Effective color charge in high temperaure gluon plasma at A_0 background

In high temperature SU(2) gluodynamics, in a relativistic background R^{ext.}_xi gauge, the effective color charge (g^2(A_0))_eff. is calculated in the presence of the A_0 condensate which is related to Polyakov's loop and also serves as the order parameter of the deconfinement phase transition at high temperature. The gauge-invariant value of the condensate ((A_0)^cl)_0 is obtained from the two-loop effective potential of order parameter W_L(A_0^cl) which is independent of the gauge-fixing parameter xi and has a nontrivial minimum position. Due to smallness of the expansion parameter ~ g^2/(8 pi^2), this potential is applicable at high temperatures beginning from the deconfinement temperature T_d. The effective charge accounts for a correlation between the one- and the two-loop terms of the W_L(A_0^cl). It results in decreasing of the effective gluon interactions in the plasma, compared to the zero condensate case. Temperature dependence of (g^2(A_0))_eff. is investigated. The importance of the found dependence for different applications is noted.