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Using the OPE, we formulate new sum rules in the heavy quark limit of QCD.These sum rules imply that the elastic Isgur-Wise function $\xi (w)$ is analternate series in powers of $(w-1)$. Moreover, one gets that the $n$-thderivative of $\xi (w)$ at $ w=1$ can be bounded by the $(n-1)$-th one, and anabsolute lower bound for the $n$-th derivative $(-1)^n \xi^{(n)}(1) \geq{(2n+1)!! \over 2^{2n}}$. Moreover, for the curvature we find $\xi ''(1) \geq{1 \over 5} [4 \rho^2 + 3(\rho^2)^2]$ where $\rho^2 = - \xi '(1)$. We show thatthe quadratic term ${3 \over 5} (\rho^2)^2$ has a transparent physicalinterpretation, as it is leading in a non-relativistic expansion in the mass ofthe light quark. These bounds should be taken into account in theparametrizations of $\xi (w)$ used to extract $|V_{cb}|$. These results areconsistent with the dispersive bounds, and they strongly reduce the allowedregion of the latter for $\xi (w)$. The method is extended to the subleadingquantities in $1/m_Q$, namely $\xi_3(w)$ and $\bar{\Lambda}\xi (w)$.}]Comment: Talk given at the ICHEP04 Conference (Beijing, August 2004

SUM RULES IN THE HEAVY QUARK LIMIT OF QCD AND ISGUR-WISE FUNCTIONS