TTP97-33 Non-Abelian Dipole Radiation and the Heavy Quark Expansion

Dipole radiation in QCD is derived to the second order in $\alpha_s$. A power-like evolution of the spin-singlet heavy quark operators is obtained to the same accuracy. We give an ${\cal O}(\alpha_s^2)$ relation between the short-distance low-scale running heavy quark mass and the $\overline{\rm MS}$ mass. We discuss the properties of an effective QCD coupling $\alpha_s^{(d)}(E)$ which governs the dipole radiation. We argue that this coupling is advantageous for describing heavy quark physics.