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µ$_{IR}$ = √ m 2 B − m 2 b [28]. The b -quark pole mass is taken as: m$_{b}$ ≃ 4 . 68 +0 . 17 − 0 07 GeV, which is the recent world average suggested by Particle Data Group [31]. As for the running coupling constant, we approximate it by a one-loop form, α$_{s}$ ( µ$_{IR}$ ) = 4 π/ (9 ln( µ 2 $_{IR}$/ Λ 2 $_{QCD}$)), where Λ$_{QCD}$ = 0 . 241 GeV that is determined by reproducing α$_{s}$ ( M$_{z}$ ) = 0 . 1176 [31]. 

Criteria (A, B, C) determine a set of parameters for each value of m$_{b}$ . In the following, we shall firstly take m$_{b}$ = 4 . 68 GeV as an explicit example to show how to determine the allowable ranges for M 2 and s$_{0}$ and to derive f$_{B}$ within these ranges. And then we shall present the results for several typical m$_{b}$ . 

Firstly, the three-dimensional figures (1,2) present the allowable range of M 2 and s$_{0}$ for sum rules I and II. The left diagram of Figs.(1,2) is for criteria (A) and (B), whose 

