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The two-mass contribution to the three-loop pure singlet operator matrix element. (English) Zbl 1380.81433
Summary: We present the two-mass QCD contributions to the pure singlet operator matrix element at three loop order in $$x$$-space. These terms are relevant for calculating the structure function $$F_2(x, Q^2)$$ at $$O(\alpha_s^3)$$ as well as for the matching relations in the variable flavor number scheme and the heavy quark distribution functions at the same order. The result for the operator matrix element is given in terms of generalized iterated integrals that include square root letters in the alphabet, depending also on the mass ratio through the main argument. Numerical results are presented.

##### MSC:
 81V05 Strong interaction, including quantum chromodynamics 81T15 Perturbative methods of renormalization applied to problems in quantum field theory 81T18 Feynman diagrams 81T80 Simulation and numerical modelling (quantum field theory) (MSC2010)