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