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

摘要

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 ξ(w) is an alternate series in powers of (w — 1). Moreover, one gets that the n-th derivative of ξ(w) at w = 1 can be bounded by the (n — l)-th one, and an absolute lower bound for the n-th derivative (-1)~n ξ~((n))(1) ≥ (2n+1)!!/2~(2n) Moreover, for the curvature we find ξ″(1) ≥ 1/5[4ρ~2 + 3(ρ~2)~2] where ρ~2 = -ξ′(1). We show that the quadratic term 3/5(ρ~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 ξ(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 ξ(w). The method is extended to the subleading quantities in 1/m_Q, namely ξ_3(w) and Λξ(W).