A novel and self-consistency analysis of the QCD running coupling $\alpha_s(Q)$ in both the perturbative and nonperturbative domains.

The QCD coupling $\alpha_s$ is the most important parameter for understanding the strong interactions among quarks and gluons. By using the well measured effective coupling $\alpha^{g_1}_{s}(Q)$ defined from the Bjorken sum rules as an explicit example, we suggest a novel way to fix the $\alpha_s$ at all scales: The QCD light-front holographic model is adopted for the $\alpha_s$ infrared behavior, and the fixed-order pQCD prediction under the principle of maximum conformality (PMC) is used for the high-energy scale behavior. By applying the PMC, a precise renormalization scheme-and-scale independent perturbative series can be achieved. By further using the physical $V$-scheme, we observe that a self-consistent and precise $\alpha_s$ running behavior in both the perturbative and the nonperturbative domains with a smooth transition from small to large scales can be achieved.