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Fakultät Physik

The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements A^(3)_Qg and ∆A^(3)_Qg

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The non-first-order-factorizable contributions to the unpolarized and polarized massive
operator matrix elements to three-loop order, A(3)
Qg and ∆A(3)
Qg, are calculated in the single-
mass case. For the 2F1-related master integrals of the problem, we use a semi-analytic
method based on series expansions and utilize the first-order differential equations for the
master integrals which does not need a special basis of the master integrals. Due to the
singularity structure of this basis a part of the integrals has to be computed to O(ε5) in
the dimensional parameter. The solutions have to be matched at a series of thresholds and
pseudo-thresholds in the region of the Bjorken variable x ∈]0, ∞[ using highly precise series
expansions to obtain the imaginary part of the physical amplitude for x ∈]0, 1] at a high
relative accuracy. We compare the present results both with previous analytic results, the
results for fixed Mellin moments, and a prediction in the small-x region. We also derive
expansions in the region of small and large values of x. With this paper, all three-loop
single-mass unpolarized and polarized operator matrix elements are calculated.


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