Analysis of strong coupling constant with machine learning and its application

In this work, we investigate the nature of the strong coupling constant and related physics. Through the analysis of accumulated experimental data from around the world, we employ the ability of machine learning to unravel its physical laws. The result of our efforts is a formula that captures the expansive panorama of the distribution of the strong coupling constant across the entire energy range. Importantly, this newly derived expression is very similar to the formula derived from the Dyson-Schwinger equations based on the framework of Yang-Mills theory. By introducing the Euler number, $e$, into the functional formula of the strong coupling constant at high energies, we have successfully solved the puzzle of the infrared divergence, which allows for a seamless transition of the strong coupling constant from the perturbative to the non-perturbative energy regime. Moreover, the obtained ghost and gluon dressing function distribution results confirm that the obtained strong coupling constant formula can well describe the physical properties of the non-perturbed regime. In addition, we investigate the QCD strong coupling constant result of the Bjorken sum rule $\Gamma_1^{p-n}$ and the quark-quark static energy $E_0(r)$, and find that the global energy scale can effectively interpret the experimental data. The results presented in this work shed light on the puzzling properties of quantum chromodynamics and the intricate interplay of strong coupling constants at both low and high energy scales.