Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2010-07-09
Physics
High Energy Physics
High Energy Physics - Phenomenology
30 pages, 11 figures, no tables
Scientific paper
The effective potential approach for composite operators has been generalized to non-zero temperatures in order to derive the analytical equation of state for pure $SU(3)$ Yang-Mills fields from first principles. The non-perturbative part of the analytical equation of state does not depend on the coupling constant, but instead introduces a dependence on the mass gap. This is responsible for the large-scale structure of the QCD ground state. Its perturbative part does analytically depend on the fine-structure constant of strong interactions as well. As it follows from our equation of state, the two massive gluonic excitations with the effective masses $m'_{eff}= 1.17 \ \GeV$ and $\bar m_{eff} = 0. 585 \ \GeV$, as well as the different types of massless gluonic excitations, are present in the $SU(3)$ gluon plasma. The pressure may continuously change around $T_c = 266.5 \ \MeV$ in order to achieve its Stefan-Boltzmann limit at high temperatures. The entropy and energy densities have jump discontinuities at $T_c$. This is a firm evidence of the first-order phase transition in $SU(3)$ pure gluon plasma. Our value for the latent heat is $\epsilon_{LH} = 1.54$ (in dimensionless units). The heat capacity has a $\delta$-type singularity (an essential discontinuity) at $T_c$, so that the speed of light squared becomes zero at this point. The proposed NP analytical approach makes it possible to control for the first time the thermodynamics of the gluon plasma at low temperatures, below $T_c$. We have also calculated the gluon condensate, and hence the trace anomaly relation, as a function of temperature. Properly scaled they decrease not as $1/T^4$ but as $1/T^2$ at high temperatures due to the explicit presence of the mass gap in the equation of state. All our numerical results are in very good agreement with corresponding lattice data at $T \geq 2 T_c$.
Gogokhia V.
Vasúth Mátyás
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