Theory of Pre-Asymptotic Effects in Weak Inclusive Decays

Abstract

I give an introduction to the theory of preasymptotic effects based on the systematic OPE/HQET expansion in $1/m_Q$ where $m_Q$ is the heavy quark mass. The general idea is explained in two most instructive examples, with an emphasis on pedagogical aspects. Some important results of the last year are reviewed. In discussing the issue of the quark-hadron duality, one of the basic ingredients of the theory, I prove that the operator product expansion {\em per se} is an asymptotic expansion. The behavior of the high order terms in this expansion determines the onset of duality and the accuracy of the duality relations. The factorial divergence of the high-order terms in OPE implies a sophisticated analytical structure in the ${\alpha }_s$ plane, with terms of the type $\exp [-\exp (1/{\alpha }_s)]$.

Talk at the Workshop ``Continuous Advances in QCD", 32 pages, 14 figures, plain LaTeX, TPI-MINN-94/17-T, figures available from the author upon request

References in corpus (4)

• Analysis of the Photon Spectrum in Inclusive $B\to X_s\gamma$ Decays
• Sum Rules for Heavy Flavor Transitions in the SV Limit
• QCD Corrections and the Endpoint of the Lepton Spectrum in Semileptonic B Decays
• A Parton Model for Inclusive Semileptonic B Meson Decays

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• Calculation of 1/m^3 terms in the total semileptonic width of D mesons.
• Improved Estimates for the Parameters of the Heavy Quark Expansion
• Parton-Hadron duality in QCD sum rules: quantum mechanical examples
• Heavy Quark Expansion and Preasymptotic Corrections to Decay Widths in the 't Hooft Model
• Pauli Interference in the 't Hooft Model: Heavy Quark Expansion and Quark-Hadron Duality
• Lectures on Heavy Quarks in Quantum Chromodynamics
• Chiral Symmetry Breaking, Duality in the \bar{Q}q Channel and b -> c anti-c s Decays
• New nonperturbative scales and glueballs in confining supersymmetric gauge theories
• Towards OPE based local quark-hadron duality: Light-quark channels
• Assuming Regge trajectories in holographic QCD: from OPE to Chiral Perturbation Theory