Heavy Quark Effective Theory beyond Perturbation Theory: Renormalons, the Pole Mass and the Residual Mass Term

Abstract

We study the asymptotic behaviour of the perturbative series in the heavy quark effective theory (HQET) using the $1/N_f$ expansion. We find that this theory suffers from an {\it ultraviolet} renormalon problem, corresponding to a non-Borel-summable behaviour of perturbation series in large orders, and leading to a principal nonperturbative ambiguity in its definition. This ambiguity is related to an {\it infrared} renormalon in the pole mass and can be understood as the necessity to include the residual mass term $\delta m$ in the definition of HQET, which must be considered as ambiguous (and possibly complex), and is required to cancel the ultraviolet renormalon singularity generated by the perturbative expansion. The formal status of $\delta m$ is thus identical to that of condensates in the conventional short-distance expansion of correlation functions in QCD. The status of the pole mass of a heavy quark, the operator product expansion for inclusive decays, and QCD sum rules in the HQET are discussed in this context.

arXiv commentLATEX, 43 pages, 6 figures appended as uu-encoded file, MPI-PhT/94-9, (Text as to appear in NPB, typing errors corrected [Eq.(3.24),(3.26)], some statements in Sect.5 more precise)

References in corpus (8)

• Inclusive Semileptonic B and Polarized Lambda_b Decays from QCD
• Nonperturbative Corrections to Inclusive Beauty and Charm Decays: QCD versus Phenomenological Models
• Infrared Factorization, Wilson Lines and the Heavy Quark Limit
• Next--to--Leading Order Corrections to Meson Masses in the Heavy Quark Effective Theory
• The Residual Mass Term in the Heavy Quark Effective Theory
• Extracting $|V_{bc}|$, $m_c$ and $m_b$ from Inclusive $D$ and $B$ Decays
• Anathematizing the Guralnik and Manohar Inequality for \barΛ
• Renormalizabilty of TH Heavy Quark Effective Theory

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