Singularity of the Exact QCD β-Function

摘要

Ryttov and Sannino suggested an exact expression for the QCD β-function. However, it has a space-like pole at a finite value of the coupling constant. The pole makes the exact β~(RS)-function undefined for some values of the running coupling a between the origin and a fixed point α~(FP). Thus, we use the property of renormalization scheme dependence to obtain a non-singular form for the exact β~(RS)-function. The modified exact β~(RS)-function has an infrared fixed point even for a small number of quark flavors.