Theory of Pre-Asymptotic Effects in Weak Inclusive Decays

1994/05/06 by M. A. Shifman, Mikhail Shifman, Shifman, M. A. · 1 citation
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Quantum Chromodynamics and Particle Interactions #Random Matrices and Applications #Stochastic processes and statistical mechanics #hep-ph #hep-th

paper · pdf · doi:10.48550/arxiv.hep-ph/9405246

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

arxiv created 1994/05/06 · openalex publication_date 1994/05/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 α_s plane, with terms of the type exp [-exp (1/α_s )].

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