The two-mass contribution to the three-loop polarized gluonic operator matrix element Agg,Q(3)

We compute the two-mass contributions to the polarized massive operator matrix element Agg,Q(3) at third order in the strong coupling constant αs in Quantum Chromodynamics analytically. These corrections are important ingredients for the matching relations in the variable flavor number scheme and for the calculation of Wilson coefficients in deep–inelastic scattering in the asymptotic regime Q2≫mc2,mb2. The analytic result is expressed in terms of nested harmonic, generalized harmonic, cyclotomic and binomial sums in N-space and by iterated integrals involving square-root valued arguments in z space, as functions of the mass ratio. Numerical results are presented. New two–scale iterative integrals are calculated.