PROBLEMATIC BOUNDS ON THE ISGUR-WISE FUNCTION

From analyticity and unitarity, the tight bound [xi'(1)+1/4]2 less-tha n-or-equal-to (N(c)-2)2/128N(c) = 2.6 X 10(-3) is derived for the slop e of the Isgur-Wise form factor, at w = v.v' = 1, with N(c) = 3 quark colors, using the same assumptions as de Rafael and Taron, whose bound on the same quantity was 20 times less restrictive. A puzzling featur e of the bound is that it appears to trivialize a two-color theory. Ev en more problematically, it is shown that with N(f) light-quark flavor s the assumptions require that N(c) greater-than-or-equal-to 2N(f), wh ich is not the case. It is suggested that this paradox requires the in clusion of large radiative corrections for its resolution.