The polarized transition matrix element Agq(N) of the variable flavor number scheme at O(αs3)

Abstract We calculate the polarized massive operator matrix element A g q ( 3 ) ( N ) to 3-loop order in Quantum Chromodynamics analytically at general values of the Mellin variable N both in the single- and double-mass case in the Larin scheme. It is a transition function required in the variable flavor number scheme at O ( α s 3 ) . We also present the results in momentum fraction space.