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Resumming phase space logarithms in inclusive semileptonic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi></mml:math>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 …