFT

Abstract

The formalism of Dashen, Ma and Bernstein (DMB) expresses the thermal partition function of a system in terms of the S-matrix operator, roughly $Z(\beta) \propto \int dE\, e^{-\beta E}\,\text{Tr}\,\ln S(E),$ where $S$ denotes the full scattering operator on the asymptotic Fock space -- i.e. including all multi-particle sectors -- defined via the Lippmann-Schwinger equation. Recently we have employed this formalism to compute the free energy of flux tubes (essentially a two-dimensional theory of derivatively coupled scalars) and the two-loop $O(\alpha_s)$ QCD thermal free energy. Moving to higher orders, it is well known that at $O(\alpha_s^2)$ in QCD, or e.g. at $O(\lambda^2)$ in $\lambda\phi^4$ theory, the free energy develops IR divergences. These IR divergences are resolved by the screening Debye mass. However, the DMB formalism expresses the free energy in terms of a trace of the S-matrix operator in the vacuum. How, then, does the Debye mass arise in this framework? In this work we address this question, thereby paving the way for higher-order applications of the DMB formalism in relativistic QFT.