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

TL;DR

This paper introduces a method based on the beta function to obtain a well-defined coupling constant across all energy regions, removing singularities and ensuring consistent asymptotic behavior.

Contribution

It presents a novel approach that yields a coupling constant free of singularities, independent of parameters and higher-loop corrections, enhancing theoretical robustness.

Findings

Singularity in coupling constants is effectively removed.

Coupling constant remains stable across different energy scales.

Method is insensitive to higher-loop corrections and renormalization schemes.

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".