We investigate the theoretical predictions for thrust distribution in the electron positron annihilation to three-jets process at NNLO for different values of the number of flavors, $N_f$. To determine the distribution along the entire renormalization group flow from the highest energies to zero energy we consider the number of flavors near the upper boundary of the conformal window. In this regime of number of flavors the theory develops a perturbative infrared interacting fixed point. We then consider also the QED thrust obtained as the limit $N_c\to 0$ of the number of colors. In this case the low energy limit is governed by an infrared free theory. Using these quantum field theories limits as theoretical laboratories we arrive at an interesting comparison between the Conventional Scale Setting - (CSS) and the Principle of Maximum Conformality (PMC_∞) methods. We show that within the perturbative regime of the conformal window and also out of the conformal window the PMC_∞ leads to a higher precision, and that reducing the number of flavors, from the upper boundary to the lower boundary, through the phase transition the curves given by the PMC_∞ method preserve with continuity the position of the peak, showing perfect agreement with the experimental data already at NNLO.

我们研究了在 NNLO 中电子正电子湮没到三射流过程中推力分布的理论预测，对于不同的味道数量值， $N_F$. 为了确定从最高能量到零能量的整个重整化群流的分布，我们考虑了保形窗口上边界附近的风味数量。在这种口味数量的体系中，该理论开发了一个微扰红外相互作用不动点。然后我们还将获得的 QED 推力视为极限$N_C\to 0$的颜色数量。在这种情况下，低能量极限由无红外理论控制。使用这些量子场论限制作为理论实验室，我们得出了传统尺度设置 - (CSS) 和最大共形原则 (PMC _∞ ) 方法之间的有趣比较。我们表明，在共形窗口的微扰范围内以及在共形窗口之外，PMC _∞导致更高的精度，并且减少了从上边界到下边界的风味数量，通过曲线的相变由 PMC _∞方法给出的峰值位置保持连续性，显示与 NNLO 已有的实验数据完全一致。