English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In our previous works the effective potential approach for compositeoperators has been generalized to non-zero temperature in order to derive theanalytical equation of state for pure SU(3) Yang-Mills fields without quarkdegrees of freedom. In the absence of external sources this is nothing but thevacuum energy density. The key element of this derivation is the introductionof a temperature dependence into the expression for the bag constant. Thenon-perturbative part of the analytical equation of state does not depend onthe coupling constant, but instead introduces a dependence on the mass gap.This is responsible for the large-scale dynamical structure of the QCD groundstate. The perturbative part of the analytical equation of state does depend onthe QCD fine-structure coupling constant $\alpha_s$. Here we develop theanalytical formalism, incorporating the perturbative part in a self-consistentway. It makes it possible to calculate the PT contributions to the equation ofstate in terms of the convergent series in integer powers of a small$\alpha_s$. We also explicitly derive and numerically calculate the firstperturbative contribution of the $\alpha_s$-order to the non-perturbative partof the equation of state derived and calculated previously. The analyticalequation of state or, equivalently, the gluon pressure is exponentiallysuppressed at low temperatures, while at temperature $T=T_c = 266.5 \ \MeV$ ithas a maximum, if divided by $T^4/3$. It demonstrates a highly non-trivialdependence on the mass gap and the temperature near to $T_c$ and up toapproximately $(3-4)T_c$. At very high temperatures its polynomial character isconfirmed, containing the terms proportional to $T^2$ and $T$ with anon-analytical dependence on the mass gap.

Analytical derivation and numerical calculation of the $\alpha_s$-order correction to the non-perturbative equation of state for SU(3) gluon matter