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The two-mass contribution to the three-loop gluonic operator matrix element \(A_{g g, Q}^{(3)}\). (English) Zbl 1391.81202
Summary: We calculate the two-mass QCD contributions to the massive operator matrix element \(A_{g g, Q}\) at \(\mathcal{O}(\alpha_s^3)\) in analytic form in Mellin \(N\)- and \(z\)-space, maintaining the complete dependence on the heavy quark mass ratio. These terms are important ingredients for the matching relations of the variable flavor number scheme in the presence of two heavy quark flavors, such as charm and bottom. In Mellin \(N\)-space the result is given in the form of nested harmonic, generalized harmonic, cyclotomic and binomial sums, with arguments depending on the mass ratio. The Mellin inversion of these quantities to \(z\)-space gives rise to generalized iterated integrals with square root valued letters in the alphabet, depending on the mass ratio as well. Numerical results are presented.

MSC:
81V05 Strong interaction, including quantum chromodynamics
81V35 Nuclear physics
81T18 Feynman diagrams
81T80 Simulation and numerical modelling (quantum field theory) (MSC2010)
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