Hadron spectra for semileptonic heavy quark decay

We calculate the leading perturbative and power corrections to the hadronic invariant mass and energy spectra in semileptonic heavy hadron decays. We apply our results to the $B$ system. Moments of the invariant mass spectrum, which vanish in the parton model, probe gluon bremsstrahlung and nonperturbative effects. Combining our results with recent data on $B$ meson branching ratios, we obtain a lower bound $\overline{\Lambda }>410\mathrm{}$ MeV and an upper bound $m_b^{\mathrm{pole}}<4.89\mathrm{}$ GeV. The Brodsky-Lepage-Mackenzie scale-setting procedure suggests that higher order perturbative corrections to the first moment of the hadronic invariant mass spectrum are small for bottom decay, and even tractable for charm decay.