The Mass Definition in Hqet and a New Determination of V${}_{\text{cb}}$

Abstract

Positive powers of the mass parameter in a physical quantity calculated with the help of heavy quark effective theory originate from a Wilson coefficient in the matching of QCD and HQET Green function. We show that this mass parameter enters the calculation as a well--defined running current mass. We further argue that the recently found ill--definition of the pole mass, which is the natural expansion parameter of HQET, does not affect a phenomenological analysis which uses truncated perturbative series. We reanalyse inclusive semileptonic decays of heavy mesons and obtain the $c$ quark mass $m_c^{\overline{\text{MS}}}(m_c)=(1.35\pm 0.20)\text{GeV}$ where the error is almost entirely due to scale--uncertainties. We also obtain $m_b^{\overline{\text{MS}}}(m_b)=(4.6\pm 0.3)\text{GeV}$ and $|V_{cb}|({\tau }_B/1.49\text{ps}{)}^{1/2}=0.036\pm 0.005$ where the errors come from the uncertainty in the kinetic energy of the heavy quark inside the meson, in the experimental branching ratios, in QCD input parameters, and scale--uncertainties.

Comments: 21 p., 5 figs, all style files incl., TUM-T31-56/R (Sec. 2 revised, phenomenological results unchanged)