Non-Abelian Dipole Radiation and the Heavy Quark Expansion

Dipole radiation in QCD is derived to the second order in ${\alpha }_s$. A powerlike evolution of the spin-singlet heavy quark operators is obtained to the same accuracy. We give an $O\left({\alpha }_s^2\right)$ relation between the short-distance low-scale running heavy quark mass and the mass in the modified minimal subtraction scheme. We discuss the properties of an effective QCD coupling ${\alpha }_s^{\left(d\right)}\left(E\right)$ which governs the dipole radiation. We argue that this coupling is advantageous for describing heavy quark physics.