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

Abstract

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 $R_Q=\sigma (e^{+}{e}^{-}\to {\gamma }^{\ast }\to Q\bar{Q}X)/\sigma (e^{+}{e}^{-}\to {\gamma }^{\ast }\to {\mu }^{+}{\mu }^{-})$ and compare with existing results. Our result for $R_Q$ is exact to order ${\alpha }_s^2$.

Comments: Latex, 22 pages