Lectures on Heavy Quarks in Quantum Chromodynamics

TL;DR

Shifman develops a coherent, QCD-based framework for heavy-quark dynamics using the Wilsonian operator product expansion and background-field methods. The approach yields a systematic $1/m_Q$ expansion with a clear separation of hard and soft physics, introducing the central parameters $\bar{\Lambda}$, $\mu_\pi^2$, and $\mu_G^2$, and establishing heavy-quark symmetry and the Isgur-Wise function. It connects inclusive widths and line shapes via local and nonlocal operator matrix elements, derives key sum rules (Bjorken, Voloshin) and Luke’s theorem, and explains the end-point spectra through light-cone distribution functions $F(x)$ and, in the SV limit, temporal distributions $G(x)$. The treatment then incorporates hard-gluon effects through perturbative Wilson coefficients, clarifying the scale dependence of basic HQ parameters and the practical use of the OPE in predicting widths and spectra for heavy-quark decays with controlled perturbative and nonperturbative contributions.

Abstract

A pedagogical introduction to the heavy quark theory is given. It is explained that various expansions in the inverse heavy quark mass $1/m_Q$ present a version of the Wilson operator product expansion in QCD. A systematic approach is developed and many practically interesting problems are considered. I show how the $1/m_Q$ expansions can be built using the background field technique and how they work in particular applications. Interplay between perturbative and nonperturbative aspects of the heavy quark theory is discussed.