Analytic Invariant Charge in QCD with Suppression of Nonperturbative Contributions at Large $Q^2$

Based on the analytic invariant charge obtained from the results of the standard perturbation theory up to the four-loop approximation, we construct a “synthetic” model of the invariant charge in quantum chromodynamics. In the suggested model, the perturbative discontinuity on the timelike semiaxis in the complex $Q^2$ plane is preserved, and nonperturbative contributions not only cancel nonphysical perturbation theory singularities in the infrared region but also rapidly decrease in the ultraviolet region. On one hand, the effective coupling function in this model is enhanced at zero (the dual superconductivity property of the quantum chromodynamics vacuum); on the other hand, a dynamical gluon mass appears. In our approach, fixing the parameter corresponding to the string tension parameter and normalizing (for example, at the point $M_\tau$) entirely fix the synthetic invariant-charge model. The dynamical gluon mass $m_{\mathrm{g}}$ is then fixed and is stable as the number of loops of the original perturbative approximation increases.