Asymptotic representations of the running parameters in Yang–Mills theories

A unique perturbative solution to the renormalization group (RG) equation for the running coupling constant (RCC) will be proven to exist. The general representations of the running coupling constant and mass in the form of asymptotic expansions are explicitly derived. A two‐parametric ambiguity is discovered in these expansions which leaves the full result invariant. This feature is observed to be an attribute of the particular type of transcendental equations resulting from the differential RG equation for the RCC.