====== TTP96-03 Resumming Phase Space Logarithms in Inclusive Semileptonic $B$ Decays ======
 
 
   <hidden TTP96-03  Resumming Phase Space Logarithms in Inclusive Semileptonic $B$ Decays > We study logarithms of the form $\ln(m_q/m_b)$ which arise in
 the inclusive semileptonic decay of a bottom quark to a quark of
 mass $m_q$.  We use the renormalization group to resum the
 leading radiative corrections to these terms, of the form
 $m_q^2\alpha_s^n\ln^n(m_q/m_b)$,
 $m_q^3\alpha_s^{n+1}\ln^n(m_q/m_b)$ and
 $m_q^4\alpha_s^n\ln^{n+1}(m_q/m_b)$.  The first two resummations are trivial,
 while the latter involves a non-trivial mixing of four-fermi operators in the
 $1/m_b$
 expansion.  We illustrate this technique in a toy model in which the
 semileptonic decay
 is mediated by a vector interaction, before treating the more complicated case
 of
 left-handed decay.
 </hidden>
|**Christian Bauer, Adam Falk and Michael Luke**  | 
|** Phys. Rev. D54 2097-2107 1996  **  |
| {{preprints:1996:ttp96-03.pdf|PDF}} {{preprints:1996:ttp96-03.ps|PostScript}} [[http://arxiv.org/abs/hep-ph/9604290|arXiv]]   |
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