On the use of the running coupling constant $\alpha_s$ in calculations of radiative energy losses of fast partons in a quark-gluon plasma

The introduction of the running coupling constant $\alpha_s$ for a gluon emission vertex in calculations of radiative energy losses of partons in a quark-gluon plasma is discussed. It is argued that the virtuality scale for the running coupling constant $\alpha_s$ for induced emission of gluons is determined by the square of the transverse momentum of an emitted gluon rather than by the square of the invariant mass of the final two-parton state often used in the literature.