Slope of the Isgur-Wise Function from a QSSR Constraint on the $\Upsilon B\bar{B}$ Couplings

We derive optimal upper and lower bounds on the slope of the Isgur-Wise function at the zero recoil point in terms of the sum of the $\Upsilon B\bar{B}$ couplings, estimated recently from a $QCD$ Spectral Sum Rule ($QSSR$). The problem is solved by means of a duality theorem in functional optimization. Optimal correlations between the slope and the convexity parameters of the Isgur-Wise function with the same input are also obtained.