Problematic bounds on the Isgur-Wise function

From analyticity and unitarity, the tight bound [ζ'(1) + 1/4]2≤(Nc-2)2/128Nc=2.6x10-3 is derived for the slope of the Isgur-Wise form factor, at w triple-bond v·v'=1, with Nc=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 feature of the bound is that it appears to trivialize a two-color theory. Even more problematically, it is shown that with Nf light-quark flavors the assumptions require that Nc≥2Nf, which is not the case. It is suggested that this paradox requires the inclusion of large radiative corrections for its resolution. 11 refs