Determination of the matrix element V(ub) from inclusive B meson decays

For years the extraction of |V_ub| was tainted by large errors due to theoretical uncertainties. Because of our inability to calculate hadronic dynamics, we are forced to resort to ad hoc models when making theoretical predictions, hence introduce errors which are very hard to quantify. However, an accurate measurement of |V_ub| is very important for testing the Cabbibo-Kobayashi-Maskawa picture of CP violation in the minimal standard model. It is highly desirable to be able to extract |V_ub| with well-defined and reasonable theoretical uncertainties.; In this dissertation, a strategy to extract |V_ub| from the electron energy spectrum of the inclusive semi-leptonic B decays is proposed, without having to model the hadronic dynamics. It is based on the observation that the long distance physics involving hadronization, of which we are ignorant, is insensitive to the short distance interactions. Therefore, the uncalculable part in B → $Xu\ell n$ is the same as that in the radiative B decays B → X_sγ. We are able to write down an analytic expression for $Vub2/V*tsVtb$ in terms of known functions. The theoretical uncertainty in this method is well-defined and estimated to be less than 10% in | V_ub|. We also apply our method to the case of hadronic mass spectrum of the inclusive semi-leptonic decays, which has the virtue that the quark-hadron duality is expected to work better.