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

TL;DR

This paper analyzes HQET beyond perturbation theory by studying renormalons within a 1/N_f expansion. It identifies a UV renormalon in HQET from the heavy-quark self-energy, requiring a residual mass term δm to absorb nonperturbative ambiguities, while the pole mass contains an IR renormalon implying an intrinsic Λ_QCD-scale uncertainty. The authors argue that physical HQET parameters must appear as invariant combinations such as Λ̄−δm, analogous to condensates in the OPE, and examine the implications for QCD sum rules and inclusive B decays. Overall, the work provides a coherent framework connecting renormalon structures, mass definitions, and nonperturbative effects in HQET, highlighting unavoidable ambiguities that must be carefully handled in phenomenological analyses.

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 $δm$ 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 $δm$ 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.