Perturbative Strong Interaction Corrections to the Heavy Quark Semileptonic Decay Rate

Abstract

We calculate the part of the order ${\alpha }_s^2$ correction to the semileptonic heavy quark decay rate proportional to the number of light quark flavors, and use our result to set the scale for evaluating the strong coupling in the order ${\alpha }_s$ term according to the scheme of Brodsky, Lepage and Mackenzie. Expressing the decay rate in terms of the heavy quark pole mass $m_Q$, we find the scale for the $\overline{MS}$ strong coupling to be $0.07m_Q$. If the decay rate is expressed in terms of the $\overline{MS}$ heavy quark mass ${\overline{m}}_Q(m_Q)$ then the scale is $0.12m_Q$. We use these results along with the existing calculations for hadronic $\tau$ decay to calculate the BLM scale for the nonleptonic decay width and the semileptonic branching ratio. The implications for the value of $|V_{bc}|$ extracted from the inclusive semileptonic $B$ meson decay rate are discussed.

7 pages in Latex plus 1 uuencoded figure, uses epsf, UTPT-94-24, CMU-HEP 94-29, CALT-68-1950 (previous results unchanged; we add a short discussion of nonleptonic decays)

References in corpus (6)

• QCD Predictions for Lepton Spectra in Inclusive Heavy Flavour Decays
• Inclusive Semileptonic B and Polarized Lambda_b Decays from QCD
• Differential Distributions in Semileptonic Decays of the Heavy Flavors in QCD
• Operator Product Expansion for Inclusive Semileptonic Decays in Heavy Quark Effective Field Theory
• The Baffling Semileptonic Branching Ratio of $B$ Mesons
• Extracting $|V_{bc}|$, $m_c$ and $m_b$ from Inclusive $D$ and $B$ Decays

Cited by in corpus (62)

• Weak Decays Beyond Leading Logarithms
• Renormalons
• Flavor Physics in the Quark Sector
• Aspects Of Heavy Quark Theory
• B decay and the Upsilon mass
• Spectator Effects in Inclusive Decays of Beauty Hadrons
• B decays in the upsilon expansion
• Complete 2-loop Quantum Electrodynamic Contributions to the Muon Lifetime in the Fermi Model
• Factorization theorems, effective field theory, and nonleptonic heavy meson decays
• Scale Setting in QCD and the Momentum Flow in Feynman Diagrams
• Mass effects in muon and semileptonic b -> c decays
• On the Precise Determination of the Fermi Coupling Constant from the Muon Lifetime
• Imprecated, yet Impeccable: On the Theoretical Evaluation of Gamma(B -> X_c \ell ν)
• High Power n of m_b in Beauty Widths and n=5 -> oo Limit
• Implications of the $B\to X\ell {\bar{\nu }}_{\ell }$ lepton spectrum for heavy quark physics
• Precision determination of |V_{ub}| from inclusive decays
• Hadron Spectra for Semileptonic Heavy Quark Decay
• The second order QCD contribution to the semileptonic b -> u decay rate
• Factorization for Power Corrections to B->Xs gamma and B-> Xu e nu
• Nonfactorizable soft gluons in nonleptonic heavy meson decays
• Next-to-leading Order Radiative Corrections to the Decay $b\to ccs$
• Resummation of Running Coupling Effects in Semileptonic B Meson Decays and Extraction of $|V_{cb}|$
• Challenges in Semileptonic B Decays
• V_{ub} from the Hadronic Invariant Mass Spectrum in Semileptonic B Decay
• Second Order Corrections to the Muon Lifetime and the Semileptonic B Decay
• A Model Independent Determination of |V_{ub}|
• Phenomenology of the $1/m_Q$ Expansion in Inclusive $B$ and $D$ Meson Decays
• Hadronic Spectral Moments in Semileptonic B Decays With a Lepton Energy Cut
• Kinetic corrections to B -> X_c l nu at one loop
• Perturbative corrections to zero recoil inclusive $B$ decay sum rules
• Improving Extractions of |Vcb| and mb from the Hadronic Invariant Mass Moments of Semileptonic Inclusive B decay
• Order alpha_s^2 beta_0 Correction to the Charged Lepton Spectrum in b \to c \ell \barν_\ell decays
• The Mass of the b Quark
• Normalizing inclusive rare B decays
• The Chromomagnetic Dipole Operator and the B Semileptonic Branching Ratio
• CALCULATION OF THE D AND B MESON LIFETIMES AND THE UNITARITY TRIANGLE PARAMETERS
• Scale setting for alpha_s beyond leading order
• On the $O({\alpha }_s^2)$ corrections to $b\to X_{u}e\bar{\nu }$ inclusive decays
• Calculation of 1/m^3 terms in the total semileptonic width of D mesons.
• Semileptonic b --> u decays: lepton invariant mass spectrum
• Hadronic mass and q^2 moments of charmless semileptonic B decay distributions
• Large Charmless Yield in B Decays and Inclusive B Decay Puzzles
• Subleading shape function contributions to the hadronic invariant mass spectrum in B -> X_u l νdecay
• Corrections to the Bjorken and Voloshin sum rules
• Internal W-emmission and W-exchange Contributions to {\bf B}\to {{\bf D}^{(*)} Decays
• Resumming Phase Space Logarithms in Inclusive Semileptonic $B$ Decays
• Running-coupling effects in the triple-differential charmless semileptonic decay width
• Nonperturbative QCD Contributions to the Semileptonic Decay Width of the B Meson
• Inclusive Decays of Bottom Hadrons in New Formulation of Heavy Quark Effective Field Theory
• Renormalization Group Improved Gap Equation for Color Superconductors
• $V_{ub}$ from the Hadron Energy Spectrum in Inclusive Semileptonic B Decays
• Right-Handed Currents in B Decay Revisited
• |V_ub| and |V_cb|, Charm Counting and Lifetime Differences in Inclusive Bottom Hadron Decays
• Higher Order QCD Corrections to $b\to c\overline{c}s$
• Phenomenology of B -> pi pi, pi K Decays at O(alpha^2 beta_0) in QCD Factorization
• Alternative Treatment of the Quark Mass in the Heavy Quark Expansion
• Phenomenology of V_ub from Ratios of Inclusive B Decay Rates
• Extracting |V_{ub}| from the inclusive charmless semileptonic branching ratio of b hadrons
• Local duality and nonleptonic B decay
• Theoretical Aspects of the Heavy Quark Expansion
• Scale Setting in Top Quark Decays
• Theory of Inclusive B Decays