2 3 4 5 6 7 31 32 33 34 35 36 37 M 2 s 0 2 4 6 8 32 34 36 0.16 0.17 0.18 0.19 M 2 s$_{0}$ f B FIG. 3. The allowable range of ( M $^{2}$,s$_{0}$ ) for sum rules I (Left diagram) and the value of f$_{B}$ within this range (Right diagram), where m$_{b}$ = 4 . 68 GeV and the non-perturbative condensates are set to be their center values. 2.5 3 3.5 4 31 32 33 34 35 36 37 38 M 2 s 0 2 2.5 3 3.5 4 30 35 40 0.2 0.21 0.22 0.23 M 2 s$_{0}$ f B FIG. 4. The allowable range of ( M $^{2}$,s$_{0}$ ) for sum rules II (Left diagram) and the value of f$_{B}$ within this range (Right diagram), where m$_{b}$ = 4 . 68 GeV and the non-perturbative condensates are set to be their center values. first and second axes are for M 2 and s$_{0}$ , and third axis is for the ratio of the continuum contribution over the total contribution for criteria (A) and the ratio of the dimension-six contribution over the total contribution for criteria (B) respectively. By setting a fixed value for s$_{0}$ , it is found that the continue contribution increases with the increment of M 2 and the contribution from the dimension-six condensate term increases with the decrement of M $^{2}$, so criterion (A) determines the upper limit of M 2 and criterion (B) determines the lower limit of M $^{2}$. Then, a possible Borel window can be obtained from criteria (A) and (B), which shall be further constrained by criterion (C). Practically, the range of ( M $^{2}$,s$_{0}$ ) can be determined numerically. The left diagram of Fig.(3) shows the allowable range of ( M $^{2}$,s$_{0}$ ) for sum rules I, which is obtained by sampling 500 × 400 points within M 2 ∈ [2 , 7] GeV 2 and s$_{0}$ ∈ [32 , 36] GeV $^{2}$. And the left diagram of Fig.(4) shows the allowable range of ( M $^{2}$,s$_{0}$ ) for 7