Radiation of Heavy Quarks

The rate for the production of massive fermions radiated off a pair of massless fermions is calculated analytically. Combined with the analytic calculation of the corresponding virtual contribution one obtains the order ${\alpha }^2$ correction to the cross section which is induced by the real and virtual radiation of a pair of massive fermions by massless fermions. Approximations valid for large and for small masses are derived and shown to agree with earlier calculations.