The Transition Matrix Element A_{gq}(N) of the Variable Flavor Number   Scheme at O(\alpha_s^3)
  We calculate the massive operator matrix element $A_{gq}^{(3)}(N)$ to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable $N$. This is the first complete transition function needed in the variable flavor number scheme obtained at $O(\alpha_s^3)$. A first independent recalculation is performed for the contributions $\propto N_F$ of the 3-loop anomalous dimension $\gamma_{gq}^{(2)}(N)$. 
J. Ablinger, J. Bl\"umlein, A. De Freitas, A. Hasselhuhn, A. von   Manteuffel, M. Round, C. Schneider and F. Wissbrock
hep-ph