On the Motion of Heavy Quarks inside Hadrons: Universal Distributions and Inclusive Decays

TL;DR

The paper develops a QCD-based framework for the motion of heavy quarks inside hadrons, showing that a universal, nonperturbative distribution function $F(x)$ governs the line shapes and spectra of inclusive decays across radiative and semileptonic channels. Through a Wilson OPE treatment and the heavy-quark expansion, the authors connect observable spectra to moments of $F(x)$, revealing a Bjorken-like scaling and demonstrating universality for a fixed final-state mass. They derive a model-independent lower bound on the heavy-quark kinetic energy $ar{\Lambda}$-dependent operator $\langle \vec{\pi}^2\rangle$, and analyze the interplay of nonperturbative motion with perturbative Sudakov corrections, mass effects of the final-state quark, and the limits of nonrelativistic models. The work clarifies how Fermi-motion-like effects arise naturally in QCD, provides practical prescriptions for separating perturbative and nonperturbative contributions, and establishes the theoretical foundation for interpreting end-point spectra in beauty decays.

Abstract

In previous papers we have pointed out that there exists a QCD analog of the phenomenological concept of the so called Fermi motion for the heavy quark inside a hadron. Here we show in a more detailed way how this comes about and we analyze the limitations of this concept. Non-perturbative as well as perturbative aspects are included. We emphasize both the similarities and the differences to the well-known treatment of deep inelastic lepton-nucleon scattering. We derive a model-independent {\em lower} bound on the kinetic energy of the heavy quark inside the hadron.