Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2004-12-10
Physics
High Energy Physics
High Energy Physics - Phenomenology
Talk given at the ICHEP04 Conference (Beijing, August 2004)
Scientific paper
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 an alternate series in powers of $(w-1)$. Moreover, one gets that the $n$-th derivative of $\xi (w)$ at $ w=1$ can be bounded by the $(n-1)$-th one, and an absolute 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 that the quadratic term ${3 \over 5} (\rho^2)^2$ has a transparent physical interpretation, as it is leading in a non-relativistic expansion in the mass of the light quark. These bounds should be taken into account in the parametrizations of $\xi (w)$ used to extract $|V_{cb}|$. These results are consistent with the dispersive bounds, and they strongly reduce the allowed region of the latter for $\xi (w)$. The method is extended to the subleading quantities in $1/m_Q$, namely $\xi_3(w)$ and $\bar{\Lambda}\xi (w)$.}]
Jugeau Frederic
Oliver L. L.
Raynal Jean-Claude
Yaouanc Alain Le
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