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We investigate the theoretical predictions for thrust distribution in theelectron positron annihilation to three-jets process at NNLO for differentvalues of the number of flavors, $N_f$. To determine the distribution along theentire renormalization group flow from the highest energies to zero energy weconsider the number of flavors near the upper boundary of the conformal window.In this regime of number of flavors the theory develops a perturbative infraredinteracting fixed point. We then consider also the QED thrust obtained as thelimit $N_c \rightarrow 0$ of the number of colors. In this case the low energylimit is governed by an infrared free theory. Using these quantum fieldtheories limits as theoretical laboratories we arrive at an interestingcomparison between the Conventional Scale Setting - (CSS) and the Principle ofMaximum Conformality (PMC$_\infty$) methods. We show that within theperturbative regime of the conformal window and also out of the conformalwindow the PMC$_\infty$ leads to a higher precision, and that reducing thenumber of flavors, from the upper boundary to the lower boundary, through thephase transition the curves given by the PMC$_\infty$ method preserve withcontinuity the position of the peak, showing perfect agreement with theexperimental data already at NNLO.

Thrust Distribution for 3-Jet Production from $e^+e^-$ Annihilation within the QCD Conformal Window and in QED