At any finite order, the renormalization scheme and scale dependence from the strong coupling constant and the perturbative coefficients do not exactly cancel, leading to the well-known renormalization scheme and scale ambiguities. As a practical approach to solve the ambiguities, the principle of minimum sensitivity (PMS) suggests to set the renormalization scale by requiring the slope of the pQCD approximant over the scheme and scale changes to vanish. In the paper, we investigate the scheme dependence of the pQCD predictions before and after applying PMS scale setting. We first transform the pQCD prediction under the MS¯¯¯¯¯¯¯-scheme to the one under an arbitrary scheme which is characterized by the scheme-dependent {βm≥2}-terms. After applying PMS scale setting, we show that the pQCD approximant is independent to the initial choice of scheme and the conventional scheme-dependence for the predictions shall be greatly suppressed.
Date Published
Monday, July 31, 2017