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sum rules II, which is obtained by sampling 400 × 500 points within M 2 ∈ [2 , 6] GeV 2 and s$_{0}$ ∈ [32 , 37] GeV $^{2}$. The right diagrams of Figs.(3,4) present the corresponding values of f$_{B}$ within its allowable region of M 2 and s$_{0}$ . For fixed M $^{2}$, it can be found that f$_{B}$ increases with the increment of s$_{0}$ . And for fixed s$_{0}$ , f$_{B}$ shall be steady under the reasonable region of the Borel parameter M $^{2}$, i.e. the uncertainty is less than 3%. By varying ( M $^{2}$,s$_{0}$ ) within their allowable region, the uncertainties of f$_{B}$ is less than 6% for sum rules I and less than 5% for sum rules II. Such small uncertainty for a fixed m$_{b}$ agrees with the requirement of the reliability of sum rules. 

Secondly, we present f$_{B}$ for several typical m$_{b}$ , i.e. m$_{b}$ =4.61 GeV, 4.68 GeV, 4.75 GeV and 4.85 GeV, respectively. The allowable region of ( M $^{2}$,s$_{0}$ ) for each m$_{b}$ can be determined through the same procedure described above. The results are put in TABs.(I,II), where the listed values of s$_{0}$ and M 2 are those that lead to the maximum value of f$_{B}$ for a particular m$_{b}$ . And the listed errors for f$_{B}$ are determined by setting the non-perturbative condensates 

