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 $$ O\left({\alpha}_s^2\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mfenced> </mml:math> 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.