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

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

1994-07-14

arxiv.org/abs/hep-ph/9407296v1

Phys.Lett. B339 (1994) 160-166

Physics

High Energy Physics

High Energy Physics - Phenomenology

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

Scientific paper

10.1016/0370-2693(94)91149-5

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 $b\rightarrow c$ transition is derived in the small velocity (SV) limit. Using this sum rule and the existing data on the momentum dependence in the $B\rightarrow D^*$ transition (the slope of the Isgur-Wise function) we obtain a new lower bound on the parameter $\mu_\pi^2 = (2M_B)^{-1}\langle B |\bar b (i\vec{D})^2 b |B\rangle $ 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.

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