Theory of Pre-Asymptotic Effects in Weak Inclusive Decays

Details Theory of Pre-Asymptotic Effects in Weak Inclusive Decays Theory of Pre-Asymptotic Effects in Weak Inclusive Decays

1994-05-06

arxiv.org/abs/hep-ph/9405246v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

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

Scientific paper

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 $\exp [-\exp (1/\alpha_s )]$.

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