The real-virtual antenna functions for $S \to Q\bar{Q} X$ at NNLO QCD

We determine, in the antenna subtraction framework for handling infrared divergences in higher order QCD calculations, the real-virtual antenna functions for processes involving the production of a pair of massive quarks by an uncolored initial state at NNLO QCD. The integrated leading and subleading color real-virtual antenna functions are computed analytically in terms of (cyclotomic) harmonic polylogarithms. As a by-product and check we compute $R_Q=\sigma(e^+e^-\to \gamma^*\to Q\bar{Q}X)/\sigma(e^+e^-\to \gamma^*\to\mu^+\mu^-)$ and compare with existing results. Our result for $R_Q$ is exact to order $\alpha_s^2$.