Resumming Phase Space Logarithms in Inclusive Semileptonic $B$ Decays

Abstract

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.

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

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Cited by in corpus (13)

• Summing Sudakov logarithms in B -> X_s + gamma in effective field theory
• Mass effects in muon and semileptonic b -> c decays
• Heavy-to-heavy quark decays at NNLO
• Renormalization Group Scaling of the 1/m^2 HQET Lagrangian
• Electroweak Absorptive Parts in NRQCD Matching Conditions
• Precise predictions for B -> Xs l+ l- in the large q^2 region
• Nonperturbative corrections to moments of the decay B -> X_s l^+ l^-
• QCD corrections to inclusive heavy hadron weak decays at ${\Lambda }_{\mathrm{QCD}}^3/m_Q^3$
• The Heavy Quark Expansion for Inclusive Semileptonic Charm Decays Revisited
• Jets in Effective Theory: Summing Phase Space Logs
• Role of "Intrinsic Charm" in Semi-Leptonic B-Meson Decays
• Nonperturbative corrections to B -> X_s l^+ l^- with phase space restrictions
• Can $B->X_c\ell \nu$ help us extract |V_{ub}| ?