Inclusive semileptonic $B$ and polarized $Λ_{b}$ decays from QCD

The differential decay spectrum

\frac{d Γ}{d E_{e} d q^{2}}

for the semileptonic decay of an unpolarized hadron containing a

b

quark and the decay spectrum

\frac{d Γ}{d E_{e} d q^{2} d cos θ}

for polarized

Λ_{b}

decay are computed to second order in the

\frac{1}{m_{b}}

expansion. Most of the

\frac{1}{m_{b}^{2}}

corrections have a simple physical interpretation, which is discussed in detail. The implications of the results for the determination of

V_{ub}

are discussed. The decay spectra for the semileptonic decay of hadrons containing a

c

quark are also given. There is a subtlety in the use of the equations of motion at order

\frac{1}{m_{b}^{2}}

in the heavy quark expansion which is explained.

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Inclusive semileptonicBand polarizedΛbdecays from QCD