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. In particular, $\mathcal{O}({\alpha }_s^2)$ relation between a short-distance low-scale running heavy quark mass and the $\text{barMS}$ mass is given. We discuss the properties of the effective QCD coupling $\text{aw}(E)$ which governs the dipole radiation. This coupling is advantageous for heavy quark physics.