A method for getting well-defined coupling constant in all region

Abstract

In this work, a way starting from beta function is presented for obtaining well-defined coupling constant in UV and IR region. In the approach presented here, obvious singularity is removed, and asymptotic behaviour is reserved fully and manifestly. Also it's shown that the freezed coupling constant is independent of dimensional parameters $\Lambda$ and not sensitive to higher-loop corrections and renormalization scheme adopted. A non-dimensional function of energy scale is introduced to play the role of "fine tuning".