Resumming Phase Space Logarithms in Inclusive Semileptonic $B$ Decays

Details Resumming Phase Space Logarithms in Inclusive Semileptonic $B$ Decays Resumming Phase Space Logarithms in Inclusive Semileptonic $B$ Decays

1996-04-11

arxiv.org/abs/hep-ph/9604290v2

Phys.Rev. D54 (1996) 2097-2107

Physics

High Energy Physics

High Energy Physics - Phenomenology

18 pages, REVTeX, 8 EPS figures embedded. Final version, to appear in Physical Review D; one reference has been added

Scientific paper

10.1103/PhysRevD.54.2097

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.

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