Thermodynamics from the S-matrix reloaded: emergent thermal mass

A bstract 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 (β) ∝ ∫ dEe − βE 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 (α s) QCD thermal free energy. Moving to higher orders, it is well known that at O (ₛ²) O α s 2 in QCD, or e. g. at O (λ 2) in λϕ 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.