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Conserved Density Fluctuation and Temporal Correlation Function in HTL Perturbation Theory

Considering recently developed Hard Thermal Loop perturbation theory that takes into account the effect of the variation of the external field through the fluctuations of a conserved quantity we calculate the temporal component of the Euclidian correlation function in the vector channel. The results are found to be in good agreement with the very recent results obtained within the quenched approximation of QCD and small values of the quark mass ($\sim 0.1T$) on improved lattices of size $128^3\times N_τ$ at ($N_τ=40, \ T=1.2T_C$), ($N_τ=48, \ T=1.45T_C$), and ($N_τ=16, \ T=2.98T_C$), where $N_τ$ is the temporal extent of the lattice. This suggests that the results from lattice QCD and Hard Thermal Loop perturbation theory are in close proximity for a quantity associated with the conserved density fluctuation.