How to Measure Kinetic Energy of the Heavy Quark Inside B Mesons?

Abstract

We discuss how one can determine the average kinetic energy of the heavy quark inside heavy mesons from differential distributions in $B$ decays. A new, so-called third, sum rule for the $b\to c$ transition is derived in the small velocity (SV) limit. Using this sum rule and the existing data on the momentum dependence in the $B\to D^{\ast }$ transition (the slope of the Isgur-Wise function) we obtain a new lower bound on the parameter ${\mu }_{\pi }^2=(2M_B{)}^{-1}⟨B|\bar{b}(i\vec{D}{)}^{2}b|B⟩$ proportional to the average kinetic energy of $b$ quark inside $B$ meson. The existing data suggest ${\mu }_{\pi }^2>0.4$~GeV${}^2$ and (from the ``optical'' sum rule) $\overline{\Lambda }>500$ MeV, albeit with some numerical uncertainties.

Comments: LaTex, 12 pages, no figures, Preprint TPI-MINN-94/25-T, UMN-TH-1263-94, UND-HEP-94-BIG07, OUT-4102-51