Resummations of free energy at high temperature

Abstract

We discuss resummation strategies for free energy in quantum field theories at nonzero temperatures T . We point out that resummations should be performed for the short-and long-distance parts separately in order to avoid spurious interference effects and double-counting. We then discuss and perform Padé resummations of these two parts for QCD at high T . The resummed results are almost invariant under variation of the renormalization and factorization scales. We perform the analysis also in the case of the massless scalar φ 4 theory.

Padé-related resummations of the pressure of quark-gluon plasma by approximate inclusion ofgs6terms

“…The only unknown parameters are δ G and δ E which will be allowed to vary in the intervals (21) and (40). The numerical analysis will be performed in analogy with that of our previous work [21]. There, expansion corresponding to present Eq.…”

“…The RS-independence of both parts separately has been demonstrated analytically in Ref. [21] by using the known perturbation series (up to order g 5 ). The separation and the µ-independence of the separate terms allows a more consistent application of Padé and Padé-related approximations: they are applied to TPS's of each quantity p E and p M+G separately.…”

“…Now comes one of the main points of the formalism of Ref. [21]: Having the separation (4) of the pressure into p E and p M+G , we can argue that both are separately physical quantities, and thus both, when calculated to all orders, are separately µ-independent. The reason for it is shown by the following indirect argument: Consider any (static) two-point-correlator within the given field theory.…”

“…In our previous paper [21] we applied this procedure to calculation of the free energy (pressure) both in QCD with n f (massless) quarks and in a φ 4 -theory. At that time the relevant TPS's had been calculated only up to terms of order g the freedom of using higher order Padé or Borel-Padé approximants and thus treating the long-range part p M+G (= −F M+G ) in a more reliable way.…”

“…The first step needed for the application of the formalism of Ref. [21] is the separation in Eq. (3) of the purely perturbative part from the contributions stemming from the (ring-)resummations.…”