Magnetic confinement and the Linde problem

Abstract

Perturbation theory of thermodynamic potentials in QCD at T > T c is considered with the nonperturbative background vacuum taken into account. It is shown that the colormagnetic confinement in the QCD vacuum prevents the infrared catastrophe of the perturbation theory present in the case of the free vacuum (the "Linde problem"). A short discussion is given of the applicability of the nonperturbative formalism at large T and of the relation with the HTL theory. The observation of A.D.Linde, that the terms O(g n ), n > 6 contribute to the order O(g 6 ) is confirmed also with the account of the colormagnetic confinement, and it is shown that the latter makes these terms IR convergent, and summable. As a result one obtains the selfconsistent theory of the gluon plasma.

Thermodynamics of a quark-gluon plasma at finite baryon density

“…But there is no restrictions on the value of colormagnetic correlator (or alternatively on the existence of colormagnetic string tension σ H ). As shown by analytic [60] and lattice studies σ H grows quadratically with temperature. As a result for T > T c there is no confining string between colour charges, but there is still non-perturbative interaction between them i.e.…”

“…It was found in [64] that CMC does not support white bound states in qq and gg systems at zero temperature, however it can create the screening mass M (T ) of isolated quarks and gluons [44][45][46][47]60], which grows with temperature so that the ratio M (T ) T is constant up to the logarithmic terms.…”

Speed of sound in the QGP and an SU(3) Yang-Mills theory

“…As it has become clear from numerous lattice and experimental studies of QCD at T > 0, the main dynamics of both hadron and QGP phases is of the nonperturbative(np) origin and should be treated within the np methods.The fundamental approach to the np QCD is developed in the framework of the Field Correlator Method(FCM) [37][38][39][40][41][42] generalized to non-zero temperatures [43][44][45][46][47]. In this paper we use the FCM to calculate the speed velocity in case of finite temperatures and taking into account the colour magnetic confinement(CMC) as it was done in [48][49][50][51][52]. The strength of this method is the ability in a self consistent manner to calculate the speed of sound both in the confinement phase and at temperatures above T C both at zero and non-zero chemical potential.…”

Field correlator method for the confinement in QCD

“…However confinement precludes the free motion of quark and gluons, placing those on the confining film of the Wilson loop. As a consequence any amplitude of the QCD PTh is IR finite at nonzero σ (for examples of IR regularization due to confinement see [93] and appendix therein). This fact must modify the standard PTh and pdf evolution equations, see [81] for recent results.…”

“…The CMC plays an especially important role in the temperature perturbation theory, where it prevents IR divergencies and allows to solve the Linde problems, by summing a converging infinite set of finite perturbative diagrams [109].…”