The Transition Matrix Element A_{gq}(N) of the Variable Flavor Number Scheme at O(α_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 $O(α_s^3)$. A first independent recalculation is performed for the contributions $\propto N_F$ of the 3-loop anomalous dimension $γ_{gq}^{(2)}(N)$.

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